Metrics for sqrt C (should all be same)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
100%	100%	0%	0%	0%	0%	0%	2

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample638.0ms (38.6%)

Memory

23.2MiB live, 761.5MiB allocated; 159ms collecting garbage

Samples

406.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 247.0ms

ival-mult: 180.0ms (72.8% of total)

ival-sqrt: 52.0ms (21% of total)

ival-true: 5.0ms (2% of total)

exact: 5.0ms (2% of total)

ival-assert: 3.0ms (1.2% of total)

adjust: 2.0ms (0.8% of total)

Bogosity

explain59.0ms (3.6%)

Memory

-9.0MiB live, 89.4MiB allocated; 13ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
117	-	4	(-5.816655712408625e-158)	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`(.f64 #s(literal 2 binary64) (.f64 x x))`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`	oflow-rescue	67	0
↳	`(.f64 #s(literal 2 binary64) (.f64 x x))`	overflow	67
↳	`(*.f64 x x)`	overflow	67
`sqrt.f64`	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`	uflow-rescue	46	0
↳	`(.f64 #s(literal 2 binary64) (.f64 x x))`	underflow	46
↳	`(*.f64 x x)`	underflow	46

Confusion

	Predicted +	Predicted -
+	113	4
-	0	139

Precision

1.0

Recall

0.9658119658119658

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	113	0	4
-	0	0	139

Precision?

1.0

Recall?

0.9658119658119658

Freqs

test

number	freq
0	143
1	113

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

24.0ms

512×

valid

Compiler

Compiled 42 to 19 computations (54.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-mult: 7.0ms (62.3% of total)

ival-sqrt: 3.0ms (26.7% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

preprocess17.0ms (1.1%)

Memory

19.4MiB live, 19.4MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	22	13
2	83	13
3	131	13
4	223	13
5	249	13
6	269	13
0	5	6
0	8	6
1	18	6
2	56	6
3	122	6
4	187	6
5	223	6
6	246	6
7	266	6
0	266	3

Stop Event

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

Calls

Call 1

Inputs
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Outputs
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(hypot.f64 x x)

Symmetry

(abs x)

Compiler

Compiled 6 to 5 computations (16.7% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	58.3%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify6.0ms (0.4%)

Memory

7.5MiB live, 7.5MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 x x))
cost-diff	3	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	16
0	8	16
1	18	16
2	56	16
3	122	16
4	187	16
5	223	16
6	246	16
7	266	16
0	266	13

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(.f64 #s(literal 2 binary64) (.f64 x x))
#s(literal 2 binary64)
(*.f64 x x)
x

Outputs
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(hypot.f64 x x)
(.f64 #s(literal 2 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 x x)
x

localize18.0ms (1.1%)

Memory

-23.4MiB live, 21.8MiB allocated; 5ms collecting garbage

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.0078125	(.f64 #s(literal 2 binary64) (.f64 x x))
accuracy	26.664966668699904	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Samples

10.0ms

256×

valid

Compiler

Compiled 18 to 7 computations (61.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-mult: 3.0ms (55.8% of total)

ival-sqrt: 2.0ms (37.2% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

series3.0ms (0.2%)

Memory

4.9MiB live, 4.9MiB allocated; 0ms collecting garbage

Counts

3 → 4

Calls

Call 1

Inputs
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(.f64 #s(literal 2 binary64) (.f64 x x))
(*.f64 x x)

Outputs
(* x (sqrt 2))
(* 2 (pow x 2))
(pow x 2)
(* -1 (* x (sqrt 2)))

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	((sqrt (* 2 (* x x))) (* 2 (* x x)) (* x x))
1.0ms	x	@	0	((sqrt (* 2 (* x x))) (* 2 (* x x)) (* x x))
1.0ms	x	@	-inf	((sqrt (* 2 (* x x))) (* 2 (* x x)) (* x x))

simplify8.0ms (0.5%)

Memory

9.2MiB live, 9.2MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	18	17
2	43	17
3	92	17
4	228	17
5	437	17
6	485	17
0	485	17

Stop Event

1×	iter limit
1×	saturated

Counts

4 → 4

Calls

Call 1

Inputs
(* x (sqrt 2))
(* 2 (pow x 2))
(pow x 2)
(* -1 (* x (sqrt 2)))

Outputs
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* 2 (pow x 2))
(.f64 (.f64 #s(literal 2 binary64) x) x)
(pow x 2)
(*.f64 x x)
(* -1 (* x (sqrt 2)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))

rewrite37.0ms (2.3%)

Memory

-7.9MiB live, 37.3MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	5	14
0	8	13
1	24	13
2	102	5
0	777	5

Stop Event

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

Counts

3 → 15

Calls

Call 1

Inputs
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(.f64 #s(literal 2 binary64) (.f64 x x))
(*.f64 x x)

Outputs
#s(literal 0 binary64)
#s(literal 0 binary64)
(.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) x))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(neg.f64 (*.f64 x x))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))

eval2.0ms (0.1%)

Memory: 3.7MiB live, 3.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 155 to 71 computations (54.2% saved)

prune2.0ms (0.1%)

Memory

3.4MiB live, 3.4MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	14	4	18
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	14	5	19

Accuracy

99.6%

Counts

19 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	58.1%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x))))
✓	58.3%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
▶	34.8%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (pow.f64 x #s(literal 4 binary64)))))
▶	99.3%	#s(approx (sqrt (* 2 (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
▶	3.6%	#s(literal 0 binary64)

Compiler

Compiled 35 to 30 computations (14.3% saved)

simplify13.0ms (0.8%)

Memory

20.5MiB live, 20.5MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x (sqrt.f64 x))
cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x)))
cost-diff	3	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x))))
cost-diff	4	(.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))
cost-diff	0	(pow.f64 x #s(literal 4 binary64))
cost-diff	0	(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
cost-diff	0	(*.f64 #s(literal 2 binary64) (sqrt.f64 (pow.f64 x #s(literal 4 binary64))))
cost-diff	0	(sqrt.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (pow.f64 x #s(literal 4 binary64)))))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
cost-diff	0	#s(approx (sqrt (* 2 (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	77
0	30	77
1	51	65
2	115	65
3	267	65
4	442	65
5	520	65
6	557	65
7	591	65
0	591	59

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(literal 0 binary64)
#s(approx (sqrt (* 2 (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
x
(sqrt.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (pow.f64 x #s(literal 4 binary64)))))
(*.f64 #s(literal 2 binary64) (sqrt.f64 (pow.f64 x #s(literal 4 binary64))))
#s(literal 2 binary64)
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(pow.f64 x #s(literal 4 binary64))
x
#s(literal 4 binary64)
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x))))
(.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x)))
#s(literal 2 binary64)
(.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))
(*.f64 x (sqrt.f64 x))
x
(sqrt.f64 x)

Outputs
#s(literal 0 binary64)
#s(approx (sqrt (* 2 (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
x
(sqrt.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 (*.f64 (sqrt.f64 (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (sqrt.f64 (pow.f64 x #s(literal 4 binary64))))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(pow.f64 x #s(literal 4 binary64))
x
#s(literal 4 binary64)
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x))))
(hypot.f64 x x)
(.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x)))
(.f64 (.f64 x x) #s(literal 2 binary64))
#s(literal 2 binary64)
(.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))
(*.f64 x x)
(*.f64 x (sqrt.f64 x))
(*.f64 (sqrt.f64 x) x)
x
(sqrt.f64 x)

localize51.0ms (3.1%)

Memory

-27.3MiB live, 68.1MiB allocated; 14ms collecting garbage

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x)))
accuracy	0.1953125	(.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))
accuracy	0.2109375	(*.f64 x (sqrt.f64 x))
accuracy	26.664966668699904	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x))))
accuracy	0.0	(pow.f64 x #s(literal 4 binary64))
accuracy	0.0078125	(*.f64 #s(literal 2 binary64) (sqrt.f64 (pow.f64 x #s(literal 4 binary64))))
accuracy	14.481391525118134	(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
accuracy	26.664966668699904	(sqrt.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (pow.f64 x #s(literal 4 binary64)))))
accuracy	0.0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.0	#s(approx (sqrt (* 2 (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
accuracy	0.4609375	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)

Samples

35.0ms

256×

valid

Compiler

Compiled 74 to 20 computations (73% saved)

Precisions

Click to see histograms. Total time spent on operations: 23.0ms

ival-mult: 10.0ms (43.8% of total)

ival-sqrt: 9.0ms (39.4% of total)

ival-pow: 3.0ms (13.1% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

series8.0ms (0.5%)

Memory

15.8MiB live, 15.8MiB allocated; 0ms collecting garbage

Counts

11 → 10

Calls

Call 1

Inputs
#s(approx (sqrt (* 2 (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (pow.f64 x #s(literal 4 binary64)))))
(*.f64 #s(literal 2 binary64) (sqrt.f64 (pow.f64 x #s(literal 4 binary64))))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(pow.f64 x #s(literal 4 binary64))
(.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x))))
(.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x)))
(*.f64 x (sqrt.f64 x))

Outputs
(* x (sqrt 2))
(* 2 (pow x 2))
(pow x 2)
(pow x 4)
(sqrt (pow x 3))
(* -1 (* x (sqrt 2)))
(* -1 (* (pow x 2) (pow (sqrt -1) 2)))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -2 (* (pow x 2) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))

Calls

3 calls:

Time	Variable		Point	Expression
5.0ms	x	@	-inf	((sqrt (* 2 (* x x))) (* (sqrt 2) x) (sqrt 2) (sqrt (* 2 (sqrt (pow x 4)))) (* 2 (sqrt (pow x 4))) (sqrt (pow x 4)) (pow x 4) (* (* x (sqrt x)) (sqrt x)) (sqrt (* 2 (* (* x (sqrt x)) (sqrt x)))) (* 2 (* (* x (sqrt x)) (sqrt x))) (* x (sqrt x)))
2.0ms	x	@	inf	((sqrt (* 2 (* x x))) (* (sqrt 2) x) (sqrt 2) (sqrt (* 2 (sqrt (pow x 4)))) (* 2 (sqrt (pow x 4))) (sqrt (pow x 4)) (pow x 4) (* (* x (sqrt x)) (sqrt x)) (sqrt (* 2 (* (* x (sqrt x)) (sqrt x)))) (* 2 (* (* x (sqrt x)) (sqrt x))) (* x (sqrt x)))
1.0ms	x	@	0	((sqrt (* 2 (* x x))) (* (sqrt 2) x) (sqrt 2) (sqrt (* 2 (sqrt (pow x 4)))) (* 2 (sqrt (pow x 4))) (sqrt (pow x 4)) (pow x 4) (* (* x (sqrt x)) (sqrt x)) (sqrt (* 2 (* (* x (sqrt x)) (sqrt x)))) (* 2 (* (* x (sqrt x)) (sqrt x))) (* x (sqrt x)))

Time

Variable

Point

Expression

5.0ms

-inf

((sqrt (* 2 (* x x))) (* (sqrt 2) x) (sqrt 2) (sqrt (* 2 (sqrt (pow x 4)))) (* 2 (sqrt (pow x 4))) (sqrt (pow x 4)) (pow x 4) (* (* x (sqrt x)) (sqrt x)) (sqrt (* 2 (* (* x (sqrt x)) (sqrt x)))) (* 2 (* (* x (sqrt x)) (sqrt x))) (* x (sqrt x)))

2.0ms

inf

((sqrt (* 2 (* x x))) (* (sqrt 2) x) (sqrt 2) (sqrt (* 2 (sqrt (pow x 4)))) (* 2 (sqrt (pow x 4))) (sqrt (pow x 4)) (pow x 4) (* (* x (sqrt x)) (sqrt x)) (sqrt (* 2 (* (* x (sqrt x)) (sqrt x)))) (* 2 (* (* x (sqrt x)) (sqrt x))) (* x (sqrt x)))

1.0ms

((sqrt (* 2 (* x x))) (* (sqrt 2) x) (sqrt 2) (sqrt (* 2 (sqrt (pow x 4)))) (* 2 (sqrt (pow x 4))) (sqrt (pow x 4)) (pow x 4) (* (* x (sqrt x)) (sqrt x)) (sqrt (* 2 (* (* x (sqrt x)) (sqrt x)))) (* 2 (* (* x (sqrt x)) (sqrt x))) (* x (sqrt x)))

simplify135.0ms (8.2%)

Memory

7.7MiB live, 51.2MiB allocated; 12ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	25	44
1	58	44
2	173	44
3	443	44
4	1225	44
5	2634	36
6	3596	36
7	4028	36
8	4380	36
9	4423	36
10	4423	36
11	4423	36
12	5326	36
13	5430	36
14	5430	36
15	5442	36
16	5442	36
17	5951	36
18	6564	36
0	6564	36

Stop Event

1×	iter limit
1×	saturated

Counts

10 → 10

Calls

Call 1

Inputs
(* x (sqrt 2))
(* 2 (pow x 2))
(pow x 2)
(pow x 4)
(sqrt (pow x 3))
(* -1 (* x (sqrt 2)))
(* -1 (* (pow x 2) (pow (sqrt -1) 2)))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -2 (* (pow x 2) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))

Outputs
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* 2 (pow x 2))
#s(literal 0 binary64)
(pow x 2)
(*.f64 x x)
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(sqrt (pow x 3))
(sqrt.f64 (pow.f64 x #s(literal 3 binary64)))
(* -1 (* x (sqrt 2)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (pow x 2) (pow (sqrt -1) 2)))
(*.f64 x x)
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 #s(literal -2 binary64)) x))
(* -2 (* (pow x 2) (pow (sqrt -1) 2)))
#s(literal 0 binary64)
(* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(sqrt.f64 (pow.f64 x #s(literal 3 binary64)))

rewrite55.0ms (3.3%)

Memory

16.7MiB live, 59.5MiB allocated; 11ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	67
0	29	46
1	65	43
2	236	22
0	1553	22

Stop Event

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

Counts

11 → 128

Calls

Call 1

Inputs
#s(approx (sqrt (* 2 (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (pow.f64 x #s(literal 4 binary64)))))
(*.f64 #s(literal 2 binary64) (sqrt.f64 (pow.f64 x #s(literal 4 binary64))))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(pow.f64 x #s(literal 4 binary64))
(.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x))))
(.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x)))
(*.f64 x (sqrt.f64 x))

Outputs
#s(approx (sqrt (* 2 (* x x))) #s(literal 0 binary64))
#s(literal 0 binary64)
(*.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
#s(literal 0 binary64)
#s(literal 0 binary64)
(.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (.f64 x (pow.f64 x #s(literal 3/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (.f64 x (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 3/4 binary64)))
(*.f64 (fabs.f64 (pow.f64 x #s(literal 3/2 binary64))) (sqrt.f64 x))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 x))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/2 binary64))))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 3/4 binary64)) x))
(*.f64 (neg.f64 (sqrt.f64 x)) (pow.f64 x #s(literal 3/2 binary64)))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) x))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (neg.f64 (sqrt.f64 x)))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (fabs.f64 (pow.f64 x #s(literal 3/2 binary64))))
(*.f64 (sqrt.f64 x) (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 x) (pow.f64 x #s(literal 3/2 binary64)))
(*.f64 x x)
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/4 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 4 binary64))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 x x))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))
(.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (neg.f64 (sqrt.f64 x))) (neg.f64 (sqrt.f64 x)))
(.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 3/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 3/4 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (sqrt.f64 x)) (sqrt.f64 x))
(.f64 (.f64 (*.f64 x x) (pow.f64 x #s(literal 3/2 binary64))) (sqrt.f64 x))
(.f64 (.f64 (*.f64 x x) (sqrt.f64 x)) (pow.f64 x #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) x)
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 x)) #s(literal 4 binary64)) (pow.f64 (neg.f64 (sqrt.f64 x)) #s(literal 4 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 4 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 4 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 4 binary64)) (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 4 binary64)))
(*.f64 (pow.f64 x #s(literal 3 binary64)) x)
(.f64 (.f64 x x) (*.f64 x x))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 x #s(literal 3 binary64))))
(.f64 (neg.f64 (sqrt.f64 x)) (.f64 (neg.f64 (sqrt.f64 x)) (pow.f64 x #s(literal 3 binary64))))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3 binary64))))
(.f64 (pow.f64 x #s(literal 3/2 binary64)) (.f64 (sqrt.f64 x) (*.f64 x x)))
(.f64 (sqrt.f64 x) (.f64 (pow.f64 x #s(literal 3/2 binary64)) (*.f64 x x)))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (pow.f64 x #s(literal 3 binary64))))
(*.f64 x (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))
(*.f64 x (pow.f64 x #s(literal 3 binary64)))
(pow.f64 (exp.f64 #s(literal 4 binary64)) (log.f64 x))
(pow.f64 (*.f64 x x) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 8 binary64))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))
(pow.f64 x #s(literal 4 binary64))
(/.f64 (-.f64 (.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) (cosh.f64 (.f64 (log.f64 x) #s(literal 4 binary64)))) (.f64 (sinh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))))) (-.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 4 binary64)))))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) (cosh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) (-.f64 (.f64 (sinh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 4 binary64)))) (.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 4 binary64)))))))
(neg.f64 (pow.f64 x #s(literal 4 binary64)))
(sqrt.f64 (pow.f64 x #s(literal 8 binary64)))
(fabs.f64 (pow.f64 x #s(literal 4 binary64)))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) (*.f64 (log.f64 x) #s(literal 2 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 x #s(literal 8 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 x x)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 4 binary64)))
(+.f64 (sinh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) (cosh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))))
(.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (.f64 x (pow.f64 x #s(literal 3/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (.f64 x (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 3/4 binary64)))
(*.f64 (fabs.f64 (pow.f64 x #s(literal 3/2 binary64))) (sqrt.f64 x))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 x))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/2 binary64))))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 3/4 binary64)) x))
(*.f64 (neg.f64 (sqrt.f64 x)) (pow.f64 x #s(literal 3/2 binary64)))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) x))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (neg.f64 (sqrt.f64 x)))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (fabs.f64 (pow.f64 x #s(literal 3/2 binary64))))
(*.f64 (sqrt.f64 x) (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 x) (pow.f64 x #s(literal 3/2 binary64)))
(*.f64 x x)
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/4 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 4 binary64))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 x x))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))
#s(literal 0 binary64)
#s(literal 0 binary64)
(.f64 (.f64 (sqrt.f64 x) (pow.f64 x #s(literal 3/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (.f64 x (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (neg.f64 (sqrt.f64 x))) (*.f64 (pow.f64 x #s(literal 1/4 binary64)) (neg.f64 (sqrt.f64 x))))
(.f64 (.f64 (neg.f64 (sqrt.f64 x)) (pow.f64 x #s(literal 1/4 binary64))) (*.f64 (neg.f64 (sqrt.f64 x)) (pow.f64 x #s(literal 1/4 binary64))))
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 x)) #s(literal 3/2 binary64)) (pow.f64 (neg.f64 (sqrt.f64 x)) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 3/2 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 3/2 binary64)) (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (sqrt.f64 x) #s(literal 3/2 binary64)) (pow.f64 (sqrt.f64 x) #s(literal 3/2 binary64)))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 x)))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) x))
(*.f64 (neg.f64 (sqrt.f64 x)) x)
(*.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
(*.f64 (sqrt.f64 x) x)
(*.f64 x (neg.f64 (sqrt.f64 x)))
(*.f64 x (sqrt.f64 x))
(pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/4 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 3 binary64))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 3/8 binary64))
(pow.f64 x #s(literal 3/2 binary64))
(neg.f64 (pow.f64 x #s(literal 3/2 binary64)))
(sqrt.f64 (pow.f64 x #s(literal 3 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 3/2 binary64)))

eval17.0ms (1%)

Memory: -9.5MiB live, 35.1MiB allocated; 5ms collecting garbage
Compiler: Compiled 1 361 to 474 computations (65.2% saved)

prune4.0ms (0.2%)

Memory

7.9MiB live, 7.9MiB allocated; 0ms collecting garbage

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	0	0	0
Picked	0	4	4
Done	0	1	1
Total	106	7	113

Accuracy

99.9%

Counts

113 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	57.9%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))))
✓	58.1%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x))))
✓	58.3%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
✓	34.8%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (pow.f64 x #s(literal 4 binary64)))))
▶	99.1%	#s(approx (sqrt (* 2 (* x x))) (*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) x))
✓	99.3%	#s(approx (sqrt (* 2 (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	3.6%	#s(literal 0 binary64)

Compiler

Compiled 56 to 48 computations (14.3% saved)

simplify10.0ms (0.6%)

Memory

8.4MiB live, 8.4MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(pow.f64 (sqrt.f64 x) #s(literal 4 binary64))
cost-diff	0	(*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)))
cost-diff	0	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))))
cost-diff	0	(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
cost-diff	0	(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) x)
cost-diff	0	#s(approx (sqrt (* 2 (* x x))) (*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) x))
cost-diff	3	(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	54
0	22	54
1	36	48
2	85	45
3	175	45
4	294	45
5	365	45
6	388	45
7	408	45
0	408	42

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize92.0ms (5.6%)

Memory

-58.6MiB live, 34.6MiB allocated; 59ms collecting garbage

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.0	(sqrt.f64 x)
accuracy	0.0078125	(*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)))
accuracy	0.5112840821270289	(pow.f64 (sqrt.f64 x) #s(literal 4 binary64))
accuracy	26.664966668699904	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))))
accuracy	0.0	(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
accuracy	0.0	#s(approx (sqrt (* 2 (* x x))) (*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) x))
accuracy	0.4609375	(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) x)
accuracy	1.0	(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))

Samples

83.0ms

256×

valid

Compiler

Compiled 48 to 16 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 75.0ms

ival-sqrt: 54.0ms (71.9% of total)

ival-pow2: 9.0ms (12% of total)

ival-mult: 6.0ms (8% of total)

ival-exp2: 3.0ms (4% of total)

ival-pow: 2.0ms (2.7% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series4.0ms (0.3%)

Memory

4.6MiB live, 4.6MiB allocated; 0ms collecting garbage

Counts

8 → 9

Calls

Call 1

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

Outputs
(* x (sqrt 2))
(* 2 (pow x 2))
(pow x 2)
(sqrt x)
(* -1 (* x (sqrt 2)))
(* -1 (* x (* (pow (sqrt -1) 2) (sqrt 2))))
(* 2 (* (pow x 2) (pow (sqrt -1) 4)))
(* (pow x 2) (pow (sqrt -1) 4))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

simplify126.0ms (7.6%)

Memory

-0.3MiB live, 136.0MiB allocated; 20ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	33
1	47	33
2	149	33
3	356	33
4	1221	33
5	2682	33
6	3247	33
7	4125	33
8	6379	33
0	8066	33

Stop Event

1×	iter limit
1×	node limit

Counts

9 → 9

Calls

Call 1

Inputs
(* x (sqrt 2))
(* 2 (pow x 2))
(pow x 2)
(sqrt x)
(* -1 (* x (sqrt 2)))
(* -1 (* x (* (pow (sqrt -1) 2) (sqrt 2))))
(* 2 (* (pow x 2) (pow (sqrt -1) 4)))
(* (pow x 2) (pow (sqrt -1) 4))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))

Outputs
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* 2 (pow x 2))
(.f64 (.f64 x x) #s(literal 2 binary64))
(pow x 2)
(*.f64 x x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* x (sqrt 2)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* 2 (* (pow x 2) (pow (sqrt -1) 4)))
(.f64 (.f64 x x) #s(literal 2 binary64))
(* (pow x 2) (pow (sqrt -1) 4))
(*.f64 x x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)

rewrite59.0ms (3.6%)

Memory

-1.3MiB live, 52.5MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	48
0	22	38
1	65	32
2	233	16
0	1391	16

Stop Event

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

Counts

8 → 102

Calls

Call 1

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

Outputs
(.f64 (.f64 (pow.f64 #s(literal 8 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 4 binary64) #s(literal 1/8 binary64)) (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)))) (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64))))
(*.f64 (pow.f64 (pow.f64 #s(literal 8 binary64) #s(literal 1/8 binary64)) #s(literal 1 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)))
(*.f64 (pow.f64 (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))) #s(literal 1 binary64)))
(*.f64 (pow.f64 #s(literal 8 binary64) #s(literal 1/8 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal 1/16 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 8 binary64) #s(literal 1/8 binary64))))
(*.f64 (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))) (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))))
(.f64 (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64))) (.f64 (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (pow.f64 (pow.f64 #s(literal 8 binary64) #s(literal 1/8 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (pow.f64 #s(literal 8 binary64) #s(literal 1/8 binary64)))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(pow.f64 #s(literal 16 binary64) #s(literal 1/8 binary64))
(pow.f64 (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))) #s(literal 2 binary64))
(pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) #s(literal 4 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))
(pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(/.f64 (-.f64 (.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))) (.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))))) (-.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (-.f64 (.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))) (.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))))))
(neg.f64 (*.f64 (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))) (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))))
(neg.f64 (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)))))
(fma.f64 (cosh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (sinh.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))))
(fma.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (cosh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sinh.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))))
(fma.f64 #s(literal 2 binary64) (.f64 (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (cosh.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))) (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))))
(sqrt.f64 #s(literal 2 binary64))
(fabs.f64 (sqrt.f64 #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 4 binary64)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64)))
(exp.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (.f64 (cosh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))) (.f64 (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))))
(+.f64 (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (cosh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))))
(+.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (sqrt (* 2 (* x x))) #s(literal 0 binary64))
#s(literal 0 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 (neg.f64 (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)))) (neg.f64 (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)))))
(*.f64 (pow.f64 (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64))) #s(literal 1 binary64)) (pow.f64 (neg.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 (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64))) (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64))))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)))
(pow.f64 (exp.f64 #s(literal 1/4 binary64)) (log.f64 #s(literal 2 binary64)))
(pow.f64 (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64))) #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 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 1 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
(/.f64 (-.f64 (.f64 (cosh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (cosh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))) (.f64 (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))))) (-.f64 (cosh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (cosh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (-.f64 (.f64 (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))) (.f64 (cosh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))))))
(neg.f64 (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))))
(sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))
(fabs.f64 (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))))
(fabs.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 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 #s(literal 4 binary64)) #s(literal 1/8 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(+.f64 (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (cosh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))))
(+.f64 (cosh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (sinh.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))))
#s(literal 0 binary64)
#s(literal 0 binary64)
(.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 4 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 4 binary64)))
(*.f64 x x)
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) x))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 4 binary64)) (log.f64 (sqrt.f64 x)))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 4 binary64))
(/.f64 (-.f64 (.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64)))) (.f64 (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))) (-.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64)))))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (-.f64 (.f64 (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64)))) (.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64)))))))
(neg.f64 (*.f64 x x))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(fabs.f64 (*.f64 x x))
(exp.f64 (fma.f64 (log.f64 (sqrt.f64 x)) #s(literal 2 binary64) (*.f64 (log.f64 (sqrt.f64 x)) #s(literal 2 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 x)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))
(*.f64 (pow.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (pow.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
(*.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) (neg.f64 (pow.f64 x #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 x #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 x #s(literal 1/4 binary64))))
(*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 x))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 x #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(sqrt.f64 x)
(fabs.f64 (sqrt.f64 x))
(exp.f64 (/.f64 (*.f64 (log.f64 (sqrt.f64 x)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 x)) #s(literal 1 binary64)))
(exp.f64 (log.f64 (sqrt.f64 x)))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 x))) (sinh.f64 (log.f64 (sqrt.f64 x))))

eval17.0ms (1.1%)

Memory: -12.5MiB live, 32.3MiB allocated; 5ms collecting garbage
Compiler: Compiled 1 731 to 458 computations (73.5% saved)

prune3.0ms (0.2%)

Memory

10.2MiB live, 10.2MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	0	0	0
Picked	2	0	2
Done	1	4	5
Total	108	5	113

Accuracy

99.9%

Counts

113 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	58.1%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x))))
✓	58.3%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
▶	99.1%	#s(approx (sqrt (* 2 (* x x))) (*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64)) x))
✓	99.3%	#s(approx (sqrt (* 2 (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	3.6%	#s(literal 0 binary64)

Compiler

Compiled 42 to 34 computations (19% saved)

simplify8.0ms (0.5%)

Memory

21.8MiB live, 21.8MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64)) x)
cost-diff	0	#s(approx (sqrt (* 2 (* x x))) (*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64)) x))
cost-diff	3	(pow.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	33
0	14	30
1	26	24
2	74	24
3	158	24
4	260	24
5	306	24
6	329	24
7	349	24
0	349	21

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (sqrt (* 2 (* x x))) (*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64)) x))
(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64)) x)
(pow.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64))
(sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
x

Outputs
#s(approx (sqrt (* 2 (* x x))) (*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64)) x))
#s(approx (sqrt (* 2 (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64)) x)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(pow.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
x

localize40.0ms (2.4%)

Memory

2.3MiB live, 47.4MiB allocated; 3ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.0	#s(approx (sqrt (* 2 (* x x))) (*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64)) x))
accuracy	0.4609375	(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64)) x)
accuracy	1.0	(pow.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64))

Samples

33.0ms

256×

valid

Compiler

Compiled 27 to 11 computations (59.3% saved)

Precisions

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

ival-mult: 19.0ms (71.8% of total)

ival-sqrt: 5.0ms (18.9% of total)

ival-pow2: 2.0ms (7.6% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

series1.0ms (0.1%)

Memory

1.8MiB live, 1.8MiB allocated; 0ms collecting garbage

Counts

5 → 2

Calls

Call 1

Inputs
(pow.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64))
#s(approx (sqrt (* 2 (* x x))) (*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64)) x))
(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64)) x)
(sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))

Outputs
(* x (sqrt 2))
(* -1 (* x (sqrt 2)))

Calls

3 calls:

Time

Variable

Point

Expression

0.0ms

-inf

((pow (sqrt (sqrt 2)) 2) (sqrt (* 2 (* x x))) (* (pow (sqrt (sqrt 2)) 2) x) (sqrt (sqrt 2)) (sqrt 2))

0.0ms

((pow (sqrt (sqrt 2)) 2) (sqrt (* 2 (* x x))) (* (pow (sqrt (sqrt 2)) 2) x) (sqrt (sqrt 2)) (sqrt 2))

0.0ms

inf

((pow (sqrt (sqrt 2)) 2) (sqrt (* 2 (* x x))) (* (pow (sqrt (sqrt 2)) 2) x) (sqrt (sqrt 2)) (sqrt 2))

simplify14.0ms (0.8%)

Memory

-43.4MiB live, 3.6MiB allocated; 3ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	13	9
2	27	9
3	28	9
0	28	9

Stop Event

1×	iter limit
1×	saturated

Counts

2 → 2

Calls

Call 1

Inputs
(* x (sqrt 2))
(* -1 (* x (sqrt 2)))

Outputs
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* -1 (* x (sqrt 2)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))

rewrite43.0ms (2.6%)

Memory

45.7MiB live, 45.7MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	31
0	14	26
1	40	21
2	160	11
0	1125	11

Stop Event

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

Counts

5 → 66

Calls

Call 1

Inputs
(pow.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64))
#s(approx (sqrt (* 2 (* x x))) (*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64)) x))
(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64)) x)
(sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))

Outputs
(.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
(*.f64 (neg.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))) (neg.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))))
(*.f64 (pow.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) #s(literal 1 binary64)))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 2 binary64))))
(pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))
(pow.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) #s(literal 2 binary64))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(/.f64 (-.f64 (.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))) (.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))))) (-.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (-.f64 (.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))) (.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))))))
(neg.f64 (*.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(neg.f64 (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))))
(fma.f64 #s(literal 2 binary64) (.f64 (sinh.f64 (.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 2 binary64)))) (cosh.f64 (*.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 2 binary64))))) (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))))
(sqrt.f64 #s(literal 2 binary64))
(fabs.f64 (sqrt.f64 #s(literal 2 binary64)))
(exp.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (sqrt (* 2 (* x x))) #s(literal 0 binary64))
#s(literal 0 binary64)
(*.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64))) (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64))))
(*.f64 (fabs.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64))) (fabs.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64))))
(*.f64 (sqrt.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))) (sqrt.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))))
(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) #s(literal 1/2 binary64)) (pow.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (sqrt.f64 #s(literal 2 binary64))))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
(sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))
(fabs.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(fabs.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(exp.f64 (/.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 2 binary64))))
(+.f64 (cosh.f64 (.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 2 binary64)))) (sinh.f64 (.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 2 binary64)))))
(.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
(*.f64 (neg.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))) (neg.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))))
(*.f64 (pow.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) #s(literal 1 binary64)))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 2 binary64))))
(pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))
(pow.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) #s(literal 2 binary64))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(/.f64 (-.f64 (.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))) (.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))))) (-.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (-.f64 (.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))) (.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))))))
(neg.f64 (*.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(neg.f64 (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))))
(fma.f64 #s(literal 2 binary64) (.f64 (sinh.f64 (.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 2 binary64)))) (cosh.f64 (*.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 2 binary64))))) (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))))
(sqrt.f64 #s(literal 2 binary64))
(fabs.f64 (sqrt.f64 #s(literal 2 binary64)))
(exp.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))) (sinh.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64)))))

eval40.0ms (2.5%)

Memory: -35.0MiB live, 17.1MiB allocated; 6ms collecting garbage
Compiler: Compiled 794 to 191 computations (75.9% saved)

prune4.0ms (0.2%)

Memory

9.9MiB live, 9.9MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	45	0	45
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	45	5	50

Accuracy

99.9%

Counts

50 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	58.1%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x))))
✓	58.3%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
✓	99.1%	#s(approx (sqrt (* 2 (* x x))) (*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64)) x))
✓	99.3%	#s(approx (sqrt (* 2 (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	3.6%	#s(literal 0 binary64)

Compiler

Compiled 112 to 69 computations (38.4% saved)

regimes14.0ms (0.8%)

Memory

-17.6MiB live, 26.6MiB allocated; 5ms collecting garbage

Counts

8 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
#s(approx (sqrt (* 2 (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x))))
#s(approx (sqrt (* 2 (* x x))) (*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64)) x))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))))
#s(approx (sqrt (* 2 (* x x))) (*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) x))

Outputs
#s(approx (sqrt (* 2 (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Calls

4 calls:

6.0ms	(*.f64 x x)
3.0ms	x
2.0ms	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
2.0ms	(.f64 #s(literal 2 binary64) (.f64 x x))

Results

Accuracy	Segments	Branch
99.3%	1	`(*.f64 x x)`
99.3%	1	`(.f64 #s(literal 2 binary64) (.f64 x x))`
99.3%	1	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`
99.3%	1	`x`

Compiler

Compiled 15 to 12 computations (20% saved)

regimes4.0ms (0.3%)

Memory

9.8MiB live, 9.8MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)

Outputs
#s(literal 0 binary64)

Calls

4 calls:

1.0ms	x
1.0ms	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
1.0ms	(.f64 #s(literal 2 binary64) (.f64 x x))
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
3.6%	1	`(*.f64 x x)`
3.6%	1	`(.f64 #s(literal 2 binary64) (.f64 x x))`
3.6%	1	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`
3.6%	1	`x`

Compiler

Compiled 15 to 12 computations (20% saved)

simplify37.0ms (2.2%)

Memory

-0.3MiB live, 45.7MiB allocated; 5ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	19	12
2	56	12
3	128	12
4	198	12
5	260	12
6	450	12
7	2120	12
8	3300	12

Stop Event

1×	node limit

Calls

Call 1

Inputs
#s(approx (sqrt (* 2 (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(literal 0 binary64)

Outputs
#s(approx (sqrt (* 2 (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(literal 0 binary64)

derivations38.0ms (2.3%)

Memory

32.5MiB live, 32.5MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	18	17
2	43	17
3	92	17
4	228	17
5	437	17
6	485	17
0	485	17
0	5	14
0	8	13
1	24	13
2	102	5
0	777	5

Stop Event

1×	done
1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit
1×	iter limit
1×	saturated

Compiler

Compiled 12 to 10 computations (16.7% saved)

preprocess21.0ms (1.3%)

Memory: -14.5MiB live, 31.2MiB allocated; 3ms collecting garbage
Compiler: Compiled 58 to 48 computations (17.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

Iter	Nodes	Cost
0	7	13
1	22	13
2	83	13
3	131	13
4	223	13
5	249	13
6	269	13
0	5	6
0	8	6
1	18	6
2	56	6
3	122	6
4	187	6
5	223	6
6	246	6
7	266	6
0	266	3

Iter	Nodes	Cost
0	8	17
1	18	17
2	43	17
3	92	17
4	228	17
5	437	17
6	485	17
0	485	17
0	5	14
0	8	13
1	24	13
2	102	5
0	777	5

Iter	Nodes	Cost
0	7	13
1	22	13
2	83	13
3	131	13
4	223	13
5	249	13
6	269	13
0	5	6
0	8	6
1	18	6
2	56	6
3	122	6
4	187	6
5	223	6
6	246	6
7	266	6
0	266	3

Iter	Nodes	Cost
0	8	17
1	18	17
2	43	17
3	92	17
4	228	17
5	437	17
6	485	17
0	485	17
0	5	14
0	8	13
1	24	13
2	102	5
0	777	5

start0.0ms (0%)

analyze0.0ms (0%)

sample638.0ms (38.6%)

explain59.0ms (3.6%)

preprocess17.0ms (1.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify6.0ms (0.4%)

localize18.0ms (1.1%)

series3.0ms (0.2%)

simplify8.0ms (0.5%)

rewrite37.0ms (2.3%)

eval2.0ms (0.1%)

prune2.0ms (0.1%)

simplify13.0ms (0.8%)

localize51.0ms (3.1%)

series8.0ms (0.5%)

simplify135.0ms (8.2%)

rewrite55.0ms (3.3%)

eval17.0ms (1%)

prune4.0ms (0.2%)

simplify10.0ms (0.6%)

localize92.0ms (5.6%)

series4.0ms (0.3%)

simplify126.0ms (7.6%)

rewrite59.0ms (3.6%)

eval17.0ms (1.1%)

prune3.0ms (0.2%)

simplify8.0ms (0.5%)

localize40.0ms (2.4%)

series1.0ms (0.1%)

simplify14.0ms (0.8%)

rewrite43.0ms (2.6%)

eval40.0ms (2.5%)

prune4.0ms (0.2%)

regimes14.0ms (0.8%)

regimes4.0ms (0.3%)

simplify37.0ms (2.2%)

derivations38.0ms (2.3%)

preprocess21.0ms (1.3%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	7	13
1	22	13
2	83	13
3	131	13
4	223	13
5	249	13
6	269	13
0	5	6
0	8	6
1	18	6
2	56	6
3	122	6
4	187	6
5	223	6
6	246	6
7	266	6
0	266	3

Iter	Nodes	Cost
0	8	17
1	18	17
2	43	17
3	92	17
4	228	17
5	437	17
6	485	17
0	485	17
0	5	14
0	8	13
1	24	13
2	102	5
0	777	5