Metrics for pow(2, 1/4) * sqrt(1 / 2^size)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze1.0ms (0%)

Memory

0.1MiB live, 0.1MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	25%	75%	0%	0%	0%	0
100%	25%	0%	75%	0%	0%	0%	1

Compiler

Compiled 20 to 16 computations (20% saved)

sample1.5s (34.1%)

Memory

141.7MiB live, 835.6MiB allocated

Samples

951.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 640.0ms

ival-pow: 247.0ms (38.6% of total)

ival-div: 155.0ms (24.2% of total)

ival-<=: 72.0ms (11.3% of total)

ival-sqrt: 68.0ms (10.6% of total)

ival-mult: 60.0ms (9.4% of total)

exact: 22.0ms (3.4% of total)

ival-and: 13.0ms (2% of total)

ival-assert: 4.0ms (0.6% of total)

Bogosity

explain221.0ms (5%)

Memory

103.4MiB live, 206.4MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`#s(literal 1 binary64)`
-	-	`(pow.f64 #s(literal 2 binary64) size)`
-	-	`(pow.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) #s(literal 4 binary64)))`
-	-	`size`
-	-	`#s(literal 4 binary64)`
-	-	`(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size))))`
-	-	`#s(literal 2 binary64)`
-	-	`(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size)))`
-	-	`(/.f64 #s(literal 1 binary64) #s(literal 4 binary64))`
-	-	`(/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size))`

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

47.0ms

512×

valid

Compiler

Compiled 92 to 34 computations (63% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

ival-pow: 14.0ms (46.7% of total)

ival-div: 7.0ms (23.4% of total)

ival-sqrt: 4.0ms (13.4% of total)

ival-mult: 3.0ms (10% of total)

ival-true: 1.0ms (3.3% of total)

exact: 1.0ms (3.3% of total)

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

preprocess1.5s (34.8%)

Memory

-188.8MiB live, 5.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	25	23
2	36	23
3	47	23
4	61	23
5	76	23
6	89	23
7	101	23
8	102	23
0	10	10
0	17	10
1	20	10
0	20	10

Stop Event

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

Calls

Call 1

Inputs
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size))))

Outputs

(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size))))

(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))

Compiler

Compiled 12 to 10 computations (16.7% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size))))

Compiler

Compiled 12 to 10 computations (16.7% saved)

simplify3.0ms (0.1%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size)))
cost-diff	0	(pow.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) #s(literal 4 binary64)))
cost-diff	0	(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size))))
cost-diff	2	(/.f64 #s(literal 1 binary64) #s(literal 4 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	32
0	17	32
1	20	32
0	20	32

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size))))
(pow.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) #s(literal 4 binary64)))
#s(literal 2 binary64)
(/.f64 #s(literal 1 binary64) #s(literal 4 binary64))
#s(literal 1 binary64)
#s(literal 4 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size)))
(/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size))
(pow.f64 #s(literal 2 binary64) size)
size

Outputs
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(pow.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) #s(literal 4 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
#s(literal 2 binary64)
(/.f64 #s(literal 1 binary64) #s(literal 4 binary64))
#s(literal 1/4 binary64)
#s(literal 1 binary64)
#s(literal 4 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size)))
(/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size))
(pow.f64 #s(literal 2 binary64) size)
size

localize29.0ms (0.7%)

Memory

10.0MiB live, 10.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(/.f64 #s(literal 1 binary64) #s(literal 4 binary64))
accuracy	0.015625	(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size)))
accuracy	0.01953125	(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size))))
accuracy	0.0234375	(/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size))

Samples

21.0ms

256×

valid

Compiler

Compiled 40 to 12 computations (70% saved)

Precisions

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

ival-pow: 6.0ms (44% of total)

ival-div: 4.0ms (29.3% of total)

ival-mult: 2.0ms (14.7% of total)

ival-sqrt: 2.0ms (14.7% of total)

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

exact: 0.0ms (0% of total)

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

series32.0ms (0.7%)

Memory

16.0MiB live, 16.0MiB allocated

Counts

5 → 14

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) #s(literal 4 binary64))
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size))))
(pow.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) #s(literal 4 binary64)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size)))
(/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size))

Outputs
(pow 2 1/4)
(+ (* -1/2 (* (pow 2 1/4) (* size (log 2)))) (pow 2 1/4))
(+ (* size (+ (* -1/2 (* (pow 2 1/4) (log 2))) (* -1/2 (* (pow 2 1/4) (* size (+ (* -1 (pow (log 2) 2)) (+ (* 1/4 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2))))))))) (pow 2 1/4))
(+ (* size (+ (* -1/2 (* (pow 2 1/4) (log 2))) (* size (+ (* -1/2 (* (pow 2 1/4) (* size (+ (* -1 (* (log 2) (+ (* -1 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2))))) (+ (* -1/2 (pow (log 2) 3)) (+ (* 1/6 (pow (log 2) 3)) (* 1/2 (* (log 2) (+ (* -1 (pow (log 2) 2)) (+ (* 1/4 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2)))))))))))) (* -1/2 (* (pow 2 1/4) (+ (* -1 (pow (log 2) 2)) (+ (* 1/4 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2)))))))))) (pow 2 1/4))
1
(+ 1 (* -1/2 (* size (log 2))))
(+ 1 (* size (+ (* -1/2 (log 2)) (* -1/2 (* size (+ (* -1 (pow (log 2) 2)) (+ (* 1/4 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2)))))))))
(+ 1 (* size (+ (* -1/2 (log 2)) (* size (+ (* -1/2 (* size (+ (* -1 (* (log 2) (+ (* -1 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2))))) (+ (* -1/2 (pow (log 2) 3)) (+ (* 1/6 (pow (log 2) 3)) (* 1/2 (* (log 2) (+ (* -1 (pow (log 2) 2)) (+ (* 1/4 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2))))))))))) (* -1/2 (+ (* -1 (pow (log 2) 2)) (+ (* 1/4 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2))))))))))
(+ 1 (* -1 (* size (log 2))))
(+ 1 (* size (- (* -1 (* size (+ (* -1 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2))))) (log 2))))
(+ 1 (* size (- (* size (- (* -1 (* size (+ (* -1 (* (log 2) (+ (* -1 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2))))) (+ (* -1/2 (pow (log 2) 3)) (* 1/6 (pow (log 2) 3)))))) (+ (* -1 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2))))) (log 2))))
(* (pow 2 1/4) (sqrt (/ 1 (pow 2 size))))
(sqrt (/ 1 (pow 2 size)))
(/ 1 (pow 2 size))

Calls

3 calls:

Time	Variable		Point	Expression
24.0ms	size	@	inf	((/ 1 4) (* (pow 2 (/ 1 4)) (sqrt (/ 1 (pow 2 size)))) (pow 2 (/ 1 4)) (sqrt (/ 1 (pow 2 size))) (/ 1 (pow 2 size)))
6.0ms	size	@	-inf	((/ 1 4) (* (pow 2 (/ 1 4)) (sqrt (/ 1 (pow 2 size)))) (pow 2 (/ 1 4)) (sqrt (/ 1 (pow 2 size))) (/ 1 (pow 2 size)))
2.0ms	size	@	0	((/ 1 4) (* (pow 2 (/ 1 4)) (sqrt (/ 1 (pow 2 size)))) (pow 2 (/ 1 4)) (sqrt (/ 1 (pow 2 size))) (/ 1 (pow 2 size)))

Time

Variable

Point

Expression

24.0ms

size

inf

((/ 1 4) (* (pow 2 (/ 1 4)) (sqrt (/ 1 (pow 2 size)))) (pow 2 (/ 1 4)) (sqrt (/ 1 (pow 2 size))) (/ 1 (pow 2 size)))

6.0ms

size

-inf

((/ 1 4) (* (pow 2 (/ 1 4)) (sqrt (/ 1 (pow 2 size)))) (pow 2 (/ 1 4)) (sqrt (/ 1 (pow 2 size))) (/ 1 (pow 2 size)))

2.0ms

size

((/ 1 4) (* (pow 2 (/ 1 4)) (sqrt (/ 1 (pow 2 size)))) (pow 2 (/ 1 4)) (sqrt (/ 1 (pow 2 size))) (/ 1 (pow 2 size)))

simplify262.0ms (6%)

Memory

-121.2MiB live, 59.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	84	302
1	284	244
2	1256	204
3	7175	202
0	8616	186

Stop Event

1×	iter limit
1×	node limit

Counts

14 → 14

Calls

Call 1

Inputs
(pow 2 1/4)
(+ (* -1/2 (* (pow 2 1/4) (* size (log 2)))) (pow 2 1/4))
(+ (* size (+ (* -1/2 (* (pow 2 1/4) (log 2))) (* -1/2 (* (pow 2 1/4) (* size (+ (* -1 (pow (log 2) 2)) (+ (* 1/4 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2))))))))) (pow 2 1/4))
(+ (* size (+ (* -1/2 (* (pow 2 1/4) (log 2))) (* size (+ (* -1/2 (* (pow 2 1/4) (* size (+ (* -1 (* (log 2) (+ (* -1 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2))))) (+ (* -1/2 (pow (log 2) 3)) (+ (* 1/6 (pow (log 2) 3)) (* 1/2 (* (log 2) (+ (* -1 (pow (log 2) 2)) (+ (* 1/4 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2)))))))))))) (* -1/2 (* (pow 2 1/4) (+ (* -1 (pow (log 2) 2)) (+ (* 1/4 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2)))))))))) (pow 2 1/4))
1
(+ 1 (* -1/2 (* size (log 2))))
(+ 1 (* size (+ (* -1/2 (log 2)) (* -1/2 (* size (+ (* -1 (pow (log 2) 2)) (+ (* 1/4 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2)))))))))
(+ 1 (* size (+ (* -1/2 (log 2)) (* size (+ (* -1/2 (* size (+ (* -1 (* (log 2) (+ (* -1 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2))))) (+ (* -1/2 (pow (log 2) 3)) (+ (* 1/6 (pow (log 2) 3)) (* 1/2 (* (log 2) (+ (* -1 (pow (log 2) 2)) (+ (* 1/4 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2))))))))))) (* -1/2 (+ (* -1 (pow (log 2) 2)) (+ (* 1/4 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2))))))))))
(+ 1 (* -1 (* size (log 2))))
(+ 1 (* size (- (* -1 (* size (+ (* -1 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2))))) (log 2))))
(+ 1 (* size (- (* size (- (* -1 (* size (+ (* -1 (* (log 2) (+ (* -1 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2))))) (+ (* -1/2 (pow (log 2) 3)) (* 1/6 (pow (log 2) 3)))))) (+ (* -1 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2))))) (log 2))))
(* (pow 2 1/4) (sqrt (/ 1 (pow 2 size))))
(sqrt (/ 1 (pow 2 size)))
(/ 1 (pow 2 size))

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

rewrite75.0ms (1.7%)

Memory

10.2MiB live, 10.2MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	25
0	17	22
1	47	21
2	163	18
0	833	18

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

5 → 136

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) #s(literal 4 binary64))
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size))))
(pow.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) #s(literal 4 binary64)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size)))
(/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size))

Outputs
#s(literal 1/4 binary64)
(.f64 (.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 (neg.f64 size) #s(literal 1/2 binary64) #s(literal 1/8 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)))
(.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 #s(literal 1/2 binary64) size) #s(literal 1/4 binary64))) (pow.f64 (pow.f64 #s(literal 1/2 binary64) size) #s(literal 1/4 binary64)))
(.f64 (.f64 (pow.f64 (pow.f64 #s(literal 1/2 binary64) size) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64))) (*.f64 (pow.f64 (pow.f64 #s(literal 1/2 binary64) size) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64))))
(.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (pow.f64 (pow.f64 #s(literal 1/2 binary64) size) #s(literal 1/4 binary64))) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (pow.f64 (pow.f64 #s(literal 1/2 binary64) size) #s(literal 1/4 binary64))))
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eval16.0ms (0.4%)

Memory: 13.2MiB live, 13.2MiB allocated
Compiler: Compiled 2 381 to 493 computations (79.3% saved)

prune2.0ms (0%)

Memory

5.7MiB live, 5.7MiB allocated

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	148	2	150
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	149	2	151

Accuracy

100.0%

Counts

151 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(pow.f64 #s(literal 2 binary64) (fma.f64 (neg.f64 size) #s(literal 1/2 binary64) #s(literal 1/4 binary64)))
▶	97.5%	#s(approx (* (pow 2 (/ 1 4)) (sqrt (/ 1 (pow 2 size)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))

Status

Accuracy

Program

▶

100.0%

(pow.f64 #s(literal 2 binary64) (fma.f64 (neg.f64 size) #s(literal 1/2 binary64) #s(literal 1/4 binary64)))

▶

97.5%

#s(approx (* (pow 2 (/ 1 4)) (sqrt (/ 1 (pow 2 size)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))

Compiler

Compiled 23 to 21 computations (8.7% saved)

simplify5.0ms (0.1%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

New	Metric	Score
cost-diff	0	(neg.f64 size)
cost-diff	0	(pow.f64 #s(literal 2 binary64) (fma.f64 (neg.f64 size) #s(literal 1/2 binary64) #s(literal 1/4 binary64)))
cost-diff	1	(fma.f64 (neg.f64 size) #s(literal 1/2 binary64) #s(literal 1/4 binary64))
cost-diff	0	(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
cost-diff	0	#s(approx (* (pow 2 (/ 1 4)) (sqrt (/ 1 (pow 2 size)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	37
0	22	37
1	32	37
2	44	37
3	54	37
4	63	37
5	75	37
6	92	37
7	100	37
8	103	37
0	103	35

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (* (pow 2 (/ 1 4)) (sqrt (/ 1 (pow 2 size)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
#s(literal 2 binary64)
#s(literal 1/4 binary64)
(pow.f64 #s(literal 2 binary64) (fma.f64 (neg.f64 size) #s(literal 1/2 binary64) #s(literal 1/4 binary64)))
#s(literal 2 binary64)
(fma.f64 (neg.f64 size) #s(literal 1/2 binary64) #s(literal 1/4 binary64))
(neg.f64 size)
size
#s(literal 1/2 binary64)
#s(literal 1/4 binary64)

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

localize45.0ms (1%)

Memory

21.1MiB live, 21.1MiB allocated

Localize:

Found 5 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 (neg.f64 size) #s(literal 1/2 binary64) #s(literal 1/4 binary64))
accuracy	0.0	(pow.f64 #s(literal 2 binary64) (fma.f64 (neg.f64 size) #s(literal 1/2 binary64) #s(literal 1/4 binary64)))
accuracy	0.0	(neg.f64 size)
accuracy	0.0	(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
accuracy	1.5766853064850765	#s(approx (* (pow 2 (/ 1 4)) (sqrt (/ 1 (pow 2 size)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))

Samples

35.0ms

256×

valid

Compiler

Compiled 39 to 19 computations (51.3% saved)

Precisions

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

ival-pow: 12.0ms (45.7% of total)

ival-div: 4.0ms (15.2% of total)

ival-mult: 4.0ms (15.2% of total)

ival-sqrt: 2.0ms (7.6% of total)

exact: 2.0ms (7.6% of total)

ival-add: 1.0ms (3.8% of total)

ival-neg: 1.0ms (3.8% of total)

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

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

series15.0ms (0.3%)

Memory

11.7MiB live, 11.7MiB allocated

Counts

5 → 15

Calls

Call 1

Inputs
#s(approx (* (pow 2 (/ 1 4)) (sqrt (/ 1 (pow 2 size)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
(fma.f64 (neg.f64 size) #s(literal 1/2 binary64) #s(literal 1/4 binary64))
(pow.f64 #s(literal 2 binary64) (fma.f64 (neg.f64 size) #s(literal 1/2 binary64) #s(literal 1/4 binary64)))
(neg.f64 size)

Outputs
(pow 2 1/4)
(+ (* -1/2 (* (pow 2 1/4) (* size (log 2)))) (pow 2 1/4))
(+ (* size (+ (* -1/2 (* (pow 2 1/4) (log 2))) (* -1/2 (* (pow 2 1/4) (* size (+ (* -1 (pow (log 2) 2)) (+ (* 1/4 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2))))))))) (pow 2 1/4))
(+ (* size (+ (* -1/2 (* (pow 2 1/4) (log 2))) (* size (+ (* -1/2 (* (pow 2 1/4) (* size (+ (* -1 (* (log 2) (+ (* -1 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2))))) (+ (* -1/2 (pow (log 2) 3)) (+ (* 1/6 (pow (log 2) 3)) (* 1/2 (* (log 2) (+ (* -1 (pow (log 2) 2)) (+ (* 1/4 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2)))))))))))) (* -1/2 (* (pow 2 1/4) (+ (* -1 (pow (log 2) 2)) (+ (* 1/4 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2)))))))))) (pow 2 1/4))
1/4
(+ 1/4 (* -1/2 size))
(+ (* size (+ (* -1/2 (* (pow 2 1/4) (log 2))) (* 1/8 (* (pow 2 1/4) (* size (pow (log 2) 2)))))) (pow 2 1/4))
(+ (* size (+ (* -1/2 (* (pow 2 1/4) (log 2))) (* size (+ (* -1/48 (* (pow 2 1/4) (* size (pow (log 2) 3)))) (* 1/8 (* (pow 2 1/4) (pow (log 2) 2))))))) (pow 2 1/4))
(* -1 size)
(* (pow 2 1/4) (sqrt (/ 1 (pow 2 size))))
(* -1/2 size)
(* size (- (* 1/4 (/ 1 size)) 1/2))
(exp (* (log 2) (- 1/4 (* 1/2 size))))
(* -1 (* size (- 1/2 (* 1/4 (/ 1 size)))))
(exp (* (log 2) (+ 1/4 (* -1/2 size))))

Calls

3 calls:

Time	Variable		Point	Expression
7.0ms	size	@	inf	((* (pow 2 (/ 1 4)) (sqrt (/ 1 (pow 2 size)))) (pow 2 1/4) (+ (* (neg size) 1/2) 1/4) (pow 2 (+ (* (neg size) 1/2) 1/4)) (neg size))
6.0ms	size	@	-inf	((* (pow 2 (/ 1 4)) (sqrt (/ 1 (pow 2 size)))) (pow 2 1/4) (+ (* (neg size) 1/2) 1/4) (pow 2 (+ (* (neg size) 1/2) 1/4)) (neg size))
1.0ms	size	@	0	((* (pow 2 (/ 1 4)) (sqrt (/ 1 (pow 2 size)))) (pow 2 1/4) (+ (* (neg size) 1/2) 1/4) (pow 2 (+ (* (neg size) 1/2) 1/4)) (neg size))

Time

Variable

Point

Expression

7.0ms

size

inf

((* (pow 2 (/ 1 4)) (sqrt (/ 1 (pow 2 size)))) (pow 2 1/4) (+ (* (neg size) 1/2) 1/4) (pow 2 (+ (* (neg size) 1/2) 1/4)) (neg size))

6.0ms

size

-inf

((* (pow 2 (/ 1 4)) (sqrt (/ 1 (pow 2 size)))) (pow 2 1/4) (+ (* (neg size) 1/2) 1/4) (pow 2 (+ (* (neg size) 1/2) 1/4)) (neg size))

1.0ms

size

((* (pow 2 (/ 1 4)) (sqrt (/ 1 (pow 2 size)))) (pow 2 1/4) (+ (* (neg size) 1/2) 1/4) (pow 2 (+ (* (neg size) 1/2) 1/4)) (neg size))

simplify157.0ms (3.6%)

Memory

-33.5MiB live, 43.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	88	252
1	278	205
2	1063	192
3	5105	183
0	8242	166

Stop Event

1×	iter limit
1×	node limit

Counts

15 → 15

Calls

Call 1

Inputs
(pow 2 1/4)
(+ (* -1/2 (* (pow 2 1/4) (* size (log 2)))) (pow 2 1/4))
(+ (* size (+ (* -1/2 (* (pow 2 1/4) (log 2))) (* -1/2 (* (pow 2 1/4) (* size (+ (* -1 (pow (log 2) 2)) (+ (* 1/4 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2))))))))) (pow 2 1/4))
(+ (* size (+ (* -1/2 (* (pow 2 1/4) (log 2))) (* size (+ (* -1/2 (* (pow 2 1/4) (* size (+ (* -1 (* (log 2) (+ (* -1 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2))))) (+ (* -1/2 (pow (log 2) 3)) (+ (* 1/6 (pow (log 2) 3)) (* 1/2 (* (log 2) (+ (* -1 (pow (log 2) 2)) (+ (* 1/4 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2)))))))))))) (* -1/2 (* (pow 2 1/4) (+ (* -1 (pow (log 2) 2)) (+ (* 1/4 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2)))))))))) (pow 2 1/4))
1/4
(+ 1/4 (* -1/2 size))
(+ (* size (+ (* -1/2 (* (pow 2 1/4) (log 2))) (* 1/8 (* (pow 2 1/4) (* size (pow (log 2) 2)))))) (pow 2 1/4))
(+ (* size (+ (* -1/2 (* (pow 2 1/4) (log 2))) (* size (+ (* -1/48 (* (pow 2 1/4) (* size (pow (log 2) 3)))) (* 1/8 (* (pow 2 1/4) (pow (log 2) 2))))))) (pow 2 1/4))
(* -1 size)
(* (pow 2 1/4) (sqrt (/ 1 (pow 2 size))))
(* -1/2 size)
(* size (- (* 1/4 (/ 1 size)) 1/2))
(exp (* (log 2) (- 1/4 (* 1/2 size))))
(* -1 (* size (- 1/2 (* 1/4 (/ 1 size)))))
(exp (* (log 2) (+ 1/4 (* -1/2 size))))

Outputs
(pow 2 1/4)
(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
(+ (* -1/2 (* (pow 2 1/4) (* size (log 2)))) (pow 2 1/4))
(.f64 (fma.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)) size #s(literal 1 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(+ (* size (+ (* -1/2 (* (pow 2 1/4) (log 2))) (* -1/2 (* (pow 2 1/4) (* size (+ (* -1 (pow (log 2) 2)) (+ (* 1/4 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2))))))))) (pow 2 1/4))
(fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) size) (fma.f64 (*.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) size) #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(+ (* size (+ (* -1/2 (* (pow 2 1/4) (log 2))) (* size (+ (* -1/2 (* (pow 2 1/4) (* size (+ (* -1 (* (log 2) (+ (* -1 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2))))) (+ (* -1/2 (pow (log 2) 3)) (+ (* 1/6 (pow (log 2) 3)) (* 1/2 (* (log 2) (+ (* -1 (pow (log 2) 2)) (+ (* 1/4 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2)))))))))))) (* -1/2 (* (pow 2 1/4) (+ (* -1 (pow (log 2) 2)) (+ (* 1/4 (pow (log 2) 2)) (* 1/2 (pow (log 2) 2)))))))))) (pow 2 1/4))
(fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (fma.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)) (.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)) #s(literal 3/8 binary64))) size) size (fma.f64 (*.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) size) #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64))))) size (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
1/4
#s(literal 1/4 binary64)
(+ 1/4 (* -1/2 size))
(fma.f64 #s(literal -1/2 binary64) size #s(literal 1/4 binary64))
(+ (* size (+ (* -1/2 (* (pow 2 1/4) (log 2))) (* 1/8 (* (pow 2 1/4) (* size (pow (log 2) 2)))))) (pow 2 1/4))
(fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) size) (fma.f64 (*.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) size) #s(literal -1/4 binary64) (log.f64 #s(literal 2 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(+ (* size (+ (* -1/2 (* (pow 2 1/4) (log 2))) (* size (+ (* -1/48 (* (pow 2 1/4) (* size (pow (log 2) 3)))) (* 1/8 (* (pow 2 1/4) (pow (log 2) 2))))))) (pow 2 1/4))
(fma.f64 (fma.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)) size #s(literal 1 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 (.f64 size size) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (fma.f64 #s(literal 1/8 binary64) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 (.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)) size) #s(literal -1/48 binary64))))))
(* -1 size)
(neg.f64 size)
(* (pow 2 1/4) (sqrt (/ 1 (pow 2 size))))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size))))
(* -1/2 size)
(*.f64 #s(literal -1/2 binary64) size)
(* size (- (* 1/4 (/ 1 size)) 1/2))
(fma.f64 #s(literal -1/2 binary64) size #s(literal 1/4 binary64))
(exp (* (log 2) (- 1/4 (* 1/2 size))))
(pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) size #s(literal 1/4 binary64)))
(* -1 (* size (- 1/2 (* 1/4 (/ 1 size)))))
(fma.f64 #s(literal -1/2 binary64) size #s(literal 1/4 binary64))
(exp (* (log 2) (+ 1/4 (* -1/2 size))))
(pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) size #s(literal 1/4 binary64)))

rewrite89.0ms (2%)

Memory

17.9MiB live, 17.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	31
0	22	30
1	78	28
2	393	28
0	3178	25

Stop Event

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

Counts

5 → 150

Calls

Call 1

Inputs
#s(approx (* (pow 2 (/ 1 4)) (sqrt (/ 1 (pow 2 size)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
(fma.f64 (neg.f64 size) #s(literal 1/2 binary64) #s(literal 1/4 binary64))
(pow.f64 #s(literal 2 binary64) (fma.f64 (neg.f64 size) #s(literal 1/2 binary64) #s(literal 1/4 binary64)))
(neg.f64 size)

Outputs
#s(approx (* (pow 2 (/ 1 4)) (sqrt (/ 1 (pow 2 size)))) (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)))
(.f64 (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)))
(*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64))))
(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)))
(pow.f64 (exp.f64 #s(literal 1/4 binary64)) (log.f64 #s(literal 2 binary64)))
(pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
(exp.f64 (fma.f64 #s(literal 1/8 binary64) (log.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/8 binary64) (log.f64 #s(literal 2 binary64)))))
(exp.f64 (.f64 (.f64 #s(literal 1/8 binary64) (log.f64 #s(literal 2 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 4 binary64)) #s(literal 1/8 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(.f64 (/.f64 (fma.f64 (.f64 size size) #s(literal 1/4 binary64) #s(literal -1/16 binary64)) (fma.f64 #s(literal -1/8 binary64) (pow.f64 size #s(literal 3 binary64)) #s(literal -1/64 binary64))) (fma.f64 (*.f64 size size) #s(literal 1/4 binary64) (fma.f64 #s(literal -1/8 binary64) size #s(literal 1/16 binary64))))
(.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 size #s(literal 3 binary64)) #s(literal 1/64 binary64)) (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) size) #s(literal 4 binary64)) (pow.f64 (fma.f64 size #s(literal 1/8 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)))) (-.f64 (fma.f64 (.f64 size size) #s(literal 1/4 binary64) #s(literal -1/16 binary64)) (.f64 size #s(literal 1/8 binary64))))
(.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 size #s(literal 3 binary64)) #s(literal 1/64 binary64)) (+.f64 (pow.f64 (fma.f64 size #s(literal 1/8 binary64) #s(literal 1/16 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) size) #s(literal 6 binary64)))) (fma.f64 (fma.f64 size #s(literal 1/8 binary64) #s(literal 1/16 binary64)) (-.f64 (fma.f64 size #s(literal 1/8 binary64) #s(literal 1/16 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) size) #s(literal 2 binary64))) (pow.f64 (.f64 #s(literal -1/2 binary64) size) #s(literal 4 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 size size) #s(literal 1/4 binary64) #s(literal -1/16 binary64)) (fma.f64 (*.f64 size size) #s(literal 1/4 binary64) #s(literal -1/16 binary64))) (fma.f64 #s(literal -1/2 binary64) size #s(literal 1/4 binary64)))
(.f64 (-.f64 #s(literal 1/16 binary64) (pow.f64 (.f64 #s(literal -1/2 binary64) size) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/2 binary64) size))))
(.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) size #s(literal -1/4 binary64)) #s(literal -1 binary64)) (fma.f64 (.f64 size size) #s(literal 1/4 binary64) #s(literal -1/16 binary64)))
(.f64 (pow.f64 (fma.f64 (.f64 size size) #s(literal 1/4 binary64) (fma.f64 size #s(literal 1/8 binary64) #s(literal 1/16 binary64))) #s(literal -1 binary64)) (fma.f64 #s(literal -1/8 binary64) (pow.f64 size #s(literal 3 binary64)) #s(literal 1/64 binary64)))
(.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) size) size #s(literal 1/16 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) size #s(literal 1/4 binary64))))
(.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 size #s(literal 3 binary64)) #s(literal 1/64 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 size size) #s(literal 1/4 binary64) (fma.f64 size #s(literal 1/8 binary64) #s(literal 1/16 binary64))))))
(.f64 (fma.f64 (.f64 size size) #s(literal 1/4 binary64) #s(literal -1/16 binary64)) (pow.f64 (fma.f64 #s(literal -1/2 binary64) size #s(literal -1/4 binary64)) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 size #s(literal 3 binary64)) #s(literal 1/64 binary64)) (pow.f64 (fma.f64 (.f64 size size) #s(literal 1/4 binary64) (fma.f64 size #s(literal 1/8 binary64) #s(literal 1/16 binary64))) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) size #s(literal 1/4 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) size #s(literal 1/4 binary64))) #s(literal -1 binary64))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) size) #s(literal 4 binary64)) #s(literal 1/256 binary64)) (pow.f64 (fma.f64 #s(literal -1/2 binary64) size #s(literal -1/4 binary64)) #s(literal -1 binary64))) (fma.f64 (*.f64 size size) #s(literal 1/4 binary64) #s(literal 1/16 binary64)))
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(pow.f64 (pow.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/8 binary64) (*.f64 size #s(literal 1/4 binary64)))) #s(literal 2 binary64))
(pow.f64 #s(literal 4 binary64) (-.f64 #s(literal 1/8 binary64) (*.f64 size #s(literal 1/4 binary64))))
(pow.f64 #s(literal 2 binary64) (*.f64 (fma.f64 #s(literal -1/2 binary64) size #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) size #s(literal 1/4 binary64)))
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))) (sqrt.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) size))))
(/.f64 (*.f64 #s(literal -1 binary64) (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))) (neg.f64 (pow.f64 (sqrt.f64 #s(literal 2 binary64)) size)))
(/.f64 (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) size))))
(/.f64 (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal -1 binary64)) (neg.f64 (pow.f64 (sqrt.f64 #s(literal 2 binary64)) size)))
(/.f64 (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (pow.f64 (pow.f64 #s(literal 2 binary64) size) #s(literal 1/4 binary64))) (pow.f64 (pow.f64 #s(literal 2 binary64) size) #s(literal 1/4 binary64)))
(/.f64 (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))) (neg.f64 (pow.f64 (sqrt.f64 #s(literal 2 binary64)) size)))
(/.f64 (pow.f64 #s(literal 2 binary64) (.f64 (.f64 size size) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/2 binary64) size #s(literal -1/4 binary64))))) (pow.f64 #s(literal 2 binary64) (/.f64 #s(literal -1/16 binary64) (fma.f64 #s(literal 1/2 binary64) size #s(literal 1/4 binary64)))))
(/.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) size))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sqrt.f64 #s(literal 2 binary64)) size) (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))))
(exp.f64 (-.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (*.f64 (log.f64 #s(literal 2 binary64)) size) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (-.f64 #s(literal 1/8 binary64) (.f64 size #s(literal 1/4 binary64))) (log.f64 #s(literal 2 binary64)) (.f64 (-.f64 #s(literal 1/8 binary64) (*.f64 size #s(literal 1/4 binary64))) (log.f64 #s(literal 2 binary64)))))
(exp.f64 (.f64 (.f64 (-.f64 #s(literal 1/8 binary64) (*.f64 size #s(literal 1/4 binary64))) (log.f64 #s(literal 2 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/8 binary64) (.f64 size #s(literal 1/4 binary64))))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 #s(literal 4 binary64)) (-.f64 #s(literal 1/8 binary64) (.f64 size #s(literal 1/4 binary64)))))
(exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) (.f64 (fma.f64 #s(literal -1/2 binary64) size #s(literal 1/4 binary64)) #s(literal 1 binary64))))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) size #s(literal 1/4 binary64))))
(.f64 (neg.f64 (.f64 size size)) (/.f64 #s(literal 1 binary64) size))
(.f64 (pow.f64 (neg.f64 size) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (.f64 size size)))
(*.f64 #s(literal -1 binary64) size)
(*.f64 size #s(literal -1 binary64))
(/.f64 (neg.f64 (neg.f64 (*.f64 size size))) (neg.f64 size))
(/.f64 (neg.f64 (pow.f64 (neg.f64 size) #s(literal 3 binary64))) (neg.f64 (*.f64 size size)))
(/.f64 (neg.f64 (*.f64 size size)) (-.f64 #s(literal 0 binary64) (neg.f64 size)))
(/.f64 (neg.f64 (*.f64 size size)) size)
(/.f64 (pow.f64 (neg.f64 size) #s(literal 3 binary64)) (+.f64 #s(literal 0 binary64) (-.f64 (.f64 size size) (.f64 #s(literal 0 binary64) (neg.f64 size)))))
(/.f64 (pow.f64 (neg.f64 size) #s(literal 3 binary64)) (*.f64 size size))
(/.f64 #s(literal 1 binary64) (/.f64 size (neg.f64 (*.f64 size size))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 size size) (pow.f64 (neg.f64 size) #s(literal 3 binary64))))
(neg.f64 size)
(fma.f64 (neg.f64 (*.f64 size size)) (/.f64 #s(literal 1 binary64) size) #s(literal 0 binary64))
(fma.f64 (pow.f64 (neg.f64 size) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 size size)) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) size #s(literal 0 binary64))
(fma.f64 size #s(literal -1 binary64) #s(literal 0 binary64))
(-.f64 (/.f64 #s(literal 0 binary64) size) (/.f64 (*.f64 size size) size))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 size size)) (/.f64 (pow.f64 size #s(literal 3 binary64)) (.f64 size size)))
(-.f64 #s(literal 0 binary64) size)
(+.f64 #s(literal 0 binary64) (neg.f64 size))
(+.f64 (neg.f64 size) #s(literal 0 binary64))

eval20.0ms (0.4%)

Memory: 14.9MiB live, 14.9MiB allocated
Compiler: Compiled 2 824 to 553 computations (80.4% saved)

prune4.0ms (0.1%)

Memory

7.2MiB live, 7.2MiB allocated

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	160	2	162
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	161	3	164

Accuracy

100.0%

Counts

164 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

100.0%

(pow.f64 #s(literal 2 binary64) (fma.f64 size #s(literal -1/2 binary64) #s(literal 1/4 binary64)))

22.5%

(pow.f64 #s(literal 2 binary64) #s(approx (+ (* (neg size) 1/2) 1/4) (*.f64 #s(literal -1/2 binary64) size)))

✓

97.5%

#s(approx (* (pow 2 (/ 1 4)) (sqrt (/ 1 (pow 2 size)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))

Compiler

Compiled 87 to 68 computations (21.8% saved)

regimes19.0ms (0.4%)

Memory

-71.3MiB live, 7.1MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
#s(approx (* (pow 2 (/ 1 4)) (sqrt (/ 1 (pow 2 size)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(pow.f64 #s(literal 2 binary64) #s(approx (+ (* (neg size) 1/2) 1/4) (*.f64 #s(literal -1/2 binary64) size)))
(pow.f64 #s(literal 2 binary64) (fma.f64 size #s(literal -1/2 binary64) #s(literal 1/4 binary64)))
(pow.f64 #s(literal 2 binary64) (fma.f64 (neg.f64 size) #s(literal 1/2 binary64) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size))))

Outputs
(pow.f64 #s(literal 2 binary64) (fma.f64 size #s(literal -1/2 binary64) #s(literal 1/4 binary64)))

Calls

5 calls:

13.0ms	(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size))))
2.0ms	size
1.0ms	(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size)))
1.0ms	(pow.f64 #s(literal 2 binary64) size)
1.0ms	(/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size))

Results

Accuracy	Segments	Branch
100.0%	1	`size`
100.0%	1	`(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size))))`
100.0%	1	`(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size)))`
100.0%	1	`(/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size))`
100.0%	1	`(pow.f64 #s(literal 2 binary64) size)`

Compiler

Compiled 27 to 25 computations (7.4% saved)

regimes6.0ms (0.1%)

Memory

5.8MiB live, 5.8MiB allocated

Accuracy

Total -48.0b remaining (-3046.7%)

Threshold costs -48b (-3046.7%)

Counts

2 → 1

Calls

Call 1

Inputs

#s(approx (* (pow 2 (/ 1 4)) (sqrt (/ 1 (pow 2 size)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))

(pow.f64 #s(literal 2 binary64) #s(approx (+ (* (neg size) 1/2) 1/4) (*.f64 #s(literal -1/2 binary64) size)))

Outputs
#s(approx (* (pow 2 (/ 1 4)) (sqrt (/ 1 (pow 2 size)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))

Calls

5 calls:

1.0ms	size
1.0ms	(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size))))
1.0ms	(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size)))
1.0ms	(pow.f64 #s(literal 2 binary64) size)
1.0ms	(/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size))

Results

Accuracy	Segments	Branch
97.5%	1	`size`
97.5%	1	`(*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size))))`
97.5%	1	`(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size)))`
97.5%	1	`(/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) size))`
97.5%	1	`(pow.f64 #s(literal 2 binary64) size)`

Compiler

Compiled 27 to 25 computations (7.4% saved)

simplify10.0ms (0.2%)

Memory

5.2MiB live, 5.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	20
1	19	20

Stop Event

1×

saturated

Calls

Call 1

Inputs

(pow.f64 #s(literal 2 binary64) (fma.f64 size #s(literal -1/2 binary64) #s(literal 1/4 binary64)))

#s(approx (* (pow 2 (/ 1 4)) (sqrt (/ 1 (pow 2 size)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))

Outputs

(pow.f64 #s(literal 2 binary64) (fma.f64 size #s(literal -1/2 binary64) #s(literal 1/4 binary64)))

#s(approx (* (pow 2 (/ 1 4)) (sqrt (/ 1 (pow 2 size)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))

soundness339.0ms (7.7%)

Memory

4.5MiB live, 4.5MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	31
0	22	30
1	78	28
2	393	28
0	3178	25
0	84	302
1	284	244
2	1256	204
3	7175	202
0	8616	186
0	10	25
0	17	22
1	47	21
2	163	18
0	833	18

Stop Event

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

Compiler

Compiled 66 to 48 computations (27.3% saved)

preprocess18.0ms (0.4%)

Memory: 11.3MiB live, 11.3MiB allocated
Compiler: Compiled 68 to 54 computations (20.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	13	23
1	25	23
2	36	23
3	47	23
4	61	23
5	76	23
6	89	23
7	101	23
8	102	23
0	10	10
0	17	10
1	20	10
0	20	10

Iter	Nodes	Cost
0	13	23
1	25	23
2	36	23
3	47	23
4	61	23
5	76	23
6	89	23
7	101	23
8	102	23
0	10	10
0	17	10
1	20	10
0	20	10

start0.0ms (0%)

analyze1.0ms (0%)

sample1.5s (34.1%)

explain221.0ms (5%)

preprocess1.5s (34.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0.1%)

localize29.0ms (0.7%)

series32.0ms (0.7%)

simplify262.0ms (6%)

rewrite75.0ms (1.7%)

eval16.0ms (0.4%)

prune2.0ms (0%)

simplify5.0ms (0.1%)

localize45.0ms (1%)

series15.0ms (0.3%)

simplify157.0ms (3.6%)

rewrite89.0ms (2%)

eval20.0ms (0.4%)

prune4.0ms (0.1%)

regimes19.0ms (0.4%)

regimes6.0ms (0.1%)

simplify10.0ms (0.2%)

soundness339.0ms (7.7%)

preprocess18.0ms (0.4%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	13	23
1	25	23
2	36	23
3	47	23
4	61	23
5	76	23
6	89	23
7	101	23
8	102	23
0	10	10
0	17	10
1	20	10
0	20	10