Metrics for log(sqrt(x*x+y*y))

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze3.0ms (0.1%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	25%	75%	0%	0%	0%	0
0%	0%	25%	75%	0%	0%	0%	1
50%	12.5%	12.5%	75%	0%	0%	0%	2
75%	18.7%	6.2%	75%	0%	0%	0%	3
87.5%	21.8%	3.1%	75%	0%	0%	0%	4
93.8%	23.4%	1.6%	75%	0%	0%	0%	5
96.9%	24.2%	0.8%	75%	0%	0%	0%	6
98.4%	24.6%	0.4%	75%	0%	0%	0%	7
99.2%	24.8%	0.2%	75%	0%	0%	0%	8
99.6%	24.9%	0.1%	75%	0%	0%	0%	9
99.8%	24.9%	0%	75%	0%	0%	0%	10
99.9%	24.9%	0%	75%	0%	0%	0%	11
100%	24.9%	0%	75%	0%	0%	0%	12

Compiler

Compiled 25 to 14 computations (44% saved)

sample1.2s (43.2%)

Memory

-10.8MiB live, 552.1MiB allocated

Samples

730.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 465.0ms

ival-hypot: 172.0ms (37% of total)

ival-log: 148.0ms (31.8% of total)

ival-<=: 104.0ms (22.3% of total)

ival-and: 24.0ms (5.2% of total)

exact: 14.0ms (3% of total)

ival-assert: 3.0ms (0.6% of total)

Bogosity

explain97.0ms (3.5%)

Memory

42.2MiB live, 42.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
55	-	8	(-5.83130609112289e-159 7.342662305596585e-277)	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
0	-	0	-	`(log.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))`
0	-	0	-	`(+.f64 (.f64 x x) (.f64 y y))`
0	-	0	-	`y`
0	-	0	-	`(*.f64 y y)`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`	uflow-rescue	47	0
↳	`(*.f64 y y)`	underflow	106
↳	`(*.f64 x x)`	underflow	128
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	47

Confusion

	Predicted +	Predicted -
+	47	5
-	0	204

Precision

1.0

Recall

0.9038461538461539

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	47	0	5
-	0	0	204

Precision?

1.0

Recall?

0.9038461538461539

Freqs

test

number	freq
0	209
1	47

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

40.0ms

512×

valid

Compiler

Compiled 77 to 25 computations (67.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-hypot: 9.0ms (35.5% of total)

ival-log: 7.0ms (27.6% of total)

ival-mult: 7.0ms (27.6% of total)

ival-add: 2.0ms (7.9% of total)

ival-true: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

preprocess16.0ms (0.6%)

Memory

5.9MiB live, 5.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	47
1	38	47
2	80	47
3	148	47
4	209	47
5	222	47
6	224	47
0	7	9
0	12	9
1	13	9
0	13	4

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(log.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))

Outputs
(log.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
(log.f64 (hypot.f64 y x))

Symmetry

(abs y)

(abs x)

(sort x y)

Compiler

Compiled 9 to 7 computations (22.2% saved)

eval0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	81.6%	(log.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify3.0ms (0.1%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(log.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
cost-diff	1	(+.f64 (.f64 x x) (.f64 y y))
cost-diff	4	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	32
0	12	32
1	13	32
0	13	21

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(log.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
(+.f64 (.f64 x x) (.f64 y y))
(*.f64 x x)
x
(*.f64 y y)
y

Outputs
(log.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
(log.f64 (hypot.f64 y x))
(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
(hypot.f64 y x)
(+.f64 (.f64 x x) (.f64 y y))
(fma.f64 y y (*.f64 x x))
(*.f64 x x)
x
(*.f64 y y)
y

localize26.0ms (0.9%)

Memory

8.6MiB live, 8.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.0	(log.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
accuracy	0.0078125	(+.f64 (.f64 x x) (.f64 y y))
accuracy	11.74470718835229	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Samples

20.0ms

256×

valid

Compiler

Compiled 34 to 9 computations (73.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-hypot: 5.0ms (41.2% of total)

ival-log: 3.0ms (24.7% of total)

ival-mult: 3.0ms (24.7% of total)

ival-add: 1.0ms (8.2% of total)

ival-true: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series19.0ms (0.7%)

Memory

-76.7MiB live, 3.6MiB allocated

Counts

4 → 51

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
(+.f64 (.f64 x x) (.f64 y y))
(log.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
(*.f64 x x)

Outputs
y
(+ y (* 1/2 (/ (pow x 2) y)))
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(pow y 2)
(+ (pow x 2) (pow y 2))
(log y)
(+ (log y) (* 1/2 (/ (pow x 2) (pow y 2))))
(+ (log y) (* (pow x 2) (+ (* -1/4 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))))
(+ (log y) (* (pow x 2) (+ (* (pow x 2) (- (* 1/6 (/ (pow x 2) (pow y 6))) (* 1/4 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))))
(pow x 2)
x
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* -1 (log (/ 1 x)))
(+ (* -1 (log (/ 1 x))) (* 1/2 (/ (pow y 2) (pow x 2))))
(+ (* -1 (log (/ 1 x))) (+ (* -1/4 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))
(+ (* -1 (log (/ 1 x))) (+ (* -1/4 (/ (pow y 4) (pow x 4))) (+ (* 1/720 (/ (+ (* 30 (pow y 6)) (* 90 (pow y 6))) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(* -1 (log (/ -1 x)))
(+ (* -1 (log (/ -1 x))) (* 1/2 (/ (pow y 2) (pow x 2))))
(+ (* -1 (log (/ -1 x))) (+ (* -1/4 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))
(+ (* -1 (log (/ -1 x))) (+ (* -1/4 (/ (pow y 4) (pow x 4))) (+ (* 1/720 (/ (+ (* 30 (pow y 6)) (* 90 (pow y 6))) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(+ x (* 1/2 (/ (pow y 2) x)))
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(log x)
(+ (log x) (* 1/2 (/ (pow y 2) (pow x 2))))
(+ (log x) (* (pow y 2) (+ (* -1/4 (/ (pow y 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ (log x) (* (pow y 2) (+ (* (pow y 2) (- (* 1/6 (/ (pow y 2) (pow x 6))) (* 1/4 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* -1 (log (/ 1 y)))
(+ (* -1 (log (/ 1 y))) (* 1/2 (/ (pow x 2) (pow y 2))))
(+ (* -1 (log (/ 1 y))) (+ (* -1/4 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))
(+ (* -1 (log (/ 1 y))) (+ (* -1/4 (/ (pow x 4) (pow y 4))) (+ (* 1/720 (/ (+ (* 30 (pow x 6)) (* 90 (pow x 6))) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(* -1 y)
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))
(* -1 (log (/ -1 y)))
(+ (* -1 (log (/ -1 y))) (* 1/2 (/ (pow x 2) (pow y 2))))
(+ (* -1 (log (/ -1 y))) (+ (* -1/4 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))
(+ (* -1 (log (/ -1 y))) (+ (* -1/4 (/ (pow x 4) (pow y 4))) (+ (* 1/720 (/ (+ (* 30 (pow x 6)) (* 90 (pow x 6))) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	((sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (log (sqrt (+ (* x x) (* y y)))) (* x x))
2.0ms	x	@	0	((sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (log (sqrt (+ (* x x) (* y y)))) (* x x))
1.0ms	y	@	0	((sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (log (sqrt (+ (* x x) (* y y)))) (* x x))
1.0ms	y	@	inf	((sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (log (sqrt (+ (* x x) (* y y)))) (* x x))
1.0ms	x	@	-inf	((sqrt (+ (* x x) (* y y))) (+ (* x x) (* y y)) (log (sqrt (+ (* x x) (* y y)))) (* x x))

simplify156.0ms (5.6%)

Memory

42.2MiB live, 42.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	186	885
1	510	863
2	1541	853
3	5419	819
0	8163	756

Stop Event

1×	iter limit
1×	node limit

Counts

51 → 49

Calls

Call 1

Inputs
y
(+ y (* 1/2 (/ (pow x 2) y)))
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(pow y 2)
(+ (pow x 2) (pow y 2))
(log y)
(+ (log y) (* 1/2 (/ (pow x 2) (pow y 2))))
(+ (log y) (* (pow x 2) (+ (* -1/4 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))))
(+ (log y) (* (pow x 2) (+ (* (pow x 2) (- (* 1/6 (/ (pow x 2) (pow y 6))) (* 1/4 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))))
(pow x 2)
x
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* -1 (log (/ 1 x)))
(+ (* -1 (log (/ 1 x))) (* 1/2 (/ (pow y 2) (pow x 2))))
(+ (* -1 (log (/ 1 x))) (+ (* -1/4 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))
(+ (* -1 (log (/ 1 x))) (+ (* -1/4 (/ (pow y 4) (pow x 4))) (+ (* 1/720 (/ (+ (* 30 (pow y 6)) (* 90 (pow y 6))) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(* -1 (log (/ -1 x)))
(+ (* -1 (log (/ -1 x))) (* 1/2 (/ (pow y 2) (pow x 2))))
(+ (* -1 (log (/ -1 x))) (+ (* -1/4 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))
(+ (* -1 (log (/ -1 x))) (+ (* -1/4 (/ (pow y 4) (pow x 4))) (+ (* 1/720 (/ (+ (* 30 (pow y 6)) (* 90 (pow y 6))) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(+ x (* 1/2 (/ (pow y 2) x)))
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(log x)
(+ (log x) (* 1/2 (/ (pow y 2) (pow x 2))))
(+ (log x) (* (pow y 2) (+ (* -1/4 (/ (pow y 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ (log x) (* (pow y 2) (+ (* (pow y 2) (- (* 1/6 (/ (pow y 2) (pow x 6))) (* 1/4 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* -1 (log (/ 1 y)))
(+ (* -1 (log (/ 1 y))) (* 1/2 (/ (pow x 2) (pow y 2))))
(+ (* -1 (log (/ 1 y))) (+ (* -1/4 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))
(+ (* -1 (log (/ 1 y))) (+ (* -1/4 (/ (pow x 4) (pow y 4))) (+ (* 1/720 (/ (+ (* 30 (pow x 6)) (* 90 (pow x 6))) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(* -1 y)
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))
(* -1 (log (/ -1 y)))
(+ (* -1 (log (/ -1 y))) (* 1/2 (/ (pow x 2) (pow y 2))))
(+ (* -1 (log (/ -1 y))) (+ (* -1/4 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))
(+ (* -1 (log (/ -1 y))) (+ (* -1/4 (/ (pow x 4) (pow y 4))) (+ (* 1/720 (/ (+ (* 30 (pow x 6)) (* 90 (pow x 6))) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))

Outputs
y
(+ y (* 1/2 (/ (pow x 2) y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y)
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(fma.f64 (fma.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 3 binary64))) x) x (/.f64 #s(literal 1/2 binary64) y)) (.f64 x x) y)
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal 1/16 binary64) x) (/.f64 x (pow.f64 y #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (.f64 x x) y))
(pow y 2)
(*.f64 y y)
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(log y)
(log.f64 y)
(+ (log y) (* 1/2 (/ (pow x 2) (pow y 2))))
(fma.f64 (/.f64 (/.f64 (*.f64 x x) y) y) #s(literal 1/2 binary64) (log.f64 y))
(+ (log y) (* (pow x 2) (+ (* -1/4 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/4 binary64) (fma.f64 (/.f64 (/.f64 (*.f64 x x) y) y) #s(literal 1/2 binary64) (log.f64 y)))
(+ (log y) (* (pow x 2) (+ (* (pow x 2) (- (* 1/6 (/ (pow x 2) (pow y 6))) (* 1/4 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))))
(fma.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) (/.f64 x y) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal 1/6 binary64) x) (/.f64 x (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal -1/4 binary64) (pow.f64 y #s(literal 4 binary64)))) (log.f64 y)))
(pow x 2)
(*.f64 x x)
x
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 y x) x)
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(fma.f64 (.f64 #s(literal -1/8 binary64) x) (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) y) (/.f64 y x) x))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(fma.f64 (fma.f64 (pow.f64 y #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))) x (.f64 (/.f64 (.f64 y y) x) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(fma.f64 y y (*.f64 x x))
(* -1 (log (/ 1 x)))
(log.f64 x)
(+ (* -1 (log (/ 1 x))) (* 1/2 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x) (log.f64 x))
(+ (* -1 (log (/ 1 x))) (+ (* -1/4 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/4 binary64) (log.f64 x)))
(+ (* -1 (log (/ 1 x))) (+ (* -1/4 (/ (pow y 4) (pow x 4))) (+ (* 1/720 (/ (+ (* 30 (pow y 6)) (* 90 (pow y 6))) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(fma.f64 (.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x) (+.f64 (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -1/4 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1/6 binary64)) (pow.f64 x #s(literal 6 binary64)))) (log.f64 x)))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(neg.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 y x) x))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(neg.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) x) (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) y) (/.f64 y x) x)))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(neg.f64 (fma.f64 (fma.f64 (pow.f64 y #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))) x (.f64 (/.f64 (.f64 y y) x) #s(literal 1/2 binary64))))
(* -1 (log (/ -1 x)))
(neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)))
(+ (* -1 (log (/ -1 x))) (* 1/2 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 (/.f64 y x) x) y) #s(literal 1/2 binary64) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) x))))
(+ (* -1 (log (/ -1 x))) (+ (* -1/4 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))
(fma.f64 (fma.f64 (.f64 (/.f64 #s(literal -1/4 binary64) (pow.f64 x #s(literal 4 binary64))) y) y (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) (.f64 y y) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) x))))
(+ (* -1 (log (/ -1 x))) (+ (* -1/4 (/ (pow y 4) (pow x 4))) (+ (* 1/720 (/ (+ (* 30 (pow y 6)) (* 90 (pow y 6))) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(fma.f64 (.f64 (fma.f64 (.f64 (/.f64 #s(literal -1/4 binary64) (pow.f64 x #s(literal 4 binary64))) y) y (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) y) y (-.f64 (/.f64 (*.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1/6 binary64)) (pow.f64 x #s(literal 6 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) x))))
(+ x (* 1/2 (/ (pow y 2) x)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 y x) x)
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64))) y) y (/.f64 #s(literal 1/2 binary64) x)) (.f64 y y) x)
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) y) (/.f64 y (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 y y) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 y y) x)
(log x)
(log.f64 x)
(+ (log x) (* 1/2 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x) (log.f64 x))
(+ (log x) (* (pow y 2) (+ (* -1/4 (/ (pow y 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (/.f64 (/.f64 y x) x) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/4 binary64) (log.f64 x)))
(+ (log x) (* (pow y 2) (+ (* (pow y 2) (- (* 1/6 (/ (pow y 2) (pow x 6))) (* 1/4 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) #s(literal 1/2 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/4 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 y #s(literal 3 binary64)))) y (log.f64 x))
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y)
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(fma.f64 (.f64 #s(literal -1/8 binary64) y) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (.f64 x x) y))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64))) y (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64)))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(fma.f64 y y (*.f64 x x))
(* -1 (log (/ 1 y)))
(log.f64 y)
(+ (* -1 (log (/ 1 y))) (* 1/2 (/ (pow x 2) (pow y 2))))
(fma.f64 (/.f64 (/.f64 (*.f64 x x) y) y) #s(literal 1/2 binary64) (log.f64 y))
(+ (* -1 (log (/ 1 y))) (+ (* -1/4 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/4 binary64) (fma.f64 (/.f64 (/.f64 (*.f64 x x) y) y) #s(literal 1/2 binary64) (log.f64 y)))
(+ (* -1 (log (/ 1 y))) (+ (* -1/4 (/ (pow x 4) (pow y 4))) (+ (* 1/720 (/ (+ (* 30 (pow x 6)) (* 90 (pow x 6))) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(fma.f64 (.f64 (/.f64 x y) #s(literal 1/2 binary64)) (/.f64 x y) (+.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/4 binary64) (pow.f64 y #s(literal 4 binary64))) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/6 binary64)) (pow.f64 y #s(literal 6 binary64)))) (log.f64 y)))
(* -1 y)
(neg.f64 y)
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))
(neg.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(neg.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) y) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (.f64 x x) y)))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))
(neg.f64 (fma.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64))) y (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64))))
(* -1 (log (/ -1 y)))
(neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) y)))
(+ (* -1 (log (/ -1 y))) (* 1/2 (/ (pow x 2) (pow y 2))))
(-.f64 (.f64 (/.f64 (/.f64 (.f64 x x) y) y) #s(literal 1/2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) y)))
(+ (* -1 (log (/ -1 y))) (+ (* -1/4 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/4 binary64) (pow.f64 y #s(literal 4 binary64))) (-.f64 (.f64 (/.f64 (/.f64 (.f64 x x) y) y) #s(literal 1/2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) y))))
(+ (* -1 (log (/ -1 y))) (+ (* -1/4 (/ (pow x 4) (pow y 4))) (+ (* 1/720 (/ (+ (* 30 (pow x 6)) (* 90 (pow x 6))) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(fma.f64 (.f64 (fma.f64 (.f64 (/.f64 #s(literal -1/4 binary64) (pow.f64 y #s(literal 4 binary64))) x) x (/.f64 (/.f64 #s(literal 1/2 binary64) y) y)) x) x (-.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/6 binary64)) (pow.f64 y #s(literal 6 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) y))))

rewrite187.0ms (6.8%)

Memory

-28.3MiB live, 49.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	27
0	12	27
1	31	27
2	199	27
3	1810	27
0	8180	16

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

4 → 254

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
(+.f64 (.f64 x x) (.f64 y y))
(log.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
(*.f64 x x)

Outputs
(.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))))) (sqrt.f64 (fma.f64 (.f64 y y) (fma.f64 y y (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(.f64 (sqrt.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) #s(literal 2 binary64))))) (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))))))
(.f64 (sqrt.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64))))) (sqrt.f64 (fma.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (-.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64)))))
(*.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (hypot.f64 y x))
(.f64 (sqrt.f64 (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x)))
(.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (.f64 (-.f64 x y) (+.f64 y x)) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(.f64 (pow.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (.f64 y y) (fma.f64 y y (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))))))
(.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (-.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64)))))
(.f64 (pow.f64 (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x)) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 y x)))
(*.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) #s(literal 1/2 binary64)) (hypot.f64 y x))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (hypot.f64 y x))
(.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (pow.f64 (.f64 (+.f64 y x) (-.f64 y x)) #s(literal -1 binary64))))
(.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 (pow.f64 (.f64 (+.f64 y x) (-.f64 y x)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (sqrt.f64 (pow.f64 (neg.f64 (.f64 (-.f64 x y) (+.f64 y x))) #s(literal -1 binary64))))
(.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (pow.f64 (pow.f64 (neg.f64 (.f64 (-.f64 x y) (+.f64 y x))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 (pow.f64 (neg.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64))))
(.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))) (pow.f64 (pow.f64 (neg.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (.f64 (-.f64 x y) (+.f64 y x)) #s(literal -1/2 binary64)) (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))))
(.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64)) (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))
(.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 y y (*.f64 x x)) #s(literal 1/4 binary64)))
(*.f64 #s(literal 1 binary64) (hypot.f64 y x))
(.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (pow.f64 (.f64 (-.f64 x y) (+.f64 y x)) #s(literal -1/2 binary64)))
(.f64 (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))))
(.f64 (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (.f64 (fma.f64 y y (.f64 x x)) (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))))
(.f64 (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 (.f64 (fma.f64 y y (.f64 x x)) (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))) #s(literal 1/2 binary64)))
(.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64)))
(.f64 (hypot.f64 y x) (sqrt.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 y x)) (*.f64 (-.f64 x y) (+.f64 y x)))))
(.f64 (hypot.f64 y x) (sqrt.f64 (.f64 (.f64 (-.f64 x y) (+.f64 y x)) (pow.f64 (.f64 (-.f64 x y) (+.f64 y x)) #s(literal -1 binary64)))))
(.f64 (hypot.f64 y x) (pow.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 y x)) (*.f64 (-.f64 x y) (+.f64 y x))) #s(literal 1/2 binary64)))
(.f64 (hypot.f64 y x) (pow.f64 (.f64 (.f64 (-.f64 x y) (+.f64 y x)) (pow.f64 (.f64 (-.f64 x y) (+.f64 y x)) #s(literal -1 binary64))) #s(literal 1/2 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (fma.f64 y y (*.f64 x x))))
(pow.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 y x)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (fma.f64 y y (*.f64 x x)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (fma.f64 y y (*.f64 x x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (fma.f64 y y (*.f64 x x)) #s(literal -1 binary64)) #s(literal -1/2 binary64))
(pow.f64 (fma.f64 y y (*.f64 x x)) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))))) (neg.f64 (neg.f64 (sqrt.f64 (*.f64 (-.f64 x y) (+.f64 y x))))))
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(+.f64 (log.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (log.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64))))
(+.f64 (log.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 1/4 binary64))) (log.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 1/4 binary64))))
(log.f64 (hypot.f64 y x))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval36.0ms (1.3%)

Memory: 25.1MiB live, 25.1MiB allocated
Compiler: Compiled 8 314 to 1 310 computations (84.2% saved)

prune5.0ms (0.2%)

Memory

10.8MiB live, 10.8MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	290	3	293
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	291	3	294

Accuracy

100.0%

Counts

294 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	81.6%	(.f64 (log.f64 (fma.f64 y y (.f64 x x))) #s(literal 1/2 binary64))
▶	100.0%	(log.f64 (hypot.f64 y x))
▶	99.1%	#s(approx (log (sqrt (+ (* x x) (* y y)))) (log.f64 y))

Compiler

Compiled 25 to 20 computations (20% saved)

simplify4.0ms (0.1%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 y y (*.f64 x x))
cost-diff	0	(log.f64 (fma.f64 y y (*.f64 x x)))
cost-diff	0	(.f64 (log.f64 (fma.f64 y y (.f64 x x))) #s(literal 1/2 binary64))
cost-diff	0	(hypot.f64 y x)
cost-diff	0	(log.f64 (hypot.f64 y x))
cost-diff	0	(log.f64 y)
cost-diff	0	#s(approx (log (sqrt (+ (* x x) (* y y)))) (log.f64 y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	52
0	24	47
1	25	47
0	25	47

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (log (sqrt (+ (* x x) (* y y)))) (log.f64 y))
(log.f64 y)
y
(log.f64 (hypot.f64 y x))
(hypot.f64 y x)
y
x
(.f64 (log.f64 (fma.f64 y y (.f64 x x))) #s(literal 1/2 binary64))
(log.f64 (fma.f64 y y (*.f64 x x)))
(fma.f64 y y (*.f64 x x))
y
(*.f64 x x)
x
#s(literal 1/2 binary64)

Outputs
#s(approx (log (sqrt (+ (* x x) (* y y)))) (log.f64 y))
(log.f64 y)
y
(log.f64 (hypot.f64 y x))
(hypot.f64 y x)
y
x
(.f64 (log.f64 (fma.f64 y y (.f64 x x))) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 y y (.f64 x x))))
(log.f64 (fma.f64 y y (*.f64 x x)))
(fma.f64 y y (*.f64 x x))
y
(*.f64 x x)
x
#s(literal 1/2 binary64)

localize45.0ms (1.6%)

Memory

14.1MiB live, 14.1MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 y y (*.f64 x x))
accuracy	0.0	(.f64 (log.f64 (fma.f64 y y (.f64 x x))) #s(literal 1/2 binary64))
accuracy	0.0	(*.f64 x x)
accuracy	11.776837453108218	(log.f64 (fma.f64 y y (*.f64 x x)))
accuracy	0.0	(hypot.f64 y x)
accuracy	0.0	(log.f64 (hypot.f64 y x))
accuracy	0.0	(log.f64 y)
accuracy	0.5982648926776902	#s(approx (log (sqrt (+ (* x x) (* y y)))) (log.f64 y))

Samples

36.0ms

256×

valid

Compiler

Compiled 64 to 15 computations (76.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 26.0ms

ival-log: 11.0ms (42.8% of total)

ival-hypot: 8.0ms (31.1% of total)

ival-mult: 5.0ms (19.5% of total)

ival-add: 1.0ms (3.9% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series87.0ms (3.1%)

Memory

-76.3MiB live, 24.2MiB allocated

Counts

8 → 88

Calls

Call 1

Inputs
#s(approx (log (sqrt (+ (* x x) (* y y)))) (log.f64 y))
(log.f64 y)
(log.f64 (hypot.f64 y x))
(hypot.f64 y x)
(.f64 (log.f64 (fma.f64 y y (.f64 x x))) #s(literal 1/2 binary64))
(log.f64 (fma.f64 y y (*.f64 x x)))
(fma.f64 y y (*.f64 x x))
(*.f64 x x)

Outputs
(log y)
(+ (log y) (* 1/2 (/ (pow x 2) (pow y 2))))
(+ (log y) (* (pow x 2) (+ (* -1/4 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))))
(+ (log y) (* (pow x 2) (+ (* (pow x 2) (- (* 1/6 (/ (pow x 2) (pow y 6))) (* 1/4 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))))
y
(+ y (* 1/2 (/ (pow x 2) y)))
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(* 1/2 (log (pow y 2)))
(+ (* 1/2 (log (pow y 2))) (* 1/2 (/ (pow x 2) (pow y 2))))
(+ (* 1/2 (log (pow y 2))) (* (pow x 2) (+ (* -1/4 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))))
(+ (* 1/2 (log (pow y 2))) (* (pow x 2) (+ (* (pow x 2) (- (* 1/6 (/ (pow x 2) (pow y 6))) (* 1/4 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))))
(log (pow y 2))
(+ (log (pow y 2)) (/ (pow x 2) (pow y 2)))
(+ (log (pow y 2)) (* (pow x 2) (+ (* -1/2 (/ (pow x 2) (pow y 4))) (/ 1 (pow y 2)))))
(+ (log (pow y 2)) (* (pow x 2) (+ (* (pow x 2) (- (* 1/3 (/ (pow x 2) (pow y 6))) (* 1/2 (/ 1 (pow y 4))))) (/ 1 (pow y 2)))))
(pow y 2)
(+ (pow x 2) (pow y 2))
(pow x 2)
(* -1 (log (/ 1 x)))
(+ (* -1 (log (/ 1 x))) (* 1/2 (/ (pow y 2) (pow x 2))))
(+ (* -1 (log (/ 1 x))) (+ (* -1/4 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))
(+ (* -1 (log (/ 1 x))) (+ (* -1/4 (/ (pow y 4) (pow x 4))) (+ (* 1/720 (/ (+ (* 30 (pow y 6)) (* 90 (pow y 6))) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))
x
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(+ (* -1 (log (/ 1 x))) (+ (* -1/4 (/ (pow y 4) (pow x 4))) (+ (* 1/6 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -2 (log (/ 1 x)))
(+ (* -2 (log (/ 1 x))) (/ (pow y 2) (pow x 2)))
(+ (* -2 (log (/ 1 x))) (+ (* -1/2 (/ (pow y 4) (pow x 4))) (/ (pow y 2) (pow x 2))))
(+ (* -2 (log (/ 1 x))) (+ (* -1/2 (/ (pow y 4) (pow x 4))) (+ (* 1/3 (/ (pow y 6) (pow x 6))) (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* -1 (log (/ -1 x)))
(+ (* -1 (log (/ -1 x))) (* 1/2 (/ (pow y 2) (pow x 2))))
(+ (* -1 (log (/ -1 x))) (+ (* -1/4 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))
(+ (* -1 (log (/ -1 x))) (+ (* -1/4 (/ (pow y 4) (pow x 4))) (+ (* 1/720 (/ (+ (* 30 (pow y 6)) (* 90 (pow y 6))) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(+ (* -1 (log (/ -1 x))) (+ (* -1/4 (/ (pow y 4) (pow x 4))) (+ (* 1/6 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -2 (log (/ -1 x)))
(+ (* -2 (log (/ -1 x))) (/ (pow y 2) (pow x 2)))
(+ (* -2 (log (/ -1 x))) (+ (* -1/2 (/ (pow y 4) (pow x 4))) (/ (pow y 2) (pow x 2))))
(+ (* -2 (log (/ -1 x))) (+ (* -1/2 (/ (pow y 4) (pow x 4))) (+ (* 1/3 (/ (pow y 6) (pow x 6))) (/ (pow y 2) (pow x 2)))))
(log x)
(+ (log x) (* 1/2 (/ (pow y 2) (pow x 2))))
(+ (log x) (* (pow y 2) (+ (* -1/4 (/ (pow y 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ (log x) (* (pow y 2) (+ (* (pow y 2) (- (* 1/6 (/ (pow y 2) (pow x 6))) (* 1/4 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(+ x (* 1/2 (/ (pow y 2) x)))
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* 1/2 (log (pow x 2)))
(+ (* 1/2 (log (pow x 2))) (* 1/2 (/ (pow y 2) (pow x 2))))
(+ (* 1/2 (log (pow x 2))) (* (pow y 2) (+ (* -1/4 (/ (pow y 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ (* 1/2 (log (pow x 2))) (* (pow y 2) (+ (* (pow y 2) (- (* 1/6 (/ (pow y 2) (pow x 6))) (* 1/4 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(log (pow x 2))
(+ (log (pow x 2)) (/ (pow y 2) (pow x 2)))
(+ (log (pow x 2)) (* (pow y 2) (+ (* -1/2 (/ (pow y 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ (log (pow x 2)) (* (pow y 2) (+ (* (pow y 2) (- (* 1/3 (/ (pow y 2) (pow x 6))) (* 1/2 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
(* -1 (log (/ 1 y)))
(+ (* -1 (log (/ 1 y))) (* 1/2 (/ (pow x 2) (pow y 2))))
(+ (* -1 (log (/ 1 y))) (+ (* -1/4 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))
(+ (* -1 (log (/ 1 y))) (+ (* -1/4 (/ (pow x 4) (pow y 4))) (+ (* 1/720 (/ (+ (* 30 (pow x 6)) (* 90 (pow x 6))) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(+ (* -1 (log (/ 1 y))) (+ (* -1/4 (/ (pow x 4) (pow y 4))) (+ (* 1/6 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(* -2 (log (/ 1 y)))
(+ (* -2 (log (/ 1 y))) (/ (pow x 2) (pow y 2)))
(+ (* -2 (log (/ 1 y))) (+ (* -1/2 (/ (pow x 4) (pow y 4))) (/ (pow x 2) (pow y 2))))
(+ (* -2 (log (/ 1 y))) (+ (* -1/2 (/ (pow x 4) (pow y 4))) (+ (* 1/3 (/ (pow x 6) (pow y 6))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* -1 (log (/ -1 y)))
(+ (* -1 (log (/ -1 y))) (* 1/2 (/ (pow x 2) (pow y 2))))
(+ (* -1 (log (/ -1 y))) (+ (* -1/4 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))
(+ (* -1 (log (/ -1 y))) (+ (* -1/4 (/ (pow x 4) (pow y 4))) (+ (* 1/720 (/ (+ (* 30 (pow x 6)) (* 90 (pow x 6))) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(+ (log -1) (* -1 (log (/ -1 y))))
(* -1 y)
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))
(+ (* -1 (log (/ -1 y))) (+ (* -1/4 (/ (pow x 4) (pow y 4))) (+ (* 1/6 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(* -2 (log (/ -1 y)))
(+ (* -2 (log (/ -1 y))) (/ (pow x 2) (pow y 2)))
(+ (* -2 (log (/ -1 y))) (+ (* -1/2 (/ (pow x 4) (pow y 4))) (/ (pow x 2) (pow y 2))))
(+ (* -2 (log (/ -1 y))) (+ (* -1/2 (/ (pow x 4) (pow y 4))) (+ (* 1/3 (/ (pow x 6) (pow y 6))) (/ (pow x 2) (pow y 2)))))

Calls

6 calls:

Time	Variable		Point	Expression
41.0ms	y	@	inf	((log (sqrt (+ (* x x) (* y y)))) (log y) (log (sqrt (+ (* y y) (* x x)))) (sqrt (+ (* y y) (* x x))) (* (log (+ (* y y) (* x x))) 1/2) (log (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* x x))
22.0ms	y	@	0	((log (sqrt (+ (* x x) (* y y)))) (log y) (log (sqrt (+ (* y y) (* x x)))) (sqrt (+ (* y y) (* x x))) (* (log (+ (* y y) (* x x))) 1/2) (log (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* x x))
18.0ms	y	@	-inf	((log (sqrt (+ (* x x) (* y y)))) (log y) (log (sqrt (+ (* y y) (* x x)))) (sqrt (+ (* y y) (* x x))) (* (log (+ (* y y) (* x x))) 1/2) (log (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* x x))
2.0ms	x	@	0	((log (sqrt (+ (* x x) (* y y)))) (log y) (log (sqrt (+ (* y y) (* x x)))) (sqrt (+ (* y y) (* x x))) (* (log (+ (* y y) (* x x))) 1/2) (log (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* x x))
1.0ms	x	@	inf	((log (sqrt (+ (* x x) (* y y)))) (log y) (log (sqrt (+ (* y y) (* x x)))) (sqrt (+ (* y y) (* x x))) (* (log (+ (* y y) (* x x))) 1/2) (log (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* x x))

simplify157.0ms (5.7%)

Memory

42.6MiB live, 42.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	261	1647
1	729	1618
2	2152	1592
3	5281	1580
0	8278	1455

Stop Event

1×	iter limit
1×	node limit

Counts

88 → 86

Calls

Call 1

Inputs
(log y)
(+ (log y) (* 1/2 (/ (pow x 2) (pow y 2))))
(+ (log y) (* (pow x 2) (+ (* -1/4 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))))
(+ (log y) (* (pow x 2) (+ (* (pow x 2) (- (* 1/6 (/ (pow x 2) (pow y 6))) (* 1/4 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))))
y
(+ y (* 1/2 (/ (pow x 2) y)))
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(* 1/2 (log (pow y 2)))
(+ (* 1/2 (log (pow y 2))) (* 1/2 (/ (pow x 2) (pow y 2))))
(+ (* 1/2 (log (pow y 2))) (* (pow x 2) (+ (* -1/4 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))))
(+ (* 1/2 (log (pow y 2))) (* (pow x 2) (+ (* (pow x 2) (- (* 1/6 (/ (pow x 2) (pow y 6))) (* 1/4 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))))
(log (pow y 2))
(+ (log (pow y 2)) (/ (pow x 2) (pow y 2)))
(+ (log (pow y 2)) (* (pow x 2) (+ (* -1/2 (/ (pow x 2) (pow y 4))) (/ 1 (pow y 2)))))
(+ (log (pow y 2)) (* (pow x 2) (+ (* (pow x 2) (- (* 1/3 (/ (pow x 2) (pow y 6))) (* 1/2 (/ 1 (pow y 4))))) (/ 1 (pow y 2)))))
(pow y 2)
(+ (pow x 2) (pow y 2))
(pow x 2)
(* -1 (log (/ 1 x)))
(+ (* -1 (log (/ 1 x))) (* 1/2 (/ (pow y 2) (pow x 2))))
(+ (* -1 (log (/ 1 x))) (+ (* -1/4 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))
(+ (* -1 (log (/ 1 x))) (+ (* -1/4 (/ (pow y 4) (pow x 4))) (+ (* 1/720 (/ (+ (* 30 (pow y 6)) (* 90 (pow y 6))) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))
x
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(+ (* -1 (log (/ 1 x))) (+ (* -1/4 (/ (pow y 4) (pow x 4))) (+ (* 1/6 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -2 (log (/ 1 x)))
(+ (* -2 (log (/ 1 x))) (/ (pow y 2) (pow x 2)))
(+ (* -2 (log (/ 1 x))) (+ (* -1/2 (/ (pow y 4) (pow x 4))) (/ (pow y 2) (pow x 2))))
(+ (* -2 (log (/ 1 x))) (+ (* -1/2 (/ (pow y 4) (pow x 4))) (+ (* 1/3 (/ (pow y 6) (pow x 6))) (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* -1 (log (/ -1 x)))
(+ (* -1 (log (/ -1 x))) (* 1/2 (/ (pow y 2) (pow x 2))))
(+ (* -1 (log (/ -1 x))) (+ (* -1/4 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))
(+ (* -1 (log (/ -1 x))) (+ (* -1/4 (/ (pow y 4) (pow x 4))) (+ (* 1/720 (/ (+ (* 30 (pow y 6)) (* 90 (pow y 6))) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(+ (* -1 (log (/ -1 x))) (+ (* -1/4 (/ (pow y 4) (pow x 4))) (+ (* 1/6 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -2 (log (/ -1 x)))
(+ (* -2 (log (/ -1 x))) (/ (pow y 2) (pow x 2)))
(+ (* -2 (log (/ -1 x))) (+ (* -1/2 (/ (pow y 4) (pow x 4))) (/ (pow y 2) (pow x 2))))
(+ (* -2 (log (/ -1 x))) (+ (* -1/2 (/ (pow y 4) (pow x 4))) (+ (* 1/3 (/ (pow y 6) (pow x 6))) (/ (pow y 2) (pow x 2)))))
(log x)
(+ (log x) (* 1/2 (/ (pow y 2) (pow x 2))))
(+ (log x) (* (pow y 2) (+ (* -1/4 (/ (pow y 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ (log x) (* (pow y 2) (+ (* (pow y 2) (- (* 1/6 (/ (pow y 2) (pow x 6))) (* 1/4 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(+ x (* 1/2 (/ (pow y 2) x)))
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* 1/2 (log (pow x 2)))
(+ (* 1/2 (log (pow x 2))) (* 1/2 (/ (pow y 2) (pow x 2))))
(+ (* 1/2 (log (pow x 2))) (* (pow y 2) (+ (* -1/4 (/ (pow y 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ (* 1/2 (log (pow x 2))) (* (pow y 2) (+ (* (pow y 2) (- (* 1/6 (/ (pow y 2) (pow x 6))) (* 1/4 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(log (pow x 2))
(+ (log (pow x 2)) (/ (pow y 2) (pow x 2)))
(+ (log (pow x 2)) (* (pow y 2) (+ (* -1/2 (/ (pow y 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ (log (pow x 2)) (* (pow y 2) (+ (* (pow y 2) (- (* 1/3 (/ (pow y 2) (pow x 6))) (* 1/2 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
(* -1 (log (/ 1 y)))
(+ (* -1 (log (/ 1 y))) (* 1/2 (/ (pow x 2) (pow y 2))))
(+ (* -1 (log (/ 1 y))) (+ (* -1/4 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))
(+ (* -1 (log (/ 1 y))) (+ (* -1/4 (/ (pow x 4) (pow y 4))) (+ (* 1/720 (/ (+ (* 30 (pow x 6)) (* 90 (pow x 6))) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(+ (* -1 (log (/ 1 y))) (+ (* -1/4 (/ (pow x 4) (pow y 4))) (+ (* 1/6 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(* -2 (log (/ 1 y)))
(+ (* -2 (log (/ 1 y))) (/ (pow x 2) (pow y 2)))
(+ (* -2 (log (/ 1 y))) (+ (* -1/2 (/ (pow x 4) (pow y 4))) (/ (pow x 2) (pow y 2))))
(+ (* -2 (log (/ 1 y))) (+ (* -1/2 (/ (pow x 4) (pow y 4))) (+ (* 1/3 (/ (pow x 6) (pow y 6))) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* -1 (log (/ -1 y)))
(+ (* -1 (log (/ -1 y))) (* 1/2 (/ (pow x 2) (pow y 2))))
(+ (* -1 (log (/ -1 y))) (+ (* -1/4 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))
(+ (* -1 (log (/ -1 y))) (+ (* -1/4 (/ (pow x 4) (pow y 4))) (+ (* 1/720 (/ (+ (* 30 (pow x 6)) (* 90 (pow x 6))) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(+ (log -1) (* -1 (log (/ -1 y))))
(* -1 y)
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))
(+ (* -1 (log (/ -1 y))) (+ (* -1/4 (/ (pow x 4) (pow y 4))) (+ (* 1/6 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(* -2 (log (/ -1 y)))
(+ (* -2 (log (/ -1 y))) (/ (pow x 2) (pow y 2)))
(+ (* -2 (log (/ -1 y))) (+ (* -1/2 (/ (pow x 4) (pow y 4))) (/ (pow x 2) (pow y 2))))
(+ (* -2 (log (/ -1 y))) (+ (* -1/2 (/ (pow x 4) (pow y 4))) (+ (* 1/3 (/ (pow x 6) (pow y 6))) (/ (pow x 2) (pow y 2)))))

Outputs
(log y)
(log.f64 y)
(+ (log y) (* 1/2 (/ (pow x 2) (pow y 2))))
(fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) x) x (log.f64 y))
(+ (log y) (* (pow x 2) (+ (* -1/4 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/4 binary64) (pow.f64 y #s(literal 4 binary64))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) x) x (log.f64 y)))
(+ (log y) (* (pow x 2) (+ (* (pow x 2) (- (* 1/6 (/ (pow x 2) (pow y 6))) (* 1/4 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))))
(fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) x) x (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) (/.f64 x (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal -1/4 binary64) (pow.f64 y #s(literal 4 binary64)))) (log.f64 y)))
y
(+ y (* 1/2 (/ (pow x 2) y)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 x x) y)
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) x) (/.f64 x (pow.f64 y #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) y)) (.f64 x x) y)
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal 1/16 binary64) x) (/.f64 x (pow.f64 y #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (.f64 x x) y))
(* 1/2 (log (pow y 2)))
(.f64 (log.f64 (.f64 y y)) #s(literal 1/2 binary64))
(+ (* 1/2 (log (pow y 2))) (* 1/2 (/ (pow x 2) (pow y 2))))
(.f64 (fma.f64 (/.f64 (/.f64 x y) y) x (log.f64 (.f64 y y))) #s(literal 1/2 binary64))
(+ (* 1/2 (log (pow y 2))) (* (pow x 2) (+ (* -1/4 (/ (pow x 2) (pow y 4))) (* 1/2 (/ 1 (pow y 2))))))
(fma.f64 (fma.f64 (/.f64 (/.f64 x y) y) x (log.f64 (.f64 y y))) #s(literal 1/2 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/4 binary64) (pow.f64 y #s(literal 4 binary64)))))
(+ (* 1/2 (log (pow y 2))) (* (pow x 2) (+ (* (pow x 2) (- (* 1/6 (/ (pow x 2) (pow y 6))) (* 1/4 (/ 1 (pow y 4))))) (* 1/2 (/ 1 (pow y 2))))))
(fma.f64 (fma.f64 (/.f64 (/.f64 x y) y) x (log.f64 (.f64 y y))) #s(literal 1/2 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) (/.f64 x (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal -1/4 binary64) (pow.f64 y #s(literal 4 binary64))))))
(log (pow y 2))
(log.f64 (*.f64 y y))
(+ (log (pow y 2)) (/ (pow x 2) (pow y 2)))
(fma.f64 (/.f64 (/.f64 x y) y) x (log.f64 (*.f64 y y)))
(+ (log (pow y 2)) (* (pow x 2) (+ (* -1/2 (/ (pow x 2) (pow y 4))) (/ 1 (pow y 2)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/2 binary64) (pow.f64 y #s(literal 4 binary64))) (fma.f64 (/.f64 (/.f64 x y) y) x (log.f64 (*.f64 y y))))
(+ (log (pow y 2)) (* (pow x 2) (+ (* (pow x 2) (- (* 1/3 (/ (pow x 2) (pow y 6))) (* 1/2 (/ 1 (pow y 4))))) (/ 1 (pow y 2)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal 1/3 binary64) x) (/.f64 x (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal -1/2 binary64) (pow.f64 y #s(literal 4 binary64)))) (fma.f64 (/.f64 (/.f64 x y) y) x (log.f64 (.f64 y y))))
(pow y 2)
(*.f64 y y)
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* -1 (log (/ 1 x)))
(log.f64 x)
(+ (* -1 (log (/ 1 x))) (* 1/2 (/ (pow y 2) (pow x 2))))
(fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) y) y (log.f64 x))
(+ (* -1 (log (/ 1 x))) (+ (* -1/4 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -1/4 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) y) y (log.f64 x)))
(+ (* -1 (log (/ 1 x))) (+ (* -1/4 (/ (pow y 4) (pow x 4))) (+ (* 1/720 (/ (+ (* 30 (pow y 6)) (* 90 (pow y 6))) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) y) y (fma.f64 (*.f64 #s(literal 1/720 binary64) (pow.f64 y #s(literal 6 binary64))) (/.f64 #s(literal 120 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/4 binary64) (log.f64 x))))
x
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))
(fma.f64 (.f64 (/.f64 (.f64 y y) x) #s(literal 1/2 binary64)) #s(literal 1 binary64) x)
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(.f64 (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) y) y #s(literal 1 binary64))) x)
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(.f64 (fma.f64 (pow.f64 y #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) y) y #s(literal 1 binary64)))) x)
(+ (* -1 (log (/ 1 x))) (+ (* -1/4 (/ (pow y 4) (pow x 4))) (+ (* 1/6 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) y) y (fma.f64 (pow.f64 y #s(literal 6 binary64)) (/.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/4 binary64) (log.f64 x))))
(* -2 (log (/ 1 x)))
(*.f64 (log.f64 x) #s(literal 2 binary64))
(+ (* -2 (log (/ 1 x))) (/ (pow y 2) (pow x 2)))
(fma.f64 (/.f64 (/.f64 y x) x) y (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+ (* -2 (log (/ 1 x))) (+ (* -1/2 (/ (pow y 4) (pow x 4))) (/ (pow y 2) (pow x 2))))
(fma.f64 (log.f64 x) #s(literal 2 binary64) (fma.f64 (/.f64 (/.f64 y x) x) y (*.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 4 binary64))))))
(+ (* -2 (log (/ 1 x))) (+ (* -1/2 (/ (pow y 4) (pow x 4))) (+ (* 1/3 (/ (pow y 6) (pow x 6))) (/ (pow y 2) (pow x 2)))))
(fma.f64 (log.f64 x) #s(literal 2 binary64) (fma.f64 (pow.f64 y #s(literal 6 binary64)) (/.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 (/.f64 y x) x) y (*.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 4 binary64)))))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(fma.f64 y y (*.f64 x x))
(* -1 (log (/ -1 x)))
(neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)))
(+ (* -1 (log (/ -1 x))) (* 1/2 (/ (pow y 2) (pow x 2))))
(fma.f64 (*.f64 (/.f64 (/.f64 y x) x) y) #s(literal 1/2 binary64) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) x))))
(+ (* -1 (log (/ -1 x))) (+ (* -1/4 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) y) (/.f64 y (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (*.f64 y y) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) x))))
(+ (* -1 (log (/ -1 x))) (+ (* -1/4 (/ (pow y 4) (pow x 4))) (+ (* 1/720 (/ (+ (* 30 (pow y 6)) (* 90 (pow y 6))) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(fma.f64 (.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) y) (/.f64 y (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) y) y (fma.f64 (.f64 (/.f64 #s(literal 120 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 y #s(literal 6 binary64))) #s(literal 1/720 binary64) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)))))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(fma.f64 (.f64 (/.f64 (.f64 y y) x) #s(literal 1/2 binary64)) #s(literal -1 binary64) (neg.f64 x))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/8 binary64) (fma.f64 (.f64 #s(literal -1/2 binary64) y) (/.f64 (/.f64 y x) x) #s(literal -1 binary64))) x)
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(fma.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/8 binary64) #s(literal -1 binary64))) x (.f64 (.f64 (/.f64 (*.f64 y y) x) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(+ (* -1 (log (/ -1 x))) (+ (* -1/4 (/ (pow y 4) (pow x 4))) (+ (* 1/6 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(fma.f64 (.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) y) (/.f64 y (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) y) y (fma.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/6 binary64) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)))))
(* -2 (log (/ -1 x)))
(*.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) #s(literal -2 binary64))
(+ (* -2 (log (/ -1 x))) (/ (pow y 2) (pow x 2)))
(fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) #s(literal -2 binary64) (*.f64 (/.f64 (/.f64 y x) x) y))
(+ (* -2 (log (/ -1 x))) (+ (* -1/2 (/ (pow y 4) (pow x 4))) (/ (pow y 2) (pow x 2))))
(fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) #s(literal -2 binary64) (fma.f64 (/.f64 (/.f64 y x) x) y (*.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 4 binary64))))))
(+ (* -2 (log (/ -1 x))) (+ (* -1/2 (/ (pow y 4) (pow x 4))) (+ (* 1/3 (/ (pow y 6) (pow x 6))) (/ (pow y 2) (pow x 2)))))
(fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) #s(literal -2 binary64) (fma.f64 (pow.f64 y #s(literal 6 binary64)) (/.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 (/.f64 y x) x) y (*.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 4 binary64)))))))
(log x)
(log.f64 x)
(+ (log x) (* 1/2 (/ (pow y 2) (pow x 2))))
(fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) y) y (log.f64 x))
(+ (log x) (* (pow y 2) (+ (* -1/4 (/ (pow y 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -1/4 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) y) y (log.f64 x)))
(+ (log x) (* (pow y 2) (+ (* (pow y 2) (- (* 1/6 (/ (pow y 2) (pow x 6))) (* 1/4 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) y) y (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/4 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 y #s(literal 4 binary64)) (log.f64 x)))
(+ x (* 1/2 (/ (pow y 2) x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x)
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) y) (/.f64 y (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) x)) (.f64 y y) x)
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) y) (/.f64 y (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 y y) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 y y) x)
(* 1/2 (log (pow x 2)))
(.f64 (log.f64 (.f64 x x)) #s(literal 1/2 binary64))
(+ (* 1/2 (log (pow x 2))) (* 1/2 (/ (pow y 2) (pow x 2))))
(.f64 (fma.f64 (/.f64 (/.f64 y x) x) y (log.f64 (.f64 x x))) #s(literal 1/2 binary64))
(+ (* 1/2 (log (pow x 2))) (* (pow y 2) (+ (* -1/4 (/ (pow y 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) y (log.f64 (.f64 x x))) #s(literal 1/2 binary64) (.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -1/4 binary64) (pow.f64 x #s(literal 4 binary64)))))
(+ (* 1/2 (log (pow x 2))) (* (pow y 2) (+ (* (pow y 2) (- (* 1/6 (/ (pow y 2) (pow x 6))) (* 1/4 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) y (log.f64 (.f64 x x))) #s(literal 1/2 binary64) (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/4 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 y #s(literal 4 binary64))))
(log (pow x 2))
(log.f64 (*.f64 x x))
(+ (log (pow x 2)) (/ (pow y 2) (pow x 2)))
(fma.f64 (/.f64 (/.f64 y x) x) y (log.f64 (*.f64 x x)))
(+ (log (pow x 2)) (* (pow y 2) (+ (* -1/2 (/ (pow y 2) (pow x 4))) (/ 1 (pow x 2)))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (/.f64 y x) x) y (log.f64 (*.f64 x x))))
(+ (log (pow x 2)) (* (pow y 2) (+ (* (pow y 2) (- (* 1/3 (/ (pow y 2) (pow x 6))) (* 1/2 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) y) (/.f64 y (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 y #s(literal 4 binary64)) (fma.f64 (/.f64 (/.f64 y x) x) y (log.f64 (.f64 x x))))
(* -1 (log (/ 1 y)))
(log.f64 y)
(+ (* -1 (log (/ 1 y))) (* 1/2 (/ (pow x 2) (pow y 2))))
(fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) x) x (log.f64 y))
(+ (* -1 (log (/ 1 y))) (+ (* -1/4 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/4 binary64) (pow.f64 y #s(literal 4 binary64))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) x) x (log.f64 y)))
(+ (* -1 (log (/ 1 y))) (+ (* -1/4 (/ (pow x 4) (pow y 4))) (+ (* 1/720 (/ (+ (* 30 (pow x 6)) (* 90 (pow x 6))) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) x) x (fma.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/720 binary64)) (/.f64 #s(literal 120 binary64) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/4 binary64) (log.f64 y))))
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(fma.f64 (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64)) #s(literal 1 binary64) y)
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64)))) y (fma.f64 (.f64 (/.f64 (*.f64 x x) y) #s(literal 1/2 binary64)) #s(literal 1 binary64) y))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 x x) y) #s(literal 1 binary64)))) y)
(+ (* -1 (log (/ 1 y))) (+ (* -1/4 (/ (pow x 4) (pow y 4))) (+ (* 1/6 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) x) x (fma.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 #s(literal 1/6 binary64) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/4 binary64) (log.f64 y))))
(* -2 (log (/ 1 y)))
(*.f64 (log.f64 y) #s(literal 2 binary64))
(+ (* -2 (log (/ 1 y))) (/ (pow x 2) (pow y 2)))
(fma.f64 (/.f64 (/.f64 x y) y) x (*.f64 (log.f64 y) #s(literal 2 binary64)))
(+ (* -2 (log (/ 1 y))) (+ (* -1/2 (/ (pow x 4) (pow y 4))) (/ (pow x 2) (pow y 2))))
(fma.f64 (log.f64 y) #s(literal 2 binary64) (fma.f64 (/.f64 (/.f64 x y) y) x (*.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/2 binary64) (pow.f64 y #s(literal 4 binary64))))))
(+ (* -2 (log (/ 1 y))) (+ (* -1/2 (/ (pow x 4) (pow y 4))) (+ (* 1/3 (/ (pow x 6) (pow y 6))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (log.f64 y) #s(literal 2 binary64) (fma.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 #s(literal 1/3 binary64) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (/.f64 (/.f64 x y) y) x (*.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/2 binary64) (pow.f64 y #s(literal 4 binary64)))))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(fma.f64 y y (*.f64 x x))
(* -1 (log (/ -1 y)))
(neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) y)))
(+ (* -1 (log (/ -1 y))) (* 1/2 (/ (pow x 2) (pow y 2))))
(fma.f64 (*.f64 (/.f64 (/.f64 x y) y) x) #s(literal 1/2 binary64) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) y))))
(+ (* -1 (log (/ -1 y))) (+ (* -1/4 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/4 binary64) (fma.f64 (*.f64 (/.f64 (/.f64 x y) y) x) #s(literal 1/2 binary64) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) y)))))
(+ (* -1 (log (/ -1 y))) (+ (* -1/4 (/ (pow x 4) (pow y 4))) (+ (* 1/720 (/ (+ (* 30 (pow x 6)) (* 90 (pow x 6))) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(fma.f64 (.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) x) (/.f64 x (pow.f64 y #s(literal 4 binary64))) (/.f64 #s(literal 1/2 binary64) (.f64 y y))) x) x (fma.f64 (.f64 (/.f64 #s(literal 120 binary64) (pow.f64 y #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/720 binary64) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) y)))))
(+ (log -1) (* -1 (log (/ -1 y))))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) y)))
(* -1 y)
(neg.f64 y)
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))
(neg.f64 (fma.f64 (.f64 (/.f64 (.f64 x x) y) #s(literal 1/2 binary64)) #s(literal 1 binary64) y))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal 1/8 binary64) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (/.f64 (/.f64 x y) y) #s(literal -1 binary64))) y)
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))
(.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal 1/8 binary64) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (/.f64 (/.f64 x y) y) #s(literal -1 binary64)))) y)
(+ (* -1 (log (/ -1 y))) (+ (* -1/4 (/ (pow x 4) (pow y 4))) (+ (* 1/6 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(fma.f64 (.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) x) (/.f64 x (pow.f64 y #s(literal 4 binary64))) (/.f64 #s(literal 1/2 binary64) (*.f64 y y))) x) x (fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1/6 binary64) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) y)))))
(* -2 (log (/ -1 y)))
(*.f64 (log.f64 (/.f64 #s(literal -1 binary64) y)) #s(literal -2 binary64))
(+ (* -2 (log (/ -1 y))) (/ (pow x 2) (pow y 2)))
(fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) y)) #s(literal -2 binary64) (*.f64 (/.f64 (/.f64 x y) y) x))
(+ (* -2 (log (/ -1 y))) (+ (* -1/2 (/ (pow x 4) (pow y 4))) (/ (pow x 2) (pow y 2))))
(fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) y)) #s(literal -2 binary64) (fma.f64 (/.f64 (/.f64 x y) y) x (*.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/2 binary64) (pow.f64 y #s(literal 4 binary64))))))
(+ (* -2 (log (/ -1 y))) (+ (* -1/2 (/ (pow x 4) (pow y 4))) (+ (* 1/3 (/ (pow x 6) (pow y 6))) (/ (pow x 2) (pow y 2)))))
(fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) y)) #s(literal -2 binary64) (fma.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 #s(literal 1/3 binary64) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (/.f64 (/.f64 x y) y) x (*.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/2 binary64) (pow.f64 y #s(literal 4 binary64)))))))

rewrite181.0ms (6.5%)

Memory

-36.6MiB live, 45.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	46
0	24	36
1	51	36
2	320	36
3	3368	36
0	8789	36

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

8 → 403

Calls

Call 1

Inputs
#s(approx (log (sqrt (+ (* x x) (* y y)))) (log.f64 y))
(log.f64 y)
(log.f64 (hypot.f64 y x))
(hypot.f64 y x)
(.f64 (log.f64 (fma.f64 y y (.f64 x x))) #s(literal 1/2 binary64))
(log.f64 (fma.f64 y y (*.f64 x x)))
(fma.f64 y y (*.f64 x x))
(*.f64 x x)

Outputs
#s(approx (log (sqrt (+ (* x x) (* y y)))) (log.f64 y))
(*.f64 (log.f64 y) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (log.f64 y))
(+.f64 (log.f64 (sqrt.f64 y)) (log.f64 (sqrt.f64 y)))
(log.f64 y)
(.f64 #s(literal 1/4 binary64) (log.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64))))
(.f64 #s(literal 2 binary64) (log.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 1/4 binary64))))
(.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 y y (.f64 x x))))
(.f64 (log.f64 (fma.f64 y y (.f64 x x))) (log.f64 (exp.f64 #s(literal 1/2 binary64))))
(.f64 (log.f64 (fma.f64 y y (.f64 x x))) #s(literal 1/2 binary64))
(neg.f64 (log.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 y x))))
(fma.f64 #s(literal 1/4 binary64) (log.f64 (fma.f64 y y (.f64 x x))) (log.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 1/4 binary64))))
(fma.f64 #s(literal 1/2 binary64) (log.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (log.f64 (pow.f64 (*.f64 (-.f64 y x) (+.f64 y x)) #s(literal -1/2 binary64))))
(fma.f64 #s(literal 1/2 binary64) (log.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (log.f64 (pow.f64 (*.f64 (-.f64 x y) (+.f64 y x)) #s(literal -1/2 binary64))))
(fma.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) (log.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/2 binary64))))
(fma.f64 (log.f64 (fma.f64 y y (.f64 x x))) #s(literal 1/4 binary64) (log.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 1/4 binary64))))
(-.f64 (log.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))))) (log.f64 (neg.f64 (sqrt.f64 (*.f64 (-.f64 y x) (+.f64 y x))))))
(-.f64 (log.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))))) (log.f64 (neg.f64 (sqrt.f64 (*.f64 (-.f64 x y) (+.f64 y x))))))
(-.f64 (log.f64 (neg.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) (log.f64 (neg.f64 (sqrt.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64)))))))
(-.f64 (log.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))))) (log.f64 (sqrt.f64 (neg.f64 (*.f64 (-.f64 y x) (+.f64 y x))))))
(-.f64 (log.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))))) (log.f64 (sqrt.f64 (neg.f64 (*.f64 (-.f64 x y) (+.f64 y x))))))
(-.f64 (log.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))))) (log.f64 (sqrt.f64 (neg.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64)))))))
(-.f64 (log.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))) (log.f64 (sqrt.f64 (*.f64 (-.f64 y x) (+.f64 y x)))))
(-.f64 (log.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (log.f64 (sqrt.f64 (*.f64 (-.f64 x y) (+.f64 y x)))))
(-.f64 (log.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (log.f64 (sqrt.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64))))))
(-.f64 #s(literal 0 binary64) (log.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 y x))))
(+.f64 (log.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))) (log.f64 (pow.f64 (*.f64 (-.f64 y x) (+.f64 y x)) #s(literal -1/2 binary64))))
(+.f64 (log.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (log.f64 (pow.f64 (*.f64 (-.f64 x y) (+.f64 y x)) #s(literal -1/2 binary64))))
(+.f64 (log.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (log.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/2 binary64))))
(+.f64 (log.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 1/4 binary64))) (log.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 1/4 binary64))))
(log.f64 (hypot.f64 y x))
(.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 (fma.f64 (.f64 x x) (fma.f64 y y (*.f64 x x)) (pow.f64 y #s(literal 4 binary64)))))
(.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))))) (sqrt.f64 (fma.f64 (.f64 x x) (fma.f64 y y (*.f64 x x)) (pow.f64 y #s(literal 4 binary64)))))
(.f64 (sqrt.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 y #s(literal 8 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) #s(literal 2 binary64))))) (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))))))
(.f64 (sqrt.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 y #s(literal 12 binary64))))) (sqrt.f64 (fma.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (-.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64))) (pow.f64 y #s(literal 8 binary64)))))
(.f64 (sqrt.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) #s(literal 2 binary64))))) (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))))))
(.f64 (sqrt.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64))))) (sqrt.f64 (fma.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (-.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64)))))
(.f64 (sqrt.f64 (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x)))
(*.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))) (hypot.f64 y x))
(*.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (hypot.f64 y x))
(.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (.f64 (-.f64 y x) (+.f64 y x)) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (.f64 (-.f64 x y) (+.f64 y x)) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(.f64 (pow.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (.f64 x x) (fma.f64 y y (*.f64 x x)) (pow.f64 y #s(literal 4 binary64)))))
(.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (.f64 x x) (fma.f64 y y (*.f64 x x)) (pow.f64 y #s(literal 4 binary64)))))
(.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 y #s(literal 8 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))))))
(.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 y #s(literal 12 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (-.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64))) (pow.f64 y #s(literal 8 binary64)))))
(.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))))))
(.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (-.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64)))))
(*.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/2 binary64)) (hypot.f64 y x))
(.f64 (pow.f64 (/.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x)) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 y x)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (hypot.f64 y x))
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(/.f64 (.f64 (-.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 x #s(literal 12 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64)))))
(/.f64 (.f64 (+.f64 (pow.f64 x #s(literal 18 binary64)) (pow.f64 y #s(literal 18 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) (pow.f64 (.f64 y x) #s(literal 6 binary64))) (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64)))))
(/.f64 (.f64 (+.f64 (pow.f64 x #s(literal 18 binary64)) (pow.f64 y #s(literal 18 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 x #s(literal 12 binary64))) (pow.f64 (.f64 y x) #s(literal 6 binary64))) (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64)))))
(/.f64 (-.f64 (.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 y x) (+.f64 y x))) (.f64 (.f64 (-.f64 y x) (+.f64 y x)) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 (*.f64 (-.f64 y x) (+.f64 y x)) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))) (.f64 (.f64 (-.f64 x y) (+.f64 y x)) (pow.f64 y #s(literal 4 binary64)))) (pow.f64 (*.f64 (-.f64 x y) (+.f64 y x)) #s(literal 2 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (fma.f64 y y (*.f64 x x)) #s(literal -1 binary64))))
(/.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 8 binary64))) (.f64 (.f64 (-.f64 x y) (+.f64 y x)) (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 y #s(literal 8 binary64)) (pow.f64 x #s(literal 8 binary64))) (.f64 (.f64 (-.f64 y x) (+.f64 y x)) (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) (.f64 (.f64 (-.f64 x y) (+.f64 y x)) (+.f64 (+.f64 (pow.f64 (*.f64 y x) #s(literal 4 binary64)) (pow.f64 y #s(literal 8 binary64))) (pow.f64 x #s(literal 8 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) (.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))))
(/.f64 (-.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 x #s(literal 12 binary64))) (.f64 (.f64 (-.f64 y x) (+.f64 y x)) (+.f64 (+.f64 (pow.f64 (*.f64 y x) #s(literal 4 binary64)) (pow.f64 x #s(literal 8 binary64))) (pow.f64 y #s(literal 8 binary64)))))
(/.f64 (-.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 x #s(literal 12 binary64))) (.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))))
(/.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 (log.f64 (fma.f64 y y (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (fma.f64 y y (*.f64 x x)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 y y (*.f64 x x)) #s(literal -1 binary64)))
(/.f64 (+.f64 (pow.f64 x #s(literal 18 binary64)) (pow.f64 y #s(literal 18 binary64))) (.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64))) (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) (pow.f64 (*.f64 y x) #s(literal 6 binary64)))))
(/.f64 (+.f64 (pow.f64 x #s(literal 18 binary64)) (pow.f64 y #s(literal 18 binary64))) (.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64))) (-.f64 (+.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 x #s(literal 12 binary64))) (pow.f64 (*.f64 y x) #s(literal 6 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (*.f64 (-.f64 y x) (+.f64 y x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (neg.f64 (*.f64 (-.f64 x y) (+.f64 y x))))
(/.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (*.f64 (-.f64 y x) (+.f64 y x)))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (*.f64 (-.f64 x y) (+.f64 y x)))
(/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64))))
(neg.f64 (/.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (*.f64 (-.f64 y x) (+.f64 y x))))
(neg.f64 (/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (*.f64 (-.f64 x y) (+.f64 y x))))
(neg.f64 (/.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64)))))
(neg.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (neg.f64 (*.f64 (-.f64 y x) (+.f64 y x)))))
(neg.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (neg.f64 (*.f64 (-.f64 x y) (+.f64 y x)))))
(neg.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (neg.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64))))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) (fma.f64 (.f64 x x) (fma.f64 y y (.f64 x x)) (pow.f64 y #s(literal 4 binary64))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 (-.f64 x y) (+.f64 y x)))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (fma.f64 y y (.f64 x x)) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x)))))
(fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (.f64 x x) (fma.f64 y y (.f64 x x)) (pow.f64 y #s(literal 4 binary64))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (-.f64 y x) (+.f64 y x)))))
(fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 y y (.f64 x x)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (-.f64 y x) (+.f64 y x)))))
(fma.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (+.f64 y x)) (/.f64 y (-.f64 y x)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (-.f64 y x) (+.f64 y x)))))
(fma.f64 (/.f64 (.f64 y y) (+.f64 y x)) (/.f64 (.f64 y y) (-.f64 y x)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (-.f64 y x) (+.f64 y x)))))
(fma.f64 (/.f64 y (+.f64 y x)) (/.f64 (pow.f64 y #s(literal 3 binary64)) (-.f64 y x)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (-.f64 y x) (+.f64 y x)))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (+.f64 y x)) (/.f64 x (-.f64 x y)) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 (-.f64 x y) (+.f64 y x)))))
(fma.f64 (/.f64 (.f64 x x) (+.f64 y x)) (/.f64 (.f64 x x) (-.f64 x y)) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 (-.f64 x y) (+.f64 y x)))))
(fma.f64 (/.f64 x (+.f64 y x)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x y)) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (*.f64 (-.f64 x y) (+.f64 y x)))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 x (.f64 (-.f64 x y) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x)))))
(fma.f64 (pow.f64 y #s(literal 3 binary64)) (/.f64 y (.f64 (-.f64 y x) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (-.f64 y x) (+.f64 y x)))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 (-.f64 y x) (+.f64 y x)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (-.f64 y x) (+.f64 y x)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 (-.f64 x y) (+.f64 y x)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x)))))
(fma.f64 (.f64 x x) (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x)))))
(fma.f64 (.f64 y y) (/.f64 (.f64 y y) (.f64 (-.f64 y x) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (-.f64 y x) (+.f64 y x)))))
(fma.f64 y (/.f64 (pow.f64 y #s(literal 3 binary64)) (.f64 (-.f64 y x) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (-.f64 y x) (+.f64 y x)))))
(fma.f64 y y (*.f64 x x))
(fma.f64 x (/.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 (-.f64 x y) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x)))))
(fma.f64 x x (*.f64 y y))
(-.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 y x) (+.f64 y x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (-.f64 y x) (+.f64 y x))))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))))
(exp.f64 (.f64 (neg.f64 (log.f64 (fma.f64 y y (.f64 x x)))) #s(literal -1 binary64)))
(exp.f64 (log.f64 (fma.f64 y y (*.f64 x x))))
(+.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 y x) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (-.f64 y x) (+.f64 y x)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 x y) (+.f64 y x)))))
(+.f64 (.f64 x x) (.f64 y y))
(+.f64 (.f64 y y) (.f64 x x))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval50.0ms (1.8%)

Memory: 38.8MiB live, 38.8MiB allocated
Compiler: Compiled 12 589 to 1 805 computations (85.7% saved)

prune9.0ms (0.3%)

Memory

17.4MiB live, 17.4MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	453	1	454
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	453	4	457

Accuracy

100.0%

Counts

457 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	81.6%	(.f64 (log.f64 (fma.f64 y y (.f64 x x))) #s(literal 1/2 binary64))
	99.6%	(.f64 #s(approx (log (+ ( y y) (* x x))) (fma.f64 (/.f64 (/.f64 x y) y) x (*.f64 (log.f64 y) #s(literal 2 binary64)))) #s(literal 1/2 binary64))
✓	100.0%	(log.f64 (hypot.f64 y x))
✓	99.1%	#s(approx (log (sqrt (+ (* x x) (* y y)))) (log.f64 y))

Compiler

Compiled 103 to 64 computations (37.9% saved)

regimes14.0ms (0.5%)

Memory

-67.2MiB live, 11.5MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
#s(approx (log (sqrt (+ (* x x) (* y y)))) (log.f64 y))
(.f64 (log.f64 (fma.f64 y y (.f64 x x))) #s(literal 1/2 binary64))
(log.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
(.f64 #s(approx (log (+ ( y y) (* x x))) (fma.f64 (/.f64 (/.f64 x y) y) x (*.f64 (log.f64 y) #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(log.f64 (hypot.f64 y x))

Outputs
(log.f64 (hypot.f64 y x))

Calls

7 calls:

4.0ms	y
2.0ms	x
2.0ms	(log.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
2.0ms	(*.f64 y y)
2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(log.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))`
100.0%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
100.0%	1	`(+.f64 (.f64 x x) (.f64 y y))`
100.0%	1	`(*.f64 x x)`
100.0%	1	`(*.f64 y y)`

Compiler

Compiled 32 to 28 computations (12.5% saved)

regimes11.0ms (0.4%)

Memory

11.0MiB live, 11.0MiB allocated

Counts

4 → 1

Calls

Call 1

Inputs
#s(approx (log (sqrt (+ (* x x) (* y y)))) (log.f64 y))
(.f64 (log.f64 (fma.f64 y y (.f64 x x))) #s(literal 1/2 binary64))
(log.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
(.f64 #s(approx (log (+ ( y y) (* x x))) (fma.f64 (/.f64 (/.f64 x y) y) x (*.f64 (log.f64 y) #s(literal 2 binary64)))) #s(literal 1/2 binary64))

Outputs
(.f64 #s(approx (log (+ ( y y) (* x x))) (fma.f64 (/.f64 (/.f64 x y) y) x (*.f64 (log.f64 y) #s(literal 2 binary64)))) #s(literal 1/2 binary64))

Calls

7 calls:

1.0ms	x
1.0ms	y
1.0ms	(log.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
1.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
1.0ms	(+.f64 (.f64 x x) (.f64 y y))

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`y`
99.6%	1	`(log.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))`
99.6%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
99.6%	1	`(+.f64 (.f64 x x) (.f64 y y))`
99.6%	1	`(*.f64 x x)`
99.6%	1	`(*.f64 y y)`

Compiler

Compiled 32 to 28 computations (12.5% saved)

regimes10.0ms (0.3%)

Memory

10.5MiB live, 10.5MiB allocated

Accuracy

Total -11.6b remaining (-1932.8%)

Threshold costs -11.6b (-1932.8%)

Counts

3 → 1

Calls

Call 1

Inputs
#s(approx (log (sqrt (+ (* x x) (* y y)))) (log.f64 y))
(.f64 (log.f64 (fma.f64 y y (.f64 x x))) #s(literal 1/2 binary64))
(log.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))

Outputs
#s(approx (log (sqrt (+ (* x x) (* y y)))) (log.f64 y))

Calls

7 calls:

2.0ms	y
1.0ms	(log.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
1.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
1.0ms	x
1.0ms	(+.f64 (.f64 x x) (.f64 y y))

Results

Accuracy	Segments	Branch
99.1%	1	`x`
99.1%	1	`y`
99.1%	1	`(log.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))`
99.1%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
99.1%	1	`(+.f64 (.f64 x x) (.f64 y y))`
99.1%	1	`(*.f64 x x)`
99.1%	1	`(*.f64 y y)`

Compiler

Compiled 32 to 28 computations (12.5% saved)

simplify9.0ms (0.3%)

Memory

5.1MiB live, 5.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	38
1	22	38

Stop Event

1×

saturated

Calls

Call 1

Inputs

(log.f64 (hypot.f64 y x))

(*.f64 #s(approx (log (+ (* y y) (* x x))) (fma.f64 (/.f64 (/.f64 x y) y) x (*.f64 (log.f64 y) #s(literal 2 binary64)))) #s(literal 1/2 binary64))

#s(approx (log (sqrt (+ (* x x) (* y y)))) (log.f64 y))

Outputs

(log.f64 (hypot.f64 y x))

(*.f64 #s(approx (log (+ (* y y) (* x x))) (fma.f64 (/.f64 (/.f64 x y) y) x (*.f64 (log.f64 y) #s(literal 2 binary64)))) #s(literal 1/2 binary64))

#s(approx (log (sqrt (+ (* x x) (* y y)))) (log.f64 y))

soundness426.0ms (15.4%)

Memory

5.1MiB live, 5.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	186	885
1	510	863
2	1541	853
3	5419	819
0	8163	756
0	261	1647
1	729	1618
2	2152	1592
3	5281	1580
0	8278	1455
0	7	27
0	12	27
1	31	27
2	199	27
3	1810	27
0	8180	16

Stop Event

1×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Compiler

Compiled 94 to 56 computations (40.4% saved)

preprocess23.0ms (0.8%)

Memory

16.2MiB live, 16.2MiB allocated

Remove

(sort x y)

(abs x)

(abs y)

Compiler

Compiled 118 to 80 computations (32.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

log(sqrt(xx+yy))

start0.0ms (0%)

analyze3.0ms (0.1%)

sample1.2s (43.2%)

explain97.0ms (3.5%)

preprocess16.0ms (0.6%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize26.0ms (0.9%)

series19.0ms (0.7%)

simplify156.0ms (5.6%)

rewrite187.0ms (6.8%)

eval36.0ms (1.3%)

prune5.0ms (0.2%)

simplify4.0ms (0.1%)

localize45.0ms (1.6%)

series87.0ms (3.1%)

simplify157.0ms (5.7%)

rewrite181.0ms (6.5%)

eval50.0ms (1.8%)

prune9.0ms (0.3%)

regimes14.0ms (0.5%)

regimes11.0ms (0.4%)

regimes10.0ms (0.3%)

simplify9.0ms (0.3%)

soundness426.0ms (15.4%)

preprocess23.0ms (0.8%)

end0.0ms (0%)

Profiling