Metrics for sqrt(1+x)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze2.0ms (0.1%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	75%	25%	0%	0%	0%	0
0%	0%	75%	25%	0%	0%	0%	1
0%	0%	37.5%	25%	0%	37.5%	0%	2
50%	18.7%	18.7%	25%	0%	37.5%	0%	3
66.7%	18.7%	9.4%	25%	0%	46.8%	0%	4
83.3%	23.4%	4.7%	25%	0%	46.8%	0%	5
90.9%	23.4%	2.3%	25%	0%	49.2%	0%	6
95.5%	24.6%	1.2%	25%	0%	49.2%	0%	7
97.7%	24.6%	0.6%	25%	0%	49.8%	0%	8
98.8%	24.9%	0.3%	25%	0%	49.8%	0%	9
99.4%	24.9%	0.1%	25%	0%	49.9%	0%	10
99.7%	25%	0.1%	25%	0%	49.9%	0%	11
99.9%	25%	0%	25%	0%	50%	0%	12

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample905.0ms (27.8%)

Memory

120.1MiB live, 538.6MiB allocated

Samples

554.0ms	8 256×	0	valid
0.0ms	5×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 362.0ms

ival-sqrt: 161.0ms (44.4% of total)

ival-sub: 68.0ms (18.8% of total)

ival-add: 56.0ms (15.5% of total)

ival-<=: 49.0ms (13.5% of total)

ival-and: 12.0ms (3.3% of total)

exact: 12.0ms (3.3% of total)

ival-assert: 3.0ms (0.8% of total)

Bogosity

explain366.0ms (11.2%)

Memory

-155.8MiB live, 154.3MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))`
-	-	`(sqrt.f64 x)`
-	-	`(sqrt.f64 (+.f64 #s(literal 1 binary64) x))`
-	-	`(+.f64 #s(literal 1 binary64) x)`
-	-	`#s(literal 1 binary64)`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

27.0ms

512×

valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-sqrt: 7.0ms (50.9% of total)

ival-add: 3.0ms (21.8% of total)

ival-sub: 2.0ms (14.5% of total)

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

exact: 0.0ms (0% of total)

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

preprocess20.0ms (0.6%)

Memory

5.2MiB live, 5.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	19	17
2	41	16
3	74	16
4	122	16
5	180	16
6	204	16
7	215	16
0	6	7
0	10	7
1	15	7
2	19	7
3	25	7
4	33	7
5	48	7
6	80	7
7	109	7
8	158	7
9	174	7
10	182	7
0	182	7

Stop Event

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

Calls

Call 1

Inputs
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))

Outputs
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify7.0ms (0.2%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(+.f64 #s(literal 1 binary64) x)
cost-diff	0	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
cost-diff	0	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	10	18
1	15	18
2	19	18
3	25	18
4	33	18
5	48	18
6	80	18
7	109	18
8	158	18
9	174	18
10	182	18
0	182	18

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(sqrt.f64 x)

Outputs
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 #s(literal 1 binary64) x)
(+.f64 x #s(literal 1 binary64))
#s(literal 1 binary64)
x
(sqrt.f64 x)

localize18.0ms (0.6%)

Memory

7.0MiB live, 7.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 #s(literal 1 binary64) x)
accuracy	0.0	(sqrt.f64 x)
accuracy	0.0078125	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy	0.02734375	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))

Samples

13.0ms

256×

valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-sqrt: 3.0ms (46.5% of total)

ival-add: 2.0ms (31% of total)

ival-sub: 1.0ms (15.5% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

1.8MiB live, 1.8MiB allocated

Counts

4 → 27

Calls

Call 1

Inputs
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
(sqrt.f64 x)

Outputs
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(+ 1 x)
(sqrt x)
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
x
(* x (+ 1 (/ 1 x)))
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	((- (sqrt (+ 1 x)) (sqrt x)) (sqrt (+ 1 x)) (+ 1 x) (sqrt x))
2.0ms	x	@	inf	((- (sqrt (+ 1 x)) (sqrt x)) (sqrt (+ 1 x)) (+ 1 x) (sqrt x))
1.0ms	x	@	0	((- (sqrt (+ 1 x)) (sqrt x)) (sqrt (+ 1 x)) (+ 1 x) (sqrt x))

simplify192.0ms (5.9%)

Memory

-30.3MiB live, 41.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	113	451
1	299	399
2	807	395
3	2292	387
4	4919	387
0	8163	351

Stop Event

1×	iter limit
1×	node limit

Counts

27 → 26

Calls

Call 1

Inputs
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(+ 1 x)
(sqrt x)
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
x
(* x (+ 1 (/ 1 x)))
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))

Outputs
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(sqrt x)
(sqrt.f64 x)
(* 1/2 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -5/128 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))) x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x)
x
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* -1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x)
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(/.f64 (fma.f64 (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) x)
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(/.f64 (fma.f64 (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal 5/128 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))) x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(*.f64 (fma.f64 (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x)

rewrite144.0ms (4.4%)

Memory

46.9MiB live, 46.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	43	16
2	295	16
3	3301	16
0	8933	16

Stop Event

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

Counts

4 → 378

Calls

Call 1

Inputs
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
(sqrt.f64 x)

Outputs
(*.f64 (/.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (pow.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) #s(literal 2 binary64)))) (-.f64 (-.f64 (-.f64 #s(literal 1 binary64) x) x) (hypot.f64 (sqrt.f64 x) x)))
(*.f64 (/.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (+.f64 (pow.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) #s(literal 3 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)))) (fma.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) (-.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) (-.f64 #s(literal 1 binary64) x)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
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(/.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (exp.f64 (neg.f64 (log1p.f64 x))))
(/.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)))
(/.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (exp.f64 (neg.f64 (log1p.f64 x)))) (fma.f64 x x #s(literal 1 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (exp.f64 (neg.f64 (log1p.f64 x)))) (+.f64 (pow.f64 (fma.f64 x x x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))
(/.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64))) (-.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 3 binary64))))
(/.f64 (*.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (hypot.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) x))
(/.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) (hypot.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) x))
(/.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (pow.f64 (.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))) (+.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -3 binary64)) (.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -3 binary64)))) (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (+.f64 (pow.f64 (.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x)))))))
(/.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (neg.f64 (-.f64 x #s(literal 1 binary64))))
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (*.f64 x x))) (-.f64 #s(literal 1 binary64) x))
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))))
(/.f64 (*.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (pow.f64 (fma.f64 x x x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(/.f64 (.f64 (+.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(/.f64 (.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (hypot.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) x)))
(/.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) (.f64 (hypot.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x (fma.f64 x x x))) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 x #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 (neg.f64 (log1p.f64 x)))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (pow.f64 (fma.f64 x x x) #s(literal 2 binary64)) #s(literal 1 binary64))))
(/.f64 (+.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) (-.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (+.f64 #s(literal -1 binary64) (*.f64 x x)) (+.f64 #s(literal -1 binary64) x))
(/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(/.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (neg.f64 x)))
(/.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) (neg.f64 x))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (exp.f64 (neg.f64 (log1p.f64 x))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 (log1p.f64 x))))
(neg.f64 (+.f64 #s(literal -1 binary64) x))
(fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x)))))
(fma.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) (+.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1 binary64))) (-.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x)))))
(fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 x x #s(literal 1 binary64)) (neg.f64 (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x)))))
(fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))) (+.f64 (pow.f64 (fma.f64 x x x) #s(literal 2 binary64)) #s(literal 1 binary64)) (neg.f64 (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x)))))
(fma.f64 (*.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1 binary64)) (sqrt.f64 x) #s(literal 1 binary64))
(fma.f64 (*.f64 (neg.f64 (sqrt.f64 x)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) (neg.f64 (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x)))))
(fma.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) x) (neg.f64 (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x)))))
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 x #s(literal 3/2 binary64))) #s(literal 1 binary64))
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)) #s(literal 1 binary64))
(fma.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) (neg.f64 x) #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64))
(fma.f64 (neg.f64 x) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)) #s(literal 1 binary64))
(fma.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x) #s(literal 1 binary64))
(fma.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (neg.f64 (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x)))))
(fma.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 x)) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) #s(literal 1 binary64))
(fma.f64 (-.f64 #s(literal 1 binary64) x) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x)))))
(fma.f64 x #s(literal -1 binary64) #s(literal 1 binary64))
(fma.f64 x #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (neg.f64 x) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 (log1p.f64 x))) (neg.f64 (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x)))))
(fma.f64 #s(literal 1 binary64) x #s(literal 1 binary64))
(-.f64 (/.f64 (*.f64 x x) (-.f64 x #s(literal 1 binary64))) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))
(-.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(-.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x))))
(-.f64 #s(literal 1 binary64) x)
(sqrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
(fabs.f64 (-.f64 #s(literal 1 binary64) x))
(hypot.f64 (neg.f64 (hypot.f64 (sqrt.f64 x) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(hypot.f64 (hypot.f64 (sqrt.f64 x) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(hypot.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (neg.f64 (hypot.f64 (sqrt.f64 x) x)))
(hypot.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (hypot.f64 (sqrt.f64 x) x))
(exp.f64 (*.f64 (neg.f64 (log1p.f64 x)) #s(literal -1 binary64)))
(exp.f64 (log1p.f64 x))
(+.f64 (neg.f64 x) #s(literal 1 binary64))
(+.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (neg.f64 (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x)))))
(+.f64 x #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (neg.f64 x))
(+.f64 #s(literal 1 binary64) x)
(.f64 (sqrt.f64 (.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 x #s(literal 1/4 binary64))))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 1/4 binary64))) (sqrt.f64 (pow.f64 x #s(literal 3/4 binary64))))
(*.f64 (sqrt.f64 (neg.f64 (sqrt.f64 x))) (sqrt.f64 (neg.f64 (sqrt.f64 x))))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 x)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 x))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 x))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/8 binary64))
(pow.f64 (neg.f64 (sqrt.f64 x)) #s(literal 1 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 x #s(literal 1/2 binary64))
(sqrt.f64 x)
(fabs.f64 (sqrt.f64 x))
(exp.f64 (.f64 (.f64 #s(literal 1/4 binary64) (log.f64 x)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 x)) #s(literal 1 binary64)))
(exp.f64 (log.f64 (sqrt.f64 x)))

eval69.0ms (2.1%)

Memory: -43.8MiB live, 36.5MiB allocated
Compiler: Compiled 7 828 to 1 474 computations (81.2% saved)

prune6.0ms (0.2%)

Memory

16.3MiB live, 16.3MiB allocated

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	399	4	403
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	399	5	404

Accuracy

100.0%

Counts

404 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
▶	98.4%	(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))
▶	97.4%	(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x))
▶	98.7%	#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
▶	98.4%	#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))

Compiler

Compiled 61 to 50 computations (18% saved)

simplify59.0ms (1.8%)

Memory

5.2MiB live, 5.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
cost-diff	0	#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
cost-diff	0	(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
cost-diff	0	(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x))
cost-diff	0	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
cost-diff	0	(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
cost-diff	0	(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
cost-diff	0	#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
cost-diff	0	(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
cost-diff	0	#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	122
0	31	122
1	49	122
2	75	122
3	168	122
4	330	122
5	667	122
6	1278	122
7	1780	122
8	2028	122
9	2136	122
10	2143	122
0	2143	122

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
#s(literal 1/2 binary64)
x
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
#s(literal 1 binary64)
(sqrt.f64 x)
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
#s(literal -1/8 binary64)
x
#s(literal 1/2 binary64)
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
#s(literal 1 binary64)
(sqrt.f64 x)
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x))
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
#s(literal 1 binary64)
(sqrt.f64 x)
x
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))
#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
#s(literal 1/2 binary64)
x
#s(literal 1 binary64)
(sqrt.f64 x)

Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
#s(literal 1/2 binary64)
x
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
#s(literal 1 binary64)
(sqrt.f64 x)
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
#s(literal -1/8 binary64)
x
#s(literal 1/2 binary64)
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
#s(literal 1 binary64)
(sqrt.f64 x)
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x))
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
#s(literal 1 binary64)
(sqrt.f64 x)
x
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))
#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
#s(literal 1/2 binary64)
x
#s(literal 1 binary64)
(sqrt.f64 x)

localize40.0ms (1.2%)

Memory

17.8MiB live, 17.8MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
accuracy	0.0	(sqrt.f64 x)
accuracy	0.02734375	(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))
accuracy	0.9647488817490505	#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
accuracy	0.0	(sqrt.f64 x)
accuracy	0.02734375	(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x))
accuracy	1.6092707916211584	#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
accuracy	0.0	(sqrt.f64 x)
accuracy	0.0078125	(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
accuracy	0.023073791389095776	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
accuracy	0.8391267520234017	#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
accuracy	0.0	(sqrt.f64 x)
accuracy	0.01171875	(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
accuracy	0.023073791389095776	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
accuracy	1.0057096617990635	#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))

Samples

28.0ms

256×

valid

Compiler

Compiled 96 to 18 computations (81.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-add: 6.0ms (36.7% of total)

ival-mult: 4.0ms (24.5% of total)

ival-sqrt: 3.0ms (18.4% of total)

ival-sub: 2.0ms (12.2% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

2.1MiB live, 2.1MiB allocated

Counts

12 → 44

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(sqrt.f64 x)
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x))
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))
#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))

Outputs
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(sqrt x)
1/2
(+ 1/2 (* -1/8 x))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(* x (- 1/2 (sqrt (/ 1 x))))
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(* -1 (sqrt x))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(* -1/8 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) (+ 1/8 (sqrt (/ 1 (pow x 3))))))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) (+ 1/8 (sqrt (/ 1 (pow x 3))))))
(* -1/8 x)
(* x (- (* 1/2 (/ 1 x)) 1/8))
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* (sqrt x) (pow (sqrt -1) 2))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (* 1/2 (/ 1 x))) 1/8))
(* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) 1/8))
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	((- (sqrt (+ 1 x)) (sqrt x)) (+ (* 1/2 x) (- 1 (sqrt x))) (- 1 (sqrt x)) (sqrt x) (- (sqrt (+ 1 x)) (sqrt x)) (+ (* (+ (* -1/8 x) 1/2) x) (- 1 (sqrt x))) (+ (* -1/8 x) 1/2) (- (sqrt (+ 1 x)) (sqrt x)) (sqrt (+ 1 x)) (- (sqrt (+ 1 x)) (sqrt x)) (sqrt (+ 1 x)) (+ (* 1/2 x) 1))
1.0ms	x	@	inf	((- (sqrt (+ 1 x)) (sqrt x)) (+ (* 1/2 x) (- 1 (sqrt x))) (- 1 (sqrt x)) (sqrt x) (- (sqrt (+ 1 x)) (sqrt x)) (+ (* (+ (* -1/8 x) 1/2) x) (- 1 (sqrt x))) (+ (* -1/8 x) 1/2) (- (sqrt (+ 1 x)) (sqrt x)) (sqrt (+ 1 x)) (- (sqrt (+ 1 x)) (sqrt x)) (sqrt (+ 1 x)) (+ (* 1/2 x) 1))
1.0ms	x	@	0	((- (sqrt (+ 1 x)) (sqrt x)) (+ (* 1/2 x) (- 1 (sqrt x))) (- 1 (sqrt x)) (sqrt x) (- (sqrt (+ 1 x)) (sqrt x)) (+ (* (+ (* -1/8 x) 1/2) x) (- 1 (sqrt x))) (+ (* -1/8 x) 1/2) (- (sqrt (+ 1 x)) (sqrt x)) (sqrt (+ 1 x)) (- (sqrt (+ 1 x)) (sqrt x)) (sqrt (+ 1 x)) (+ (* 1/2 x) 1))

Time

Variable

Point

Expression

2.0ms

-inf

((- (sqrt (+ 1 x)) (sqrt x)) (+ (* 1/2 x) (- 1 (sqrt x))) (- 1 (sqrt x)) (sqrt x) (- (sqrt (+ 1 x)) (sqrt x)) (+ (* (+ (* -1/8 x) 1/2) x) (- 1 (sqrt x))) (+ (* -1/8 x) 1/2) (- (sqrt (+ 1 x)) (sqrt x)) (sqrt (+ 1 x)) (- (sqrt (+ 1 x)) (sqrt x)) (sqrt (+ 1 x)) (+ (* 1/2 x) 1))

1.0ms

inf

((- (sqrt (+ 1 x)) (sqrt x)) (+ (* 1/2 x) (- 1 (sqrt x))) (- 1 (sqrt x)) (sqrt x) (- (sqrt (+ 1 x)) (sqrt x)) (+ (* (+ (* -1/8 x) 1/2) x) (- 1 (sqrt x))) (+ (* -1/8 x) 1/2) (- (sqrt (+ 1 x)) (sqrt x)) (sqrt (+ 1 x)) (- (sqrt (+ 1 x)) (sqrt x)) (sqrt (+ 1 x)) (+ (* 1/2 x) 1))

1.0ms

((- (sqrt (+ 1 x)) (sqrt x)) (+ (* 1/2 x) (- 1 (sqrt x))) (- 1 (sqrt x)) (sqrt x) (- (sqrt (+ 1 x)) (sqrt x)) (+ (* (+ (* -1/8 x) 1/2) x) (- 1 (sqrt x))) (+ (* -1/8 x) 1/2) (- (sqrt (+ 1 x)) (sqrt x)) (sqrt (+ 1 x)) (- (sqrt (+ 1 x)) (sqrt x)) (sqrt (+ 1 x)) (+ (* 1/2 x) 1))

simplify260.0ms (8%)

Memory

-62.4MiB live, 46.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	147	618
1	391	557
2	1077	545
3	2768	530
4	5751	530
0	8087	482

Stop Event

1×	iter limit
1×	node limit

Counts

44 → 44

Calls

Call 1

Inputs
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(sqrt x)
1/2
(+ 1/2 (* -1/8 x))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(* x (- 1/2 (sqrt (/ 1 x))))
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(* -1 (sqrt x))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(* -1/8 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) (+ 1/8 (sqrt (/ 1 (pow x 3))))))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) (+ 1/8 (sqrt (/ 1 (pow x 3))))))
(* -1/8 x)
(* x (- (* 1/2 (/ 1 x)) 1/8))
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* (sqrt x) (pow (sqrt -1) 2))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (* 1/2 (/ 1 x))) 1/8))
(* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) 1/8))
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))

Outputs
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(sqrt x)
(sqrt.f64 x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/8 x))
(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -5/128 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))) x)
(* x (- 1/2 (sqrt (/ 1 x))))
(*.f64 (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(fma.f64 (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x #s(literal 1 binary64))
(* -1 (sqrt x))
(neg.f64 (sqrt.f64 x))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(fma.f64 (neg.f64 x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(* -1/8 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/8 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 x)) (+ 1/8 (sqrt (/ 1 (pow x 3))))))
(*.f64 (fma.f64 (-.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) x #s(literal 1/2 binary64)) x)
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) (+ 1/8 (sqrt (/ 1 (pow x 3))))))
(fma.f64 (fma.f64 (-.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* -1/8 x)
(*.f64 #s(literal -1/8 binary64) x)
(* x (- (* 1/2 (/ 1 x)) 1/8))
(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* -1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x)
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(/.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) x)
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(/.f64 (fma.f64 #s(literal 5/128 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) (fma.f64 #s(literal -1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))) x)
(* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(*.f64 (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(fma.f64 (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x #s(literal 1 binary64))
(* (sqrt x) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 x))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(fma.f64 (neg.f64 x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (* 1/2 (/ 1 x))) 1/8))
(*.f64 (fma.f64 (-.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) x #s(literal 1/2 binary64)) x)
(* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) 1/8))
(fma.f64 (fma.f64 (-.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(*.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x)

rewrite210.0ms (6.5%)

Memory

-22.3MiB live, 59.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	100
0	31	100
1	148	100
2	1220	100
0	8579	100

Stop Event

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

Counts

12 → 408

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(sqrt.f64 x)
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x))
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))
#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))

Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(*.f64 (-.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64)) x) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 x))))
(.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 #s(literal 1/2 binary64) x))))
(.f64 (-.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64)) (+.f64 x (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 x))))))
(.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (*.f64 x x)) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (sqrt.f64 x)))))
(.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 #s(literal 1/2 binary64) x)))))))
(.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (*.f64 x x)) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) (pow.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (sqrt.f64 x)) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (.f64 #s(literal -1/2 binary64) (.f64 x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))))))
(.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64))) (pow.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 #s(literal 1/2 binary64) x)))) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (sqrt.f64 x))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (sqrt.f64 x)))) (.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (sqrt.f64 x))) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (sqrt.f64 x))))) (+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (sqrt.f64 x))) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (sqrt.f64 x)))))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 (-.f64 (sqrt.f64 x) (.f64 #s(literal 1/2 binary64) x)) (-.f64 (sqrt.f64 x) (.f64 #s(literal 1/2 binary64) x)))) (+.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (.f64 #s(literal 1/2 binary64) x))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 1/2 binary64) x (neg.f64 (sqrt.f64 x))) (fma.f64 #s(literal 1/2 binary64) x (neg.f64 (sqrt.f64 x))))) (-.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) x (neg.f64 (sqrt.f64 x)))))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 x) (.f64 #s(literal 1/2 binary64) x)) (fma.f64 #s(literal -1 binary64) (sqrt.f64 x) (.f64 #s(literal 1/2 binary64) x)))) (-.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 x) (.f64 #s(literal 1/2 binary64) x))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (sqrt.f64 x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (sqrt.f64 x))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (sqrt.f64 x))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (sqrt.f64 x))) (fma.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (sqrt.f64 x))) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (sqrt.f64 x))) (.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (*.f64 x x)) (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (sqrt.f64 x))) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (sqrt.f64 x)))))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (sqrt.f64 x) (.f64 #s(literal 1/2 binary64) x)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 (-.f64 (sqrt.f64 x) (.f64 #s(literal 1/2 binary64) x)) (-.f64 (sqrt.f64 x) (.f64 #s(literal 1/2 binary64) x)) (.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))))))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal 1/2 binary64) x (neg.f64 (sqrt.f64 x))) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) x (neg.f64 (sqrt.f64 x))) (fma.f64 #s(literal 1/2 binary64) x (neg.f64 (sqrt.f64 x)))) (.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) x (neg.f64 (sqrt.f64 x)))))))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 x) (.f64 #s(literal 1/2 binary64) x)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 x) (.f64 #s(literal 1/2 binary64) x)) (fma.f64 #s(literal -1 binary64) (sqrt.f64 x) (.f64 #s(literal 1/2 binary64) x))) (.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 x) (.f64 #s(literal 1/2 binary64) x))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64)) x)) (neg.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (.f64 x x)))) (neg.f64 (-.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (neg.f64 (+.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64)) (+.f64 x (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 x))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))))) (neg.f64 (neg.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (sqrt.f64 x)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) x)))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (sqrt.f64 x))) (.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (sqrt.f64 x)) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)))) (*.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (sqrt.f64 x)) (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (sqrt.f64 x))))
(/.f64 (-.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64)) x) (-.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (neg.f64 (sqrt.f64 x))))
(/.f64 (-.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64)) x) (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 x)))
(/.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (.f64 x x))) (-.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))))
(/.f64 (-.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (+.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64)) (-.f64 x (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (neg.f64 (sqrt.f64 x))))))
(/.f64 (-.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (+.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64)) (+.f64 x (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 x)))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)))) (neg.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (sqrt.f64 x))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (.f64 #s(literal -1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) x))))))
(/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (sqrt.f64 x)))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (.f64 #s(literal -1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 x)) (-.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 #s(literal 1/2 binary64) x)) (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64)) (+.f64 x (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 x)))) (-.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (.f64 #s(literal -1/2 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))))) (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))) #s(literal 1 binary64)))
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(+.f64 (neg.f64 (sqrt.f64 x)) #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))))
(+.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (*.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64))))
(+.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (*.f64 (neg.f64 (sqrt.f64 x)) #s(literal 1 binary64)))
(+.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (neg.f64 (sqrt.f64 x)))
#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
(.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)))))
(.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))))))
(.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (*.f64 #s(literal -1/2 binary64) x)))))
(.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)))) (.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) #s(literal -1 binary64)))) (+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))) (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) #s(literal -1 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))) (fma.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) #s(literal -1 binary64)) (.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))) (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x)))) (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1 binary64))) (neg.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (.f64 #s(literal -1/2 binary64) x)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (.f64 #s(literal -1/2 binary64) x))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (.f64 #s(literal -1/2 binary64) x))) (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))))
(fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) #s(literal -1 binary64)) (neg.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) #s(literal -1 binary64))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
(-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))) (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) #s(literal -1 binary64)))
(+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))) (neg.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) #s(literal -1 binary64))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))

eval62.0ms (1.9%)

Memory: 51.2MiB live, 51.2MiB allocated
Compiler: Compiled 17 256 to 1 751 computations (89.9% saved)

prune14.0ms (0.4%)

Memory

-56.4MiB live, 20.7MiB allocated

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	518	2	520
Fresh	0	0	0
Picked	0	4	4
Done	0	1	1
Total	518	7	525

Accuracy

100.0%

Counts

525 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
✓	98.4%	(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))
✓	97.4%	(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x))
✓	98.7%	#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
✓	98.4%	#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
	98.4%	#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (-.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))))
	2.7%	#s(approx (- (sqrt (+ 1 x)) (sqrt x)) #s(approx (+ (* (+ (* -1/8 x) 1/2) x) (- 1 (sqrt x))) (.f64 (.f64 x x) #s(literal -1/8 binary64))))

Compiler

Compiled 206 to 120 computations (41.7% saved)

regimes4.0ms (0.1%)

Memory

3.7MiB live, 3.7MiB allocated

Counts

7 → 1

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) #s(approx (+ (* (+ (* -1/8 x) 1/2) x) (- 1 (sqrt x))) (.f64 (.f64 x x) #s(literal -1/8 binary64))))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x))
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (-.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))))
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))

Outputs
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))

Calls

2 calls:

2.0ms	x
2.0ms	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes4.0ms (0.1%)

Memory

3.6MiB live, 3.6MiB allocated

Counts

6 → 1

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) #s(approx (+ (* (+ (* -1/8 x) 1/2) x) (- 1 (sqrt x))) (.f64 (.f64 x x) #s(literal -1/8 binary64))))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x))
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (-.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))))
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))

Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))

Calls

2 calls:

2.0ms	x
2.0ms	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
98.7%	1	`x`
98.7%	1	`(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes4.0ms (0.1%)

Memory

3.5MiB live, 3.5MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) #s(approx (+ (* (+ (* -1/8 x) 1/2) x) (- 1 (sqrt x))) (.f64 (.f64 x x) #s(literal -1/8 binary64))))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x))
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (-.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))))

Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (-.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))))

Calls

2 calls:

2.0ms	x
1.0ms	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
98.4%	1	`x`
98.4%	1	`(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes3.0ms (0.1%)

Memory

3.2MiB live, 3.2MiB allocated

Counts

4 → 1

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) #s(approx (+ (* (+ (* -1/8 x) 1/2) x) (- 1 (sqrt x))) (.f64 (.f64 x x) #s(literal -1/8 binary64))))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x))
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))

Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))

Calls

2 calls:

2.0ms	x
1.0ms	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
98.4%	1	`x`
98.4%	1	`(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes3.0ms (0.1%)

Memory

2.8MiB live, 2.8MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs

#s(approx (- (sqrt (+ 1 x)) (sqrt x)) #s(approx (+ (* (+ (* -1/8 x) 1/2) x) (- 1 (sqrt x))) (*.f64 (*.f64 x x) #s(literal -1/8 binary64))))

(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x))

Outputs
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x))

Calls

2 calls:

1.0ms	x
1.0ms	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
97.4%	1	`(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))`
97.4%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes2.0ms (0.1%)

Memory

2.7MiB live, 2.7MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) #s(approx (+ (* (+ (* -1/8 x) 1/2) x) (- 1 (sqrt x))) (.f64 (.f64 x x) #s(literal -1/8 binary64))))

Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) #s(approx (+ (* (+ (* -1/8 x) 1/2) x) (- 1 (sqrt x))) (.f64 (.f64 x x) #s(literal -1/8 binary64))))

Calls

2 calls:

1.0ms	x
1.0ms	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
2.7%	1	`x`
2.7%	1	`(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify96.0ms (3%)

Memory

14.4MiB live, 14.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	91
1	56	91
2	91	91
3	211	91
4	398	91
5	738	91
6	1656	91
7	2714	91
8	4362	91
9	6769	91

Stop Event

1×	node limit

Calls

Call 1

Inputs
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (-.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))))
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x))
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) #s(approx (+ (* (+ (* -1/8 x) 1/2) x) (- 1 (sqrt x))) (.f64 (.f64 x x) #s(literal -1/8 binary64))))

Outputs
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (-.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))))
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x))
#s(approx (- (sqrt (+ 1 x)) (sqrt x)) #s(approx (+ (* (+ (* -1/8 x) 1/2) x) (- 1 (sqrt x))) (.f64 (.f64 x x) #s(literal -1/8 binary64))))

soundness729.0ms (22.4%)

Memory

7.9MiB live, 7.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	147	618
1	391	557
2	1077	545
3	2768	530
4	5751	530
0	8087	482
0	20	100
0	31	100
1	148	100
2	1220	100
0	8579	100
0	113	451
1	299	399
2	807	395
3	2292	387
4	4919	387
0	8163	351

Stop Event

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

Compiler

Compiled 144 to 81 computations (43.8% saved)

preprocess29.0ms (0.9%)

Memory: 21.7MiB live, 21.7MiB allocated
Compiler: Compiled 196 to 84 computations (57.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

sqrt(1+x) - sqrt(x)

start0.0ms (0%)

analyze2.0ms (0.1%)

sample905.0ms (27.8%)

explain366.0ms (11.2%)

preprocess20.0ms (0.6%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify7.0ms (0.2%)

localize18.0ms (0.6%)

series5.0ms (0.1%)

simplify192.0ms (5.9%)

rewrite144.0ms (4.4%)

eval69.0ms (2.1%)

prune6.0ms (0.2%)

simplify59.0ms (1.8%)

localize40.0ms (1.2%)

series5.0ms (0.1%)

simplify260.0ms (8%)

rewrite210.0ms (6.5%)

eval62.0ms (1.9%)

prune14.0ms (0.4%)

regimes4.0ms (0.1%)

regimes4.0ms (0.1%)

regimes4.0ms (0.1%)

regimes3.0ms (0.1%)

regimes3.0ms (0.1%)

regimes2.0ms (0.1%)

simplify96.0ms (3%)

soundness729.0ms (22.4%)

preprocess29.0ms (0.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	17
1	19	17
2	41	16
3	74	16
4	122	16
5	180	16
6	204	16
7	215	16
0	6	7
0	10	7
1	15	7
2	19	7
3	25	7
4	33	7
5	48	7
6	80	7
7	109	7
8	158	7
9	174	7
10	182	7
0	182	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	15	18
2	19	18
3	25	18
4	33	18
5	48	18
6	80	18
7	109	18
8	158	18
9	174	18
10	182	18
0	182	18

Iter	Nodes	Cost
0	8	17
1	19	17
2	41	16
3	74	16
4	122	16
5	180	16
6	204	16
7	215	16
0	6	7
0	10	7
1	15	7
2	19	7
3	25	7
4	33	7
5	48	7
6	80	7
7	109	7
8	158	7
9	174	7
10	182	7
0	182	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	15	18
2	19	18
3	25	18
4	33	18
5	48	18
6	80	18
7	109	18
8	158	18
9	174	18
10	182	18
0	182	18

Iter	Nodes	Cost
0	8	17
1	19	17
2	41	16
3	74	16
4	122	16
5	180	16
6	204	16
7	215	16
0	6	7
0	10	7
1	15	7
2	19	7
3	25	7
4	33	7
5	48	7
6	80	7
7	109	7
8	158	7
9	174	7
10	182	7
0	182	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	15	18
2	19	18
3	25	18
4	33	18
5	48	18
6	80	18
7	109	18
8	158	18
9	174	18
10	182	18
0	182	18