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

0.2MiB live, 0.2MiB 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)

sample851.0ms (43%)

Memory

37.4MiB live, 733.6MiB allocated; 137ms collecting garbage

Samples

503.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 230.0ms

ival-mult: 133.0ms (57.8% of total)

ival-sqrt: 81.0ms (35.2% of total)

ival-true: 6.0ms (2.6% of total)

exact: 5.0ms (2.2% of total)

ival-assert: 3.0ms (1.3% of total)

adjust: 2.0ms (0.9% of total)

Bogosity

explain79.0ms (4%)

Memory

-5.0MiB live, 96.6MiB allocated; 14ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
144	-	-	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`
0	-	-	`#s(literal 2 binary64)`
0	-	-	`(*.f64 x x)`
0	-	-	`(.f64 #s(literal 2 binary64) (.f64 x x))`
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)))`	uflow-rescue	75	0
↳	`(.f64 #s(literal 2 binary64) (.f64 x x))`	underflow	75
↳	`(*.f64 x x)`	underflow	75
`sqrt.f64`	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`	oflow-rescue	69	0
↳	`(.f64 #s(literal 2 binary64) (.f64 x x))`	overflow	69
↳	`(*.f64 x x)`	overflow	69

Confusion

	Predicted +	Predicted -
+	144	0
-	0	112

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	144	0	0
-	0	0	112

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	112
1	144

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

41.0ms

512×

valid

Compiler

Compiled 42 to 19 computations (54.8% saved)

Precisions

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

ival-mult: 7.0ms (60.2% of total)

ival-sqrt: 3.0ms (25.8% 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)

preprocess18.0ms (0.9%)

Memory

19.5MiB live, 19.5MiB 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: 0.2MiB live, 0.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	47.5%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify7.0ms (0.3%)

Memory

3.8MiB live, 3.8MiB 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

localize40.0ms (2%)

Memory

-21.7MiB live, 24.3MiB allocated; 7ms collecting garbage

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.0	(.f64 #s(literal 2 binary64) (.f64 x x))
accuracy	33.63154214162149	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Samples

13.0ms

256×

valid

Compiler

Compiled 18 to 7 computations (61.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-mult: 5.0ms (72.1% of total)

ival-sqrt: 2.0ms (28.8% 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

4.5MiB live, 4.5MiB 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))

simplify9.0ms (0.4%)

Memory

8.1MiB live, 8.1MiB 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)))

rewrite40.0ms (2%)

Memory

-14.7MiB live, 28.6MiB allocated; 7ms 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

3.2MiB live, 3.2MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	15	3	18
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	15	4	19

Accuracy

99.5%

Counts

19 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	47.4%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x))))
✓	47.5%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
▶	99.3%	#s(approx (sqrt (* 2 (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
▶	3.9%	#s(literal 0 binary64)

Compiler

Compiled 28 to 23 computations (17.9% saved)

simplify12.0ms (0.6%)

Memory

14.8MiB live, 14.8MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 7 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	(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	14	54
0	21	54
1	40	42
2	104	42
3	248	42
4	422	42
5	504	42
6	544	42
7	578	42
0	578	36

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) (.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) (.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)

localize154.0ms (7.8%)

Memory

-15.2MiB live, 37.5MiB allocated; 10ms collecting garbage

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0.0	(sqrt.f64 x)
accuracy	0.1328125	(.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))
accuracy	0.18359375	(*.f64 x (sqrt.f64 x))
accuracy	33.63154214162149	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x))))
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	0.44921875	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)

Samples

27.0ms

256×

valid

Compiler

Compiled 51 to 15 computations (70.6% saved)

Precisions

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

ival-mult: 9.0ms (57.9% of total)

ival-sqrt: 6.0ms (38.6% 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)

series7.0ms (0.3%)

Memory

12.5MiB live, 12.5MiB allocated; 0ms collecting garbage

Counts

8 → 11

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))
(.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))
(sqrt.f64 x)

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

Calls

3 calls:

Time	Variable		Point	Expression
4.0ms	x	@	-inf	((sqrt (* 2 (* x x))) (* (sqrt 2) x) (sqrt 2) (* (* x (sqrt x)) (sqrt x)) (sqrt (* 2 (* (* x (sqrt x)) (sqrt x)))) (* 2 (* (* x (sqrt x)) (sqrt x))) (* x (sqrt x)) (sqrt x))
1.0ms	x	@	inf	((sqrt (* 2 (* x x))) (* (sqrt 2) x) (sqrt 2) (* (* x (sqrt x)) (sqrt x)) (sqrt (* 2 (* (* x (sqrt x)) (sqrt x)))) (* 2 (* (* x (sqrt x)) (sqrt x))) (* x (sqrt x)) (sqrt x))
1.0ms	x	@	0	((sqrt (* 2 (* x x))) (* (sqrt 2) x) (sqrt 2) (* (* x (sqrt x)) (sqrt x)) (sqrt (* 2 (* (* x (sqrt x)) (sqrt x)))) (* 2 (* (* x (sqrt x)) (sqrt x))) (* x (sqrt x)) (sqrt x))

Time

Variable

Point

Expression

4.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

simplify136.0ms (6.9%)

Memory

-13.7MiB live, 31.5MiB allocated; 5ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	26	45
1	64	45
2	197	45
3	492	45
4	1347	45
5	2815	37
6	3768	37
7	4196	37
8	4548	37
9	4591	37
10	4591	37
11	4591	37
12	5503	37
13	5607	37
14	5607	37
15	5622	37
16	5622	37
17	6138	37
18	6807	37
0	6807	37

Stop Event

1×	iter limit
1×	saturated

Counts

11 → 11

Calls

Call 1

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

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

rewrite69.0ms (3.5%)

Memory

28.7MiB live, 116.8MiB allocated; 11ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	49
0	20	38
1	49	31
2	188	16
0	998	16

Stop Event

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

Counts

8 → 82

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

eval27.0ms (1.4%)

Memory: -36.3MiB live, 26.5MiB allocated; 15ms collecting garbage
Compiler: Compiled 1 386 to 433 computations (68.8% saved)

prune4.0ms (0.2%)

Memory

11.2MiB live, 11.2MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	104	2	106
Fresh	0	0	0
Picked	0	3	3
Done	0	1	1
Total	104	6	110

Accuracy

99.9%

Counts

110 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	47.3%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))))
✓	47.4%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x))))
✓	47.5%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
▶	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))
✓	3.9%	#s(literal 0 binary64)

Compiler

Compiled 49 to 41 computations (16.3% saved)

simplify11.0ms (0.6%)

Memory

-29.8MiB live, 17.2MiB allocated; 2ms 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)

localize39.0ms (2%)

Memory

2.1MiB live, 48.1MiB allocated; 4ms collecting garbage

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)))
accuracy	0.0	(sqrt.f64 x)
accuracy	0.3832589356003984	(pow.f64 (sqrt.f64 x) #s(literal 4 binary64))
accuracy	33.63154214162149	(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	0.44921875	(*.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

28.0ms

256×

valid

Compiler

Compiled 48 to 16 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-mult: 6.0ms (31% of total)

ival-sqrt: 5.0ms (25.8% of total)

ival-exp2: 3.0ms (15.5% of total)

ival-pow: 2.0ms (10.3% of total)

ival-pow2: 2.0ms (10.3% 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 (0.2%)

Memory

6.2MiB live, 6.2MiB 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))

simplify134.0ms (6.8%)

Memory

33.5MiB live, 166.4MiB allocated; 32ms 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)

rewrite44.0ms (2.2%)

Memory

-7.9MiB live, 37.9MiB allocated; 4ms 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))))

eval13.0ms (0.7%)

Memory: 22.5MiB live, 22.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 731 to 458 computations (73.5% saved)

prune6.0ms (0.3%)

Memory

-36.4MiB live, 9.4MiB allocated; 3ms 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	0	4	4
Total	107	5	112

Accuracy

99.9%

Counts

112 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	47.4%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x))))
✓	47.5%	(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))
✓	3.9%	#s(literal 0 binary64)

Compiler

Compiled 42 to 34 computations (19% saved)

simplify8.0ms (0.4%)

Memory

9.0MiB live, 9.0MiB 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

localize25.0ms (1.3%)

Memory

33.8MiB live, 33.8MiB allocated; 0ms 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	0.44921875	(*.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

19.0ms

256×

valid

Compiler

Compiled 27 to 11 computations (59.3% saved)

Precisions

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

ival-mult: 5.0ms (40.5% of total)

ival-sqrt: 5.0ms (40.5% of total)

ival-pow2: 2.0ms (16.2% 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)

series27.0ms (1.4%)

Memory

-31.4MiB live, 19.8MiB allocated; 20ms 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

26.0ms

((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))

0.0ms

inf

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

simplify3.0ms (0.1%)

Memory

3.9MiB live, 3.9MiB allocated; 0ms 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)))

rewrite47.0ms (2.4%)

Memory

-3.8MiB live, 42.0MiB allocated; 7ms 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)))))

eval5.0ms (0.3%)

Memory: 10.0MiB live, 10.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 794 to 191 computations (75.9% saved)

prune3.0ms (0.2%)

Memory

7.4MiB live, 7.4MiB 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
✓	47.4%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x))))
✓	47.5%	(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))
✓	3.9%	#s(literal 0 binary64)

Compiler

Compiled 105 to 65 computations (38.1% saved)

regimes13.0ms (0.6%)

Memory

-27.4MiB live, 18.2MiB allocated; 4ms collecting garbage

Counts

7 → 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) (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:

5.0ms	(*.f64 x x)
2.0ms	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 (0.2%)

Memory

9.4MiB live, 9.4MiB 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
3.9%	1	`(*.f64 x x)`
3.9%	1	`(.f64 #s(literal 2 binary64) (.f64 x x))`
3.9%	1	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`
3.9%	1	`x`

Compiler

Compiled 15 to 12 computations (20% saved)

simplify64.0ms (3.2%)

Memory

-8.3MiB live, 37.0MiB allocated; 6ms 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)

derivations39.0ms (1.9%)

Memory

42.4MiB live, 42.4MiB 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)

preprocess26.0ms (1.3%)

Memory: -8.8MiB live, 39.1MiB allocated; 9ms 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%)

sample851.0ms (43%)

explain79.0ms (4%)

preprocess18.0ms (0.9%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify7.0ms (0.3%)

localize40.0ms (2%)

series3.0ms (0.2%)

simplify9.0ms (0.4%)

rewrite40.0ms (2%)

eval2.0ms (0.1%)

prune2.0ms (0.1%)

simplify12.0ms (0.6%)

localize154.0ms (7.8%)

series7.0ms (0.3%)

simplify136.0ms (6.9%)

rewrite69.0ms (3.5%)

eval27.0ms (1.4%)

prune4.0ms (0.2%)

simplify11.0ms (0.6%)

localize39.0ms (2%)

series4.0ms (0.2%)

simplify134.0ms (6.8%)

rewrite44.0ms (2.2%)

eval13.0ms (0.7%)

prune6.0ms (0.3%)

simplify8.0ms (0.4%)

localize25.0ms (1.3%)

series27.0ms (1.4%)

simplify3.0ms (0.1%)

rewrite47.0ms (2.4%)

eval5.0ms (0.3%)

prune3.0ms (0.2%)

regimes13.0ms (0.6%)

regimes4.0ms (0.2%)

simplify64.0ms (3.2%)

derivations39.0ms (1.9%)

preprocess26.0ms (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