Metrics for sqrt C (should all be same)

start0.0ms (0%)

Memory: 0.1MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

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)

sample726.0ms (26.7%)

Memory

39.7MiB live, 742.8MiB allocated

Samples

511.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 254.0ms

ival-mult: 185.0ms (72.9% of total)

ival-sqrt: 56.0ms (22.1% of total)

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

exact: 4.0ms (1.6% of total)

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

Bogosity

explain60.0ms (2.2%)

Memory

12.3MiB live, 56.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
138	-	4	(-4.199406377893121e-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)))`	uflow-rescue	73	0
↳	`(.f64 #s(literal 2 binary64) (.f64 x x))`	underflow	73
↳	`(*.f64 x x)`	underflow	73
`sqrt.f64`	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`	oflow-rescue	61	0
↳	`(.f64 #s(literal 2 binary64) (.f64 x x))`	overflow	61
↳	`(*.f64 x x)`	overflow	59

Confusion

	Predicted +	Predicted -
+	134	4
-	0	118

Precision

1.0

Recall

0.9710144927536232

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	134	0	4
-	0	0	118

Precision?

1.0

Recall?

0.9710144927536232

Freqs

test

number	freq
0	122
1	134

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

22.0ms

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 (62.4% of total)

ival-sqrt: 4.0ms (35.7% of total)

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

exact: 0.0ms (0% of total)

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

preprocess54.0ms (2%)

Memory

-26.2MiB live, 20.1MiB allocated

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
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.6%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify6.0ms (0.2%)

Memory

7.1MiB live, 7.1MiB allocated

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

localize15.0ms (0.5%)

Memory

21.7MiB live, 21.7MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.00390625	(.f64 #s(literal 2 binary64) (.f64 x x))
accuracy	31.58678972424293	(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 (56.1% of total)

ival-sqrt: 2.0ms (37.4% of total)

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

exact: 0.0ms (0% of total)

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

series11.0ms (0.4%)

Memory

-45.8MiB live, 5.1MiB allocated

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
9.0ms	x	@	0	((sqrt (* 2 (* x x))) (* 2 (* x x)) (* x x))
1.0ms	x	@	inf	((sqrt (* 2 (* x x))) (* 2 (* x x)) (* x x))
1.0ms	x	@	-inf	((sqrt (* 2 (* x x))) (* 2 (* x x)) (* x x))

simplify8.0ms (0.3%)

Memory

12.2MiB live, 12.2MiB allocated

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)))

rewrite36.0ms (1.3%)

Memory

6.7MiB live, 52.3MiB allocated

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: 3.5MiB live, 3.5MiB allocated
Compiler: Compiled 155 to 71 computations (54.2% saved)

prune3.0ms (0.1%)

Memory

5.5MiB live, 5.5MiB allocated

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	13	5	18
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	13	6	19

Accuracy

99.6%

Counts

19 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.6%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
▶	50.5%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x))))
✓	50.6%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
▶	28.4%	(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))
▶	4.0%	#s(literal 0 binary64)

Compiler

Compiled 76 to 65 computations (14.5% saved)

simplify13.0ms (0.5%)

Memory

14.0MiB live, 14.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score
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	(pow.f64 x #s(literal 2 binary64))
cost-diff	0	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
cost-diff	3	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
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	22	93
0	36	105
1	57	81
2	120	81
3	266	81
4	435	81
5	510	81
6	547	81
7	581	81
0	581	72

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

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

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

localize106.0ms (3.9%)

Memory

-31.9MiB live, 107.7MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score
accuracy	0.0	(pow.f64 x #s(literal 4 binary64))
accuracy	0.00390625	(*.f64 #s(literal 2 binary64) (sqrt.f64 (pow.f64 x #s(literal 4 binary64))))
accuracy	14.102114812924217	(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
accuracy	31.58678972424293	(sqrt.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (pow.f64 x #s(literal 4 binary64)))))
accuracy	0.00390625	(pow.f64 x #s(literal 2 binary64))
accuracy	0.00390625	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
accuracy	31.58678972424293	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
accuracy	0.00390625	(.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x)))
accuracy	0.18359375	(*.f64 x (sqrt.f64 x))
accuracy	0.19140625	(.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))
accuracy	31.58678972424293	(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	0.43359375	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)

Samples

84.0ms

256×

valid

Compiler

Compiled 90 to 23 computations (74.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

ival-mult: 12.0ms (38.1% of total)

ival-sqrt: 10.0ms (31.8% of total)

ival-pow2: 6.0ms (19.1% of total)

ival-pow: 3.0ms (9.5% of total)

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

exact: 0.0ms (0% of total)

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

series8.0ms (0.3%)

Memory

34.1MiB live, 34.1MiB allocated

Counts

14 → 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))
(.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 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
(pow.f64 x #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))

Outputs
(* x (sqrt 2))
(pow x 2)
(* 2 (pow x 2))
(sqrt (pow x 3))
(pow x 4)
(* -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) (* (* x (sqrt x)) (sqrt x)) (sqrt (* 2 (* (* x (sqrt x)) (sqrt x)))) (* 2 (* (* x (sqrt x)) (sqrt x))) (* x (sqrt x)) (sqrt (* 2 (pow x 2))) (* 2 (pow x 2)) (pow x 2) (sqrt (* 2 (sqrt (pow x 4)))) (* 2 (sqrt (pow x 4))) (sqrt (pow x 4)) (pow x 4))
2.0ms	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 (* 2 (pow x 2))) (* 2 (pow x 2)) (pow x 2) (sqrt (* 2 (sqrt (pow x 4)))) (* 2 (sqrt (pow x 4))) (sqrt (pow x 4)) (pow x 4))
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 (* 2 (pow x 2))) (* 2 (pow x 2)) (pow x 2) (sqrt (* 2 (sqrt (pow x 4)))) (* 2 (sqrt (pow x 4))) (sqrt (pow x 4)) (pow x 4))

Time

Variable

Point

Expression

5.0ms

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

2.0ms

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

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

simplify135.0ms (5%)

Memory

-5.7MiB live, 36.7MiB allocated

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	1230	44
5	2643	36
6	3588	36
7	4024	36
8	4376	36
9	4419	36
10	4419	36
11	4419	36
12	5368	36
13	5472	36
14	5472	36
15	5484	36
16	5484	36
17	5981	36
18	6667	36
0	6667	36

Stop Event

1×	iter limit
1×	saturated

Counts

10 → 10

Calls

Call 1

Inputs
(* x (sqrt 2))
(pow x 2)
(* 2 (pow x 2))
(sqrt (pow x 3))
(pow x 4)
(* -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)
(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)))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(* -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 (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)))

rewrite49.0ms (1.8%)

Memory

2.7MiB live, 49.2MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	81
0	35	61
1	76	59
2	257	17
3	1797	17
0	9824	17

Stop Event

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

Counts

14 → 46

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

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

eval4.0ms (0.1%)

Memory: 7.8MiB live, 7.8MiB allocated
Compiler: Compiled 502 to 142 computations (71.7% saved)

prune3.0ms (0.1%)

Memory

6.4MiB live, 6.4MiB allocated

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	28	3	31
Fresh	0	0	0
Picked	1	4	5
Done	0	1	1
Total	29	8	37

Accuracy

99.9%

Counts

37 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	50.6%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
✓	50.5%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x))))
▶	37.0%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 #s(approx (* x (sqrt x)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x))))
✓	50.6%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
✓	28.4%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (pow.f64 x #s(literal 4 binary64)))))
▶	99.0%	#s(approx (sqrt (* 2 (* x x))) (*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x))
✓	99.3%	#s(approx (sqrt (* 2 (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
▶	20.4%	#s(approx (sqrt (* 2 (* x x))) x)

Compiler

Compiled 77 to 63 computations (18.2% saved)

simplify20.0ms (0.7%)

Memory

-32.5MiB live, 12.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (* x (sqrt x)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))))
cost-diff	0	(.f64 #s(approx ( x (sqrt x)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x))
cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 #s(approx (* x (sqrt x)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))
cost-diff	0	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 #s(approx (* x (sqrt x)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x))))
cost-diff	0	(pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))
cost-diff	0	(*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x)
cost-diff	0	#s(approx (sqrt (* 2 (* x x))) (*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x))
cost-diff	2	(pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))
cost-diff	0	#s(approx (sqrt (* 2 (* x x))) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	104
0	31	104
1	51	98
2	123	98
3	241	98
4	407	98
5	526	98
6	617	98
7	661	98
8	681	98
9	691	98
0	691	92

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (sqrt (* 2 (* x x))) x)
x
#s(approx (sqrt (* 2 (* x x))) (*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x))
(*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x)
(pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))
#s(literal 4 binary64)
#s(literal 1/8 binary64)
#s(literal 2 binary64)
x
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 #s(approx (* x (sqrt x)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x))))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (* x (sqrt x)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))
#s(literal 2 binary64)
(.f64 #s(approx ( x (sqrt x)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x))
#s(approx (* x (sqrt x)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))))
(sqrt.f64 (pow.f64 x #s(literal 3 binary64)))
(pow.f64 x #s(literal 3 binary64))
x
#s(literal 3 binary64)
(sqrt.f64 x)

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

localize65.0ms (2.4%)

Memory

4.7MiB live, 101.3MiB allocated

Localize:

Found 9 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(.f64 #s(literal 2 binary64) (.f64 #s(approx (* x (sqrt x)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))
accuracy	0.19140625	(.f64 #s(approx ( x (sqrt x)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x))
accuracy	18.79565318864556	(sqrt.f64 (pow.f64 x #s(literal 3 binary64)))
accuracy	31.58678972424293	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 #s(approx (* x (sqrt x)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x))))
accuracy	0.0	(pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))
accuracy	0.0	#s(approx (sqrt (* 2 (* x x))) (*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x))
accuracy	0.43359375	(*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x)
accuracy	1.0	(pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))
accuracy	50.97296482738591	#s(approx (sqrt (* 2 (* x x))) x)

Samples

44.0ms

256×

valid

Compiler

Compiled 76 to 20 computations (73.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

ival-mult: 19.0ms (55.4% of total)

ival-sqrt: 6.0ms (17.5% of total)

ival-pow: 6.0ms (17.5% of total)

ival-pow2: 2.0ms (5.8% of total)

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

exact: 0.0ms (0% of total)

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

series68.0ms (2.5%)

Memory

-1.4MiB live, 89.8MiB allocated

Counts

10 → 11

Calls

Call 1

Inputs
#s(approx (sqrt (* 2 (* x x))) x)
(pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))
#s(approx (sqrt (* 2 (* x x))) (*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x))
(*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x)
(pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 #s(approx (* x (sqrt x)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x))))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (* x (sqrt x)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))
(.f64 #s(approx ( x (sqrt x)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x))
#s(approx (* x (sqrt x)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))))
(sqrt.f64 (pow.f64 x #s(literal 3 binary64)))

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

Calls

3 calls:

Time

Variable

Point

Expression

39.0ms

((sqrt (* 2 (* x x))) (pow (pow 4 1/8) 2) (sqrt (* 2 (* x x))) (* (pow (pow 4 1/8) 2) x) (pow 4 1/8) (sqrt (* 2 (* (* x (sqrt x)) (sqrt x)))) (* 2 (* (* x (sqrt x)) (sqrt x))) (* (* x (sqrt x)) (sqrt x)) (* x (sqrt x)) (sqrt (pow x 3)))

22.0ms

-inf

((sqrt (* 2 (* x x))) (pow (pow 4 1/8) 2) (sqrt (* 2 (* x x))) (* (pow (pow 4 1/8) 2) x) (pow 4 1/8) (sqrt (* 2 (* (* x (sqrt x)) (sqrt x)))) (* 2 (* (* x (sqrt x)) (sqrt x))) (* (* x (sqrt x)) (sqrt x)) (* x (sqrt x)) (sqrt (pow x 3)))

7.0ms

inf

((sqrt (* 2 (* x x))) (pow (pow 4 1/8) 2) (sqrt (* 2 (* x x))) (* (pow (pow 4 1/8) 2) x) (pow 4 1/8) (sqrt (* 2 (* (* x (sqrt x)) (sqrt x)))) (* 2 (* (* x (sqrt x)) (sqrt x))) (* (* x (sqrt x)) (sqrt x)) (* x (sqrt x)) (sqrt (pow x 3)))

simplify148.0ms (5.4%)

Memory

-1.1MiB live, 54.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	27	55
1	61	51
2	176	51
3	448	51
4	1231	51
5	2664	43
6	3620	43
7	4053	43
8	4410	43
9	4453	43
10	4453	43
11	4453	43
12	5457	43
13	5585	43
14	5585	43
15	5610	43
16	5610	43
17	6202	43
18	6839	43
0	6839	43

Stop Event

1×	iter limit
1×	saturated

Counts

11 → 11

Calls

Call 1

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

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

rewrite108.0ms (4%)

Memory

33.1MiB live, 123.0MiB allocated

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	91
0	31	63
1	85	59
2	322	51
3	1972	34
0	8367	34

Stop Event

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

Counts

10 → 271

Calls

Call 1

Inputs
#s(approx (sqrt (* 2 (* x x))) x)
(pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))
#s(approx (sqrt (* 2 (* x x))) (*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x))
(*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x)
(pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 #s(approx (* x (sqrt x)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x))))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (* x (sqrt x)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))
(.f64 #s(approx ( x (sqrt x)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x))
#s(approx (* x (sqrt x)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))))
(sqrt.f64 (pow.f64 x #s(literal 3 binary64)))

Outputs
#s(approx (sqrt (* 2 (* x x))) x)
(*.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 (fabs.f64 (pow.f64 #s(literal 4 binary64) #s(literal 7/32 binary64))) (pow.f64 #s(literal 16 binary64) #s(literal 1/64 binary64)))
(*.f64 (pow.f64 (neg.f64 (pow.f64 #s(literal 16 binary64) #s(literal 1/64 binary64))) #s(literal 4 binary64)) (pow.f64 (neg.f64 (pow.f64 #s(literal 16 binary64) #s(literal 1/64 binary64))) #s(literal 4 binary64)))
(*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 7/32 binary64)) #s(literal 1 binary64)) (pow.f64 #s(literal 16 binary64) #s(literal 1/64 binary64)))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 7/32 binary64)) (pow.f64 #s(literal 16 binary64) #s(literal 1/64 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) (pow.f64 #s(literal 16 binary64) #s(literal 1/32 binary64)))
(*.f64 (pow.f64 #s(literal 16 binary64) #s(literal 1/64 binary64)) (fabs.f64 (pow.f64 #s(literal 4 binary64) #s(literal 7/32 binary64))))
(*.f64 (pow.f64 #s(literal 16 binary64) #s(literal 1/64 binary64)) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 7/32 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 #s(literal 16 binary64) #s(literal 1/64 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal 7/32 binary64)))
(*.f64 (pow.f64 #s(literal 16 binary64) #s(literal 1/32 binary64)) (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)))
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(fma.f64 #s(approx (* x (sqrt x)) (pow.f64 x #s(literal 3/2 binary64))) (cosh.f64 (log.f64 (sqrt.f64 x))) (.f64 #s(approx ( x (sqrt x)) (pow.f64 x #s(literal 3/2 binary64))) (sinh.f64 (log.f64 (sqrt.f64 x)))))
(+.f64 (.f64 (neg.f64 (neg.f64 #s(approx ( x (sqrt x)) (pow.f64 x #s(literal 3/2 binary64))))) (cosh.f64 (log.f64 (sqrt.f64 x)))) (.f64 (neg.f64 (neg.f64 #s(approx ( x (sqrt x)) (pow.f64 x #s(literal 3/2 binary64))))) (sinh.f64 (log.f64 (sqrt.f64 x)))))
(+.f64 (.f64 #s(approx ( x (sqrt x)) (pow.f64 x #s(literal 3/2 binary64))) (cosh.f64 (log.f64 (sqrt.f64 x)))) (.f64 #s(approx ( x (sqrt x)) (pow.f64 x #s(literal 3/2 binary64))) (sinh.f64 (log.f64 (sqrt.f64 x)))))
#s(approx (* x (sqrt x)) (pow.f64 x #s(literal 3/2 binary64)))
(.f64 (.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (pow.f64 x #s(literal 1/4 binary64)))) (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (pow.f64 x #s(literal 1/4 binary64)))))
(.f64 (.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) (neg.f64 (sqrt.f64 x))) (*.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) (neg.f64 (sqrt.f64 x))))
(*.f64 (neg.f64 (neg.f64 (pow.f64 x #s(literal 3/4 binary64)))) (neg.f64 (neg.f64 (pow.f64 x #s(literal 3/4 binary64)))))
(*.f64 (neg.f64 (neg.f64 (pow.f64 x #s(literal 3/4 binary64)))) (neg.f64 (pow.f64 x #s(literal 3/4 binary64))))
(*.f64 (neg.f64 (neg.f64 (pow.f64 x #s(literal 3/4 binary64)))) (pow.f64 x #s(literal 3/4 binary64)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 9/4 binary64))) (pow.f64 x #s(literal 3/8 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 9/2 binary64)) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/8 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 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 (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 (neg.f64 (sqrt.f64 x)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
(*.f64 (pow.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) #s(literal 3 binary64)) (pow.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) #s(literal 3 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 5/4 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (neg.f64 (pow.f64 x #s(literal 3/4 binary64))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (pow.f64 x #s(literal 3/4 binary64))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (neg.f64 (pow.f64 x #s(literal 3/4 binary64))) #s(literal 1 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 9/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3/8 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 3/4 binary64)) (pow.f64 x #s(literal 3/8 binary64)))
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 x)) #s(literal 1 binary64)) x)
(*.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 x #s(literal 5/4 binary64)) (neg.f64 (pow.f64 x #s(literal 1/4 binary64))))
(*.f64 (pow.f64 x #s(literal 5/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 5/4 binary64)))
(*.f64 (neg.f64 (pow.f64 x #s(literal 3/4 binary64))) (neg.f64 (neg.f64 (pow.f64 x #s(literal 3/4 binary64)))))
(*.f64 (neg.f64 (pow.f64 x #s(literal 3/4 binary64))) (neg.f64 (pow.f64 x #s(literal 3/4 binary64))))
(*.f64 (neg.f64 (pow.f64 x #s(literal 3/4 binary64))) (pow.f64 x #s(literal 3/4 binary64)))
(*.f64 (pow.f64 x #s(literal 3/8 binary64)) (sqrt.f64 (pow.f64 x #s(literal 9/4 binary64))))
(*.f64 (pow.f64 x #s(literal 3/8 binary64)) (pow.f64 (pow.f64 x #s(literal 9/2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 x #s(literal 3/8 binary64)) (pow.f64 (pow.f64 x #s(literal 9/4 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 x #s(literal 3/8 binary64)) (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 3/4 binary64)))
(*.f64 (neg.f64 (sqrt.f64 x)) x)
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 (pow.f64 x #s(literal 5/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 5/4 binary64)))
(*.f64 (pow.f64 x #s(literal 3/4 binary64)) (neg.f64 (neg.f64 (pow.f64 x #s(literal 3/4 binary64)))))
(*.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 (neg.f64 (sqrt.f64 x)) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 (neg.f64 (pow.f64 x #s(literal 3/4 binary64))) #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal 3/4 binary64)) (neg.f64 (pow.f64 x #s(literal 3/4 binary64))))
(*.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
(*.f64 x (pow.f64 (neg.f64 (sqrt.f64 x)) #s(literal 1 binary64)))
(*.f64 x (neg.f64 (sqrt.f64 x)))
(*.f64 x (sqrt.f64 x))
(*.f64 (sqrt.f64 x) x)
(pow.f64 (exp.f64 #s(literal 3/2 binary64)) (log.f64 x))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 x) #s(literal 3 binary64)))
(pow.f64 (neg.f64 (pow.f64 x #s(literal 3/4 binary64))) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 3 binary64)) (/.f64 (log.f64 x) #s(literal 2 binary64)))
(pow.f64 (exp.f64 #s(literal 3 binary64)) (log.f64 (sqrt.f64 x)))
(pow.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/8 binary64))
(pow.f64 (neg.f64 (sqrt.f64 x)) #s(literal 3 binary64))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 6 binary64))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 3/8 binary64))
(pow.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 2 binary64))
(pow.f64 x #s(literal 3/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 3 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1 binary64))
(pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/4 binary64))
(/.f64 (-.f64 (.f64 (cosh.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x))) (cosh.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x)))) (.f64 (sinh.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x))) (sinh.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x))))) (-.f64 (cosh.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x))) (sinh.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x)))))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x))) (cosh.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x))) (-.f64 (.f64 (sinh.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x))) (sinh.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x)))) (.f64 (cosh.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x))) (sinh.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x)))))))
(/.f64 (hypot.f64 (pow.f64 (cosh.f64 (.f64 #s(literal -3 binary64) (log.f64 x))) #s(literal 3/2 binary64)) (pow.f64 (sinh.f64 (.f64 (log.f64 x) #s(literal 3 binary64))) #s(literal 3/2 binary64))) (sqrt.f64 (+.f64 (pow.f64 (cosh.f64 (.f64 #s(literal -3 binary64) (log.f64 x))) #s(literal 2 binary64)) (-.f64 (pow.f64 (sinh.f64 (.f64 (log.f64 x) #s(literal 3 binary64))) #s(literal 2 binary64)) (.f64 (cosh.f64 (.f64 #s(literal -3 binary64) (log.f64 x))) (sinh.f64 (*.f64 (log.f64 x) #s(literal 3 binary64))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))))
(neg.f64 (pow.f64 x #s(literal 3/2 binary64)))
(fma.f64 (neg.f64 (sqrt.f64 x)) (cosh.f64 (log.f64 x)) (*.f64 (neg.f64 (sqrt.f64 x)) (sinh.f64 (log.f64 x))))
(fma.f64 x (cosh.f64 (log.f64 (sqrt.f64 x))) (*.f64 x (sinh.f64 (log.f64 (sqrt.f64 x)))))
(fma.f64 (sqrt.f64 x) (cosh.f64 (log.f64 x)) (*.f64 (sqrt.f64 x) (sinh.f64 (log.f64 x))))
(sqrt.f64 (pow.f64 x #s(literal 3 binary64)))
(fabs.f64 (pow.f64 x #s(literal 3/2 binary64)))
(exp.f64 (+.f64 (/.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x)) #s(literal 2 binary64)) (.f64 (*.f64 #s(literal 3/2 binary64) (log.f64 x)) #s(literal 1/2 binary64))))
(exp.f64 (+.f64 (/.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x)) #s(literal 2 binary64)) (.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)) #s(literal 1/4 binary64))))
(exp.f64 (+.f64 (/.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x)) #s(literal 2 binary64)) (.f64 (log.f64 x) #s(literal 3/4 binary64))))
(exp.f64 (fma.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x)) #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x)) #s(literal 2 binary64))))
(exp.f64 (fma.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x)) #s(literal 1/2 binary64) (.f64 (*.f64 #s(literal 3/2 binary64) (log.f64 x)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x)) #s(literal 1/2 binary64) (.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)) #s(literal 1/4 binary64))))
(exp.f64 (fma.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x)) #s(literal 1/2 binary64) (.f64 (log.f64 x) #s(literal 3/4 binary64))))
(exp.f64 (fma.f64 (.f64 (log.f64 x) #s(literal 3 binary64)) #s(literal 1/4 binary64) (/.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x)) #s(literal 2 binary64))))
(exp.f64 (fma.f64 (.f64 (log.f64 x) #s(literal 3 binary64)) #s(literal 1/4 binary64) (.f64 (*.f64 #s(literal 3/2 binary64) (log.f64 x)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (.f64 (log.f64 x) #s(literal 3 binary64)) #s(literal 1/4 binary64) (.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)) #s(literal 1/4 binary64))))
(exp.f64 (fma.f64 (.f64 (log.f64 x) #s(literal 3 binary64)) #s(literal 1/4 binary64) (.f64 (log.f64 x) #s(literal 3/4 binary64))))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 3/4 binary64) (/.f64 (*.f64 #s(literal 3/2 binary64) (log.f64 x)) #s(literal 2 binary64))))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 3/4 binary64) (.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 3/4 binary64) (.f64 (.f64 (log.f64 x) #s(literal 3 binary64)) #s(literal 1/4 binary64))))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 3/4 binary64) (*.f64 (log.f64 x) #s(literal 3/4 binary64))))
(exp.f64 (.f64 (/.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 3/2 binary64) (log.f64 x)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 3/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 6 binary64) (log.f64 x)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 x #s(literal 3/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 x)) #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 3/4 binary64)))
(exp.f64 (*.f64 #s(literal 3/2 binary64) (log.f64 x)))
(+.f64 (.f64 (neg.f64 (sqrt.f64 x)) (cosh.f64 (log.f64 x))) (.f64 (neg.f64 (sqrt.f64 x)) (sinh.f64 (log.f64 x))))
(+.f64 (.f64 x (cosh.f64 (log.f64 (sqrt.f64 x)))) (.f64 x (sinh.f64 (log.f64 (sqrt.f64 x)))))
(+.f64 (.f64 (sqrt.f64 x) (cosh.f64 (log.f64 x))) (.f64 (sqrt.f64 x) (sinh.f64 (log.f64 x))))
(+.f64 (neg.f64 (cosh.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x)))) (neg.f64 (sinh.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x)))))
(+.f64 (cosh.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x))) (sinh.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x))))

eval53.0ms (2%)

Memory: -30.3MiB live, 67.2MiB allocated
Compiler: Compiled 6 452 to 1 432 computations (77.8% saved)

prune5.0ms (0.2%)

Memory

14.9MiB live, 14.9MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	276	1	277
Fresh	0	0	0
Picked	2	1	3
Done	1	4	5
Total	279	6	285

Accuracy

99.9%

Counts

285 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	50.6%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
✓	50.5%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x))))
✓	50.6%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
▶	99.0%	#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))
✓	20.4%	#s(approx (sqrt (* 2 (* x x))) x)

Compiler

Compiled 55 to 43 computations (21.8% saved)

simplify8.0ms (0.3%)

Memory

9.1MiB live, 9.1MiB allocated

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

localize26.0ms (1%)

Memory

-6.4MiB live, 39.6MiB allocated

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	0.43359375	(*.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

20.0ms

256×

valid

Compiler

Compiled 27 to 11 computations (59.3% saved)

Precisions

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

ival-sqrt: 7.0ms (49% of total)

ival-mult: 5.0ms (35% of total)

ival-pow2: 2.0ms (14% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

2.0MiB live, 2.0MiB allocated

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))

simplify3.0ms (0.1%)

Memory

4.0MiB live, 4.0MiB allocated

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 (1.7%)

Memory

6.5MiB live, 51.0MiB allocated

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)))))

eval11.0ms (0.4%)

Memory: -33.2MiB live, 10.8MiB allocated
Compiler: Compiled 794 to 191 computations (75.9% saved)

prune6.0ms (0.2%)

Memory

11.9MiB live, 11.9MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	45	0	45
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	45	6	51

Accuracy

99.9%

Counts

51 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	50.6%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
✓	50.5%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x))))
✓	50.6%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
✓	99.0%	#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))
✓	20.4%	#s(approx (sqrt (* 2 (* x x))) x)

Compiler

Compiled 147 to 88 computations (40.1% saved)

regimes12.0ms (0.4%)

Memory

21.1MiB live, 21.1MiB allocated

Counts

10 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
#s(approx (sqrt (* 2 (* x x))) x)
#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))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #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))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 #s(approx (* x (sqrt x)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x))))
#s(approx (sqrt (* 2 (* x x))) (*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x))

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

Calls

4 calls:

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

regimes5.0ms (0.2%)

Memory

9.6MiB live, 9.6MiB allocated

Counts

2 → 1

Calls

Call 1

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

Outputs
#s(approx (sqrt (* 2 (* x x))) x)

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
20.4%	1	`(*.f64 x x)`
20.4%	1	`(.f64 #s(literal 2 binary64) (.f64 x x))`
20.4%	1	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`
20.4%	1	`x`

Compiler

Compiled 15 to 12 computations (20% saved)

regimes12.0ms (0.4%)

Memory

-45.3MiB live, 10.1MiB allocated

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:

9.0ms	(.f64 #s(literal 2 binary64) (.f64 x x))
1.0ms	x
1.0ms	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
4.0%	1	`(*.f64 x x)`
4.0%	1	`(.f64 #s(literal 2 binary64) (.f64 x x))`
4.0%	1	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`
4.0%	1	`x`

Compiler

Compiled 15 to 12 computations (20% saved)

simplify40.0ms (1.5%)

Memory

-2.0MiB live, 43.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	20	20
2	57	20
3	128	20
4	199	20
5	261	20
6	451	20
7	2047	20
8	3202	20

Stop Event

1×	node limit

Calls

Call 1

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

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

derivations813.0ms (29.9%)

Memory

85.9MiB live, 153.0MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	81
0	35	61
1	76	59
2	257	17
3	1797	17
0	9824	17
0	5	14
0	8	13
1	24	13
2	102	5
0	777	5
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×	done
1×	iter limit
1×	saturated
1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit

Compiler

Compiled 20 to 11 computations (45% saved)

preprocess30.0ms (1.1%)

Memory: -54.9MiB live, 33.7MiB allocated
Compiler: Compiled 74 to 50 computations (32.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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	22	104
0	31	104
1	51	98
2	123	98
3	241	98
4	407	98
5	526	98
6	617	98
7	661	98
8	681	98
9	691	98
0	691	92

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	22	104
0	31	104
1	51	98
2	123	98
3	241	98
4	407	98
5	526	98
6	617	98
7	661	98
8	681	98
9	691	98
0	691	92

start0.0ms (0%)

analyze0.0ms (0%)

sample726.0ms (26.7%)

explain60.0ms (2.2%)

preprocess54.0ms (2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify6.0ms (0.2%)

localize15.0ms (0.5%)

series11.0ms (0.4%)

simplify8.0ms (0.3%)

rewrite36.0ms (1.3%)

eval2.0ms (0.1%)

prune3.0ms (0.1%)

simplify13.0ms (0.5%)

localize106.0ms (3.9%)

series8.0ms (0.3%)

simplify135.0ms (5%)

rewrite49.0ms (1.8%)

eval4.0ms (0.1%)

prune3.0ms (0.1%)

simplify20.0ms (0.7%)

localize65.0ms (2.4%)

series68.0ms (2.5%)

simplify148.0ms (5.4%)

rewrite108.0ms (4%)

eval53.0ms (2%)

prune5.0ms (0.2%)

simplify8.0ms (0.3%)

localize26.0ms (1%)

series1.0ms (0%)

simplify3.0ms (0.1%)

rewrite47.0ms (1.7%)

eval11.0ms (0.4%)

prune6.0ms (0.2%)

regimes12.0ms (0.4%)

regimes5.0ms (0.2%)

regimes12.0ms (0.4%)

simplify40.0ms (1.5%)

derivations813.0ms (29.9%)

preprocess30.0ms (1.1%)

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	22	104
0	31	104
1	51	98
2	123	98
3	241	98
4	407	98
5	526	98
6	617	98
7	661	98
8	681	98
9	691	98
0	691	92