Metrics for Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, A

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze1.0ms (0.1%)

Memory

2.4MiB live, 2.4MiB 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
50%	50%	50%	0%	0%	0%	0%	2
75%	75%	25%	0%	0%	0%	0%	3
87.5%	87.5%	12.5%	0%	0%	0%	0%	4
93.8%	93.7%	6.2%	0%	0%	0%	0%	5
96.9%	96.8%	3.1%	0%	0%	0%	0%	6
98.4%	98.4%	1.6%	0%	0%	0%	0%	7
99.2%	99.2%	0.8%	0%	0%	0%	0%	8
99.6%	99.6%	0.4%	0%	0%	0%	0%	9
99.8%	99.8%	0.2%	0%	0%	0%	0%	10
99.9%	99.9%	0.1%	0%	0%	0%	0%	11
100%	99.9%	0%	0%	0%	0%	0%	12

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample457.0ms (21.1%)

Memory

26.7MiB live, 1 093.3MiB allocated

Samples

277.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 140.0ms

ival-mult: 66.0ms (47.2% of total)

ival-div: 59.0ms (42.2% of total)

ival-true: 6.0ms (4.3% of total)

exact: 5.0ms (3.6% of total)

ival-assert: 3.0ms (2.1% of total)

Bogosity

explain44.0ms (2%)

Memory

-9.4MiB live, 111.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
5	-	-	`(/.f64 #s(literal 1 binary64) (*.f64 x x))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(*.f64 x x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`(/.f64 #s(literal 1 binary64) (*.f64 x x))`	n/o	5	0
↳	`(*.f64 x x)`	overflow	73

Confusion

	Predicted +	Predicted -
+	5	0
-	0	251

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	5	0	0
-	0	0	251

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	251
1	5

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

21.0ms

512×

valid

Compiler

Compiled 29 to 16 computations (44.8% saved)

Precisions

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

ival-mult: 6.0ms (53.4% of total)

ival-div: 5.0ms (44.5% of total)

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

exact: 0.0ms (0% of total)

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

preprocess17.0ms (0.8%)

Memory

1.1MiB live, 40.2MiB allocated

Algorithm

1×	egg-herbie

Rules

30×	`associate-/r*`
26×	`unsub-neg`
26×	`div-sub`
24×	`distribute-lft-neg-in`
20×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	24	10
2	67	10
3	135	10
4	185	10
5	223	10
6	235	10
0	4	5
0	6	5
1	10	5
0	10	5

Stop Event

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

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (*.f64 x x))

Outputs
(/.f64 #s(literal 1 binary64) (*.f64 x x))

Symmetry

(abs x)

Compiler

Compiled 5 to 4 computations (20% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.9%	(/.f64 #s(literal 1 binary64) (*.f64 x x))

Compiler

Compiled 5 to 4 computations (20% saved)

simplify3.0ms (0.1%)

Memory

7.4MiB live, 7.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Rules

6×	`lower-/.f32`
4×	`lower-/.f64`
2×	`lift-/.f64`
2×	`1-exp`
2×	`lift-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	10
0	6	10
1	10	10
0	10	10

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (*.f64 x x))
#s(literal 1 binary64)
(*.f64 x x)
x

Outputs
(/.f64 #s(literal 1 binary64) (*.f64 x x))
#s(literal 1 binary64)
(*.f64 x x)
x

localize14.0ms (0.6%)

Memory

-7.7MiB live, 31.3MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(*.f64 x x)
accuracy	0.7198032840812708	(/.f64 #s(literal 1 binary64) (*.f64 x x))

Samples

9.0ms

256×

valid

Compiler

Compiled 12 to 6 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-div: 2.0ms (53.5% of total)

ival-mult: 2.0ms (53.5% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0.1%)

Memory

5.7MiB live, 5.7MiB allocated

Counts

2 → 24

Calls

Call 1

Inputs
#s(alt (/.f64 #s(literal 1 binary64) (.f64 x x)) (patch (/.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())

Inputs

#s(alt (/.f64 #s(literal 1 binary64) (*.f64 x x)) (patch (/.f64 #s(literal 1 binary64) (*.f64 x x)) #<representation binary64>) () ())

#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())

Outputs
#s(alt (/ 1 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x x)) (patch (/.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x x)) (patch (/.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x x)) (patch (/.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x x)) (patch (/.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x x)) (patch (/.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x x)) (patch (/.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x x)) (patch (/.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x x)) (patch (/.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x x)) (patch (/.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x x)) (patch (/.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x x)) (patch (/.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x x)) (patch (/.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	((/ 1 (* x x)) (* x x))
0.0ms	x	@	inf	((/ 1 (* x x)) (* x x))
0.0ms	x	@	-inf	((/ 1 (* x x)) (* x x))

simplify3.0ms (0.1%)

Memory

7.8MiB live, 7.8MiB allocated

Algorithm

1×	egg-herbie

Rules

6×	`lower-/.f32`
6×	`lower-/.f64`
2×	`lower-*.f64`
2×	`lower-pow.f64`
2×	`1-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	96
1	8	96
2	10	96
0	10	96

Stop Event

1×	iter limit
1×	saturated

Counts

24 → 24

Calls

Call 1

Inputs
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

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

rewrite69.0ms (3.2%)

Memory

-39.5MiB live, 96.7MiB allocated

Rules

426×	`lower-*.f32`
424×	`lower-*.f64`
306×	`lower-/.f32`
304×	`lower-/.f64`
242×	`lower-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	4	8
0	6	8
1	20	6
2	72	6
3	260	6
0	1092	6

Stop Event

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

Counts

2 → 110

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 x x)

Outputs
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eval14.0ms (0.6%)

Memory: 2.5MiB live, 41.6MiB allocated
Compiler: Compiled 1 151 to 263 computations (77.2% saved)

prune4.0ms (0.2%)

Memory

14.4MiB live, 14.4MiB allocated

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	131	3	134
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	131	4	135

Accuracy

100.0%

Counts

135 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(pow.f64 x #s(literal -2 binary64))
▶	99.8%	(/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 x))
▶	98.6%	(/.f64 #s(literal 1 binary64) (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)))
✓	98.9%	(/.f64 #s(literal 1 binary64) (*.f64 x x))

Compiler

Compiled 23 to 18 computations (21.7% saved)

simplify25.0ms (1.2%)

Memory

-13.5MiB live, 25.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 x #s(literal -2 binary64))
cost-diff	0	(neg.f64 x)
cost-diff	0	(/.f64 #s(literal -1 binary64) x)
cost-diff	512	(/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 x))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(*.f64 x (sqrt.f64 x))
cost-diff	0	(/.f64 #s(literal 1 binary64) (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)))
cost-diff	1600	(.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))

Rules

224×	`lower-fma.f64`
224×	`lower-fma.f32`
224×	`lower-*.f32`
220×	`lower-*.f64`
154×	`times-frac`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	42
0	20	45
1	34	33
2	56	33
3	109	33
4	180	33
5	218	33
6	252	33
7	275	33
8	297	33
9	322	33
10	336	33
11	422	33
12	566	33
13	605	33
14	607	33
15	608	33
0	608	33

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize39.0ms (1.8%)

Memory

-5.4MiB live, 72.9MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 x #s(literal -2 binary64))
accuracy	0	(/.f64 #s(literal -1 binary64) x)
accuracy	0	(neg.f64 x)
accuracy	0.11328125	(/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 x))
accuracy	0	(sqrt.f64 x)
accuracy	0.1484375	(*.f64 x (sqrt.f64 x))
accuracy	0.185878759768442	(.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))
accuracy	0.7198032840812708	(/.f64 #s(literal 1 binary64) (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)))

Samples

28.0ms

256×

valid

Compiler

Compiled 44 to 14 computations (68.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-pow: 6.0ms (33.3% of total)

ival-div: 5.0ms (27.8% of total)

ival-mult: 3.0ms (16.7% of total)

ival-sqrt: 2.0ms (11.1% of total)

ival-neg: 1.0ms (5.6% of total)

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

exact: 0.0ms (0% of total)

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

series8.0ms (0.4%)

Memory

17.9MiB live, 17.9MiB allocated

Counts

8 → 96

Calls

Call 1

Inputs
#s(alt (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)) (patch (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))) (patch (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))) #<representation binary64>) () ())
#s(alt (.f64 x (sqrt.f64 x)) (patch (.f64 x (sqrt.f64 x)) #<representation binary64>) () ())
#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())
#s(alt (/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 x)) (patch (/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 x)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1 binary64) x) (patch (/.f64 #s(literal -1 binary64) x) #<representation binary64>) () ())
#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())
#s(alt (pow.f64 x #s(literal -2 binary64)) (patch (pow.f64 x #s(literal -2 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)) (patch (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)) (patch (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)) (patch (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)) (patch (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))) (patch (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))) (patch (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))) (patch (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))) (patch (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (sqrt (pow x 3)) (taylor 0 x) (#s(alt (.f64 x (sqrt.f64 x)) (patch (.f64 x (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (pow x 3)) (taylor 0 x) (#s(alt (.f64 x (sqrt.f64 x)) (patch (.f64 x (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (pow x 3)) (taylor 0 x) (#s(alt (.f64 x (sqrt.f64 x)) (patch (.f64 x (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (pow x 3)) (taylor 0 x) (#s(alt (.f64 x (sqrt.f64 x)) (patch (.f64 x (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 x)) (patch (/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 x)) (patch (/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 x)) (patch (/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 x)) (patch (/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ -1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) x) (patch (/.f64 #s(literal -1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) x) (patch (/.f64 #s(literal -1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) x) (patch (/.f64 #s(literal -1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) x) (patch (/.f64 #s(literal -1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor 0 x) (#s(alt (pow.f64 x #s(literal -2 binary64)) (patch (pow.f64 x #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor 0 x) (#s(alt (pow.f64 x #s(literal -2 binary64)) (patch (pow.f64 x #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor 0 x) (#s(alt (pow.f64 x #s(literal -2 binary64)) (patch (pow.f64 x #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor 0 x) (#s(alt (pow.f64 x #s(literal -2 binary64)) (patch (pow.f64 x #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)) (patch (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)) (patch (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)) (patch (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)) (patch (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))) (patch (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))) (patch (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))) (patch (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))) (patch (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (sqrt (pow x 3)) (taylor inf x) (#s(alt (.f64 x (sqrt.f64 x)) (patch (.f64 x (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (pow x 3)) (taylor inf x) (#s(alt (.f64 x (sqrt.f64 x)) (patch (.f64 x (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (pow x 3)) (taylor inf x) (#s(alt (.f64 x (sqrt.f64 x)) (patch (.f64 x (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (pow x 3)) (taylor inf x) (#s(alt (.f64 x (sqrt.f64 x)) (patch (.f64 x (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor inf x) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 x)) (patch (/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor inf x) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 x)) (patch (/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor inf x) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 x)) (patch (/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor inf x) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 x)) (patch (/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ -1 x) (taylor inf x) (#s(alt (/.f64 #s(literal -1 binary64) x) (patch (/.f64 #s(literal -1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -1 x) (taylor inf x) (#s(alt (/.f64 #s(literal -1 binary64) x) (patch (/.f64 #s(literal -1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -1 x) (taylor inf x) (#s(alt (/.f64 #s(literal -1 binary64) x) (patch (/.f64 #s(literal -1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -1 x) (taylor inf x) (#s(alt (/.f64 #s(literal -1 binary64) x) (patch (/.f64 #s(literal -1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor inf x) (#s(alt (pow.f64 x #s(literal -2 binary64)) (patch (pow.f64 x #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor inf x) (#s(alt (pow.f64 x #s(literal -2 binary64)) (patch (pow.f64 x #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor inf x) (#s(alt (pow.f64 x #s(literal -2 binary64)) (patch (pow.f64 x #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor inf x) (#s(alt (pow.f64 x #s(literal -2 binary64)) (patch (pow.f64 x #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 2) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)) (patch (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 2) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)) (patch (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 2) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)) (patch (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 2) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)) (patch (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ -1 (* (pow x 2) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))) (patch (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ -1 (* (pow x 2) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))) (patch (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ -1 (* (pow x 2) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))) (patch (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ -1 (* (pow x 2) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))) (patch (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 x (sqrt.f64 x)) (patch (.f64 x (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 x (sqrt.f64 x)) (patch (.f64 x (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 x (sqrt.f64 x)) (patch (.f64 x (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 x (sqrt.f64 x)) (patch (.f64 x (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 x)) (patch (/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 x)) (patch (/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 x)) (patch (/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 x)) (patch (/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ -1 x) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) x) (patch (/.f64 #s(literal -1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -1 x) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) x) (patch (/.f64 #s(literal -1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -1 x) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) x) (patch (/.f64 #s(literal -1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -1 x) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) x) (patch (/.f64 #s(literal -1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor -inf x) (#s(alt (pow.f64 x #s(literal -2 binary64)) (patch (pow.f64 x #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor -inf x) (#s(alt (pow.f64 x #s(literal -2 binary64)) (patch (pow.f64 x #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor -inf x) (#s(alt (pow.f64 x #s(literal -2 binary64)) (patch (pow.f64 x #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor -inf x) (#s(alt (pow.f64 x #s(literal -2 binary64)) (patch (pow.f64 x #s(literal -2 binary64)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

4.0ms

-inf

((* (* x (sqrt x)) (sqrt x)) (/ 1 (* (* x (sqrt x)) (sqrt x))) (* x (sqrt x)) (sqrt x) (/ (/ -1 x) (neg x)) (/ -1 x) (neg x) (pow x -2))

2.0ms

inf

((* (* x (sqrt x)) (sqrt x)) (/ 1 (* (* x (sqrt x)) (sqrt x))) (* x (sqrt x)) (sqrt x) (/ (/ -1 x) (neg x)) (/ -1 x) (neg x) (pow x -2))

1.0ms

((* (* x (sqrt x)) (sqrt x)) (/ 1 (* (* x (sqrt x)) (sqrt x))) (* x (sqrt x)) (sqrt x) (/ (/ -1 x) (neg x)) (/ -1 x) (neg x) (pow x -2))

simplify64.0ms (2.9%)

Memory

3.9MiB live, 42.7MiB allocated

Algorithm

1×	egg-herbie

Rules

608×	`lower-*.f64`
608×	`lower-fma.f64`
608×	`lower-fma.f32`
608×	`lower-*.f32`
392×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	348
1	46	348
2	119	348
3	268	348
4	673	348
5	1132	348
6	1458	348
7	1834	348
8	2076	348
9	2113	348
10	2113	348
11	2113	348
12	2113	348
13	2113	348
0	2113	348

Stop Event

1×	iter limit
1×	saturated

Counts

96 → 96

Calls

Call 1

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

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

rewrite86.0ms (4%)

Memory

-8.1MiB live, 111.5MiB allocated

Rules

382×	`lower-*.f32`
378×	`lower-*.f64`
232×	`lower-/.f32`
226×	`lower-/.f64`
164×	`lower-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	36
0	20	45
1	62	22
2	268	21
0	1155	21

Stop Event

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

Counts

8 → 414

Calls

Call 1

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

Outputs
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eval55.0ms (2.5%)

Memory: 28.4MiB live, 103.1MiB allocated
Compiler: Compiled 4 917 to 800 computations (83.7% saved)

prune24.0ms (1.1%)

Memory

-34.1MiB live, 44.5MiB allocated

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	539	1	540
Fresh	0	0	0
Picked	0	3	3
Done	0	1	1
Total	539	5	544

Accuracy

100.0%

Counts

544 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(pow.f64 x #s(literal -2 binary64))
▶	99.6%	(/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (neg.f64 x))
✓	99.8%	(/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 x))
✓	98.6%	(/.f64 #s(literal 1 binary64) (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)))
✓	98.9%	(/.f64 #s(literal 1 binary64) (*.f64 x x))

Compiler

Compiled 33 to 25 computations (24.2% saved)

simplify25.0ms (1.2%)

Memory

33.4MiB live, 33.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(/.f64 #s(literal -1 binary64) (sqrt.f64 x))
cost-diff	512	(/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (neg.f64 x))
cost-diff	1984	(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x))

Rules

224×	`lower-*.f64`
224×	`lower-fma.f64`
224×	`lower-fma.f32`
224×	`lower-*.f32`
158×	`times-frac`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	7	27
0	12	27
1	21	19
2	43	18
3	106	18
4	177	18
5	211	18
6	243	18
7	266	18
8	293	18
9	319	18
10	327	18
11	406	18
12	550	18
13	589	18
14	591	18
15	592	18
0	592	18

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize25.0ms (1.2%)

Memory

-1.8MiB live, 35.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(neg.f64 x)
accuracy	0.11328125	(/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (neg.f64 x))
accuracy	0.21875	(/.f64 #s(literal -1 binary64) (sqrt.f64 x))
accuracy	0.34375	(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x))

Samples

20.0ms

256×

valid

Compiler

Compiled 29 to 9 computations (69% saved)

Precisions

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

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

ival-sqrt: 6.0ms (43.6% of total)

ival-neg: 1.0ms (7.3% of total)

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

exact: 0.0ms (0% of total)

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

series9.0ms (0.4%)

Memory

-28.0MiB live, 10.4MiB allocated

Counts

5 → 60

Calls

Call 1

Inputs
#s(alt (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (patch (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())
#s(alt (/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (neg.f64 x)) (patch (/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (neg.f64 x)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())
#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())
#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())

Outputs
#s(alt (/ -1 x) (taylor 0 x) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (patch (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ -1 x) (taylor 0 x) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (patch (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ -1 x) (taylor 0 x) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (patch (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ -1 x) (taylor 0 x) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (patch (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (neg.f64 x)) (patch (/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (neg.f64 x)) (patch (/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (neg.f64 x)) (patch (/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (neg.f64 x)) (patch (/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 x))) (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 x))) (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 x))) (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 x))) (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ -1 x) (taylor inf x) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (patch (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ -1 x) (taylor inf x) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (patch (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ -1 x) (taylor inf x) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (patch (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ -1 x) (taylor inf x) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (patch (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor inf x) (#s(alt (/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (neg.f64 x)) (patch (/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor inf x) (#s(alt (/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (neg.f64 x)) (patch (/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor inf x) (#s(alt (/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (neg.f64 x)) (patch (/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor inf x) (#s(alt (/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (neg.f64 x)) (patch (/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 x))) (taylor inf x) (#s(alt (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 x))) (taylor inf x) (#s(alt (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 x))) (taylor inf x) (#s(alt (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 x))) (taylor inf x) (#s(alt (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ 1 (* x (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (patch (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (* x (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (patch (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (* x (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (patch (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (* x (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (patch (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ -1 (* (pow x 2) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (neg.f64 x)) (patch (/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ -1 (* (pow x 2) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (neg.f64 x)) (patch (/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ -1 (* (pow x 2) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (neg.f64 x)) (patch (/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ -1 (* (pow x 2) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (neg.f64 x)) (patch (/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 x))) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 x))) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 x))) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 x))) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

5.0ms

-inf

((/ (/ -1 (sqrt x)) (sqrt x)) (/ (/ (/ -1 (sqrt x)) (sqrt x)) (neg x)) (/ -1 (sqrt x)) (sqrt x) (neg x))

1.0ms

((/ (/ -1 (sqrt x)) (sqrt x)) (/ (/ (/ -1 (sqrt x)) (sqrt x)) (neg x)) (/ -1 (sqrt x)) (sqrt x) (neg x))

1.0ms

inf

((/ (/ -1 (sqrt x)) (sqrt x)) (/ (/ (/ -1 (sqrt x)) (sqrt x)) (neg x)) (/ -1 (sqrt x)) (sqrt x) (neg x))

simplify50.0ms (2.3%)

Memory

4.9MiB live, 52.2MiB allocated

Algorithm

1×	egg-herbie

Rules

420×	`lower-*.f64`
420×	`lower-fma.f64`
420×	`lower-fma.f32`
420×	`lower-*.f32`
212×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	204
1	38	204
2	87	204
3	156	204
4	315	204
5	556	204
6	954	204
7	1260	204
8	1414	204
9	1434	204
10	1434	204
11	1434	204
0	1434	204

Stop Event

1×	iter limit
1×	saturated

Counts

60 → 60

Calls

Call 1

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

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

rewrite64.0ms (2.9%)

Memory

5.7MiB live, 121.4MiB allocated

Rules

1 544×	`lower-fma.f64`
1 544×	`lower-fma.f32`
1 168×	`lower-*.f64`
1 168×	`lower-*.f32`
1 154×	`frac-times`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	7	25
0	12	25
1	43	16
2	262	15
3	2190	12
0	8042	12

Stop Event

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

Counts

5 → 783

Calls

Call 1

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

Outputs
#<batchref>
#<batchref>
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#<batchref>
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#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
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eval119.0ms (5.5%)

Memory: 11.1MiB live, 204.5MiB allocated
Compiler: Compiled 13 343 to 2 177 computations (83.7% saved)

prune17.0ms (0.8%)

Memory

12.7MiB live, 49.4MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	983	2	985
Fresh	0	0	0
Picked	0	1	1
Done	1	3	4
Total	984	6	990

Accuracy

100.0%

Counts

990 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(pow.f64 x #s(literal -2 binary64))
▶	99.6%	(/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 x))) (sqrt.f64 x)) (neg.f64 x))
✓	99.6%	(/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (neg.f64 x))
✓	98.6%	(/.f64 #s(literal 1 binary64) (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)))
✓	98.9%	(/.f64 #s(literal 1 binary64) (*.f64 x x))
▶	99.8%	#s(approx (/ (/ (/ -1 (sqrt x)) (sqrt x)) (neg x)) (/.f64 (/.f64 #s(literal 1 binary64) x) x))

Compiler

Compiled 45 to 33 computations (26.7% saved)

simplify286.0ms (13.2%)

Memory

-136.1MiB live, 90.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 x)))
cost-diff	512	(/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 x))) (sqrt.f64 x)) (neg.f64 x))
cost-diff	704	(/.f64 x (sqrt.f64 x))
cost-diff	1984	(/.f64 (/.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 x))) (sqrt.f64 x))
cost-diff	0	(/.f64 #s(literal 1 binary64) x)
cost-diff	0	#s(approx (/ (/ (/ -1 (sqrt x)) (sqrt x)) (neg x)) (/.f64 (/.f64 #s(literal 1 binary64) x) x))
cost-diff	384	(/.f64 (/.f64 #s(literal 1 binary64) x) x)

Rules

3 316×	`lower-*.f64`
3 316×	`lower-*.f32`
2 570×	`lower-fma.f64`
2 570×	`lower-fma.f32`
2 504×	`lower-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	63
0	26	58
1	45	54
2	97	46
3	296	41
4	1043	41
5	2219	41
6	3542	41
7	4379	41
8	5670	41
9	6501	41
10	6976	41
11	7565	41
0	8094	41

Stop Event

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

Calls

Call 1

Inputs
#s(approx (/ (/ (/ -1 (sqrt x)) (sqrt x)) (neg x)) (/.f64 (/.f64 #s(literal 1 binary64) x) x))
(/.f64 (/.f64 #s(literal 1 binary64) x) x)
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 x))) (sqrt.f64 x)) (neg.f64 x))
(/.f64 (/.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 x))) (sqrt.f64 x))
(/.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 x)))
#s(literal -1 binary64)
(/.f64 x (sqrt.f64 x))
x
(sqrt.f64 x)
(neg.f64 x)

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

localize57.0ms (2.6%)

Memory

-18.0MiB live, 62.7MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0.11328125	(/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 x))) (sqrt.f64 x)) (neg.f64 x))
accuracy	0.21875	(/.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 x)))
accuracy	0.34375	(/.f64 (/.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 x))) (sqrt.f64 x))
accuracy	0.45703125	(/.f64 x (sqrt.f64 x))
accuracy	0	(/.f64 #s(literal 1 binary64) x)
accuracy	0	#s(approx (/ (/ (/ -1 (sqrt x)) (sqrt x)) (neg x)) (/.f64 (/.f64 #s(literal 1 binary64) x) x))
accuracy	0.11328125	(/.f64 (/.f64 #s(literal 1 binary64) x) x)

Samples

32.0ms

256×

valid

Compiler

Compiled 59 to 16 computations (72.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-div: 20.0ms (84.2% of total)

ival-sqrt: 2.0ms (8.4% of total)

ival-neg: 1.0ms (4.2% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.2%)

Memory

9.2MiB live, 9.2MiB allocated

Counts

7 → 84

Calls

Call 1

Inputs
#s(alt (/.f64 (/.f64 #s(literal 1 binary64) x) x) (patch (/.f64 (/.f64 #s(literal 1 binary64) x) x) #<representation binary64>) () ())
#s(alt #s(approx (/ (/ (/ -1 (sqrt x)) (sqrt x)) (neg x)) (/.f64 (/.f64 #s(literal 1 binary64) x) x)) (patch #s(approx (/ (/ (/ -1 (sqrt x)) (sqrt x)) (neg x)) (/.f64 (/.f64 #s(literal 1 binary64) x) x)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())
#s(alt (/.f64 (/.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 x))) (sqrt.f64 x)) (patch (/.f64 (/.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 x))) (sqrt.f64 x)) #<representation binary64>) () ())
#s(alt (/.f64 x (sqrt.f64 x)) (patch (/.f64 x (sqrt.f64 x)) #<representation binary64>) () ())
#s(alt (/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 x))) (sqrt.f64 x)) (neg.f64 x)) (patch (/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 x))) (sqrt.f64 x)) (neg.f64 x)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 x))) (patch (/.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 x))) #<representation binary64>) () ())

Outputs
#s(alt (/ 1 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 (/.f64 #s(literal 1 binary64) x) x) (patch (/.f64 (/.f64 #s(literal 1 binary64) x) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 (/.f64 #s(literal 1 binary64) x) x) (patch (/.f64 (/.f64 #s(literal 1 binary64) x) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 (/.f64 #s(literal 1 binary64) x) x) (patch (/.f64 (/.f64 #s(literal 1 binary64) x) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 (/.f64 #s(literal 1 binary64) x) x) (patch (/.f64 (/.f64 #s(literal 1 binary64) x) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor 0 x) (#s(alt #s(approx (/ (/ (/ -1 (sqrt x)) (sqrt x)) (neg x)) (/.f64 (/.f64 #s(literal 1 binary64) x) x)) (patch #s(approx (/ (/ (/ -1 (sqrt x)) (sqrt x)) (neg x)) (/.f64 (/.f64 #s(literal 1 binary64) x) x)) #<representation binary64>) () ())) ())
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Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

-inf

((/ (/ 1 x) x) (/ (/ (/ -1 (sqrt x)) (sqrt x)) (neg x)) (/ 1 x) (/ (/ -1 (/ x (sqrt x))) (sqrt x)) (/ x (sqrt x)) (/ (/ (/ -1 (/ x (sqrt x))) (sqrt x)) (neg x)) (/ -1 (/ x (sqrt x))))

1.0ms

((/ (/ 1 x) x) (/ (/ (/ -1 (sqrt x)) (sqrt x)) (neg x)) (/ 1 x) (/ (/ -1 (/ x (sqrt x))) (sqrt x)) (/ x (sqrt x)) (/ (/ (/ -1 (/ x (sqrt x))) (sqrt x)) (neg x)) (/ -1 (/ x (sqrt x))))

1.0ms

inf

((/ (/ 1 x) x) (/ (/ (/ -1 (sqrt x)) (sqrt x)) (neg x)) (/ 1 x) (/ (/ -1 (/ x (sqrt x))) (sqrt x)) (/ x (sqrt x)) (/ (/ (/ -1 (/ x (sqrt x))) (sqrt x)) (neg x)) (/ -1 (/ x (sqrt x))))

simplify17.0ms (0.8%)

Memory

-22.8MiB live, 13.6MiB allocated

Algorithm

1×	egg-herbie

Rules

64×	`associate-/r*`
60×	`lower-+.f64`
60×	`lower-+.f32`
58×	`lower-*.f64`
58×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	336
1	26	336
2	53	336
3	86	336
4	110	336
5	120	336
6	137	336
7	156	336
8	170	336
9	192	336
10	211	336
11	233	336
12	235	336
0	235	336

Stop Event

1×	iter limit
1×	saturated

Counts

84 → 84

Calls

Call 1

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

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

rewrite86.0ms (4%)

Memory

0.6MiB live, 87.2MiB allocated

Rules

896×	`lower-*.f64`
896×	`lower-*.f32`
668×	`lower-/.f32`
656×	`lower-/.f64`
496×	`times-frac`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	55
0	26	48
1	97	33
2	590	25
0	2530	25

Stop Event

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

Counts

7 → 320

Calls

Call 1

Inputs
(/.f64 (/.f64 #s(literal 1 binary64) x) x)
#s(approx (/ (/ (/ -1 (sqrt x)) (sqrt x)) (neg x)) (/.f64 (/.f64 #s(literal 1 binary64) x) x))
(/.f64 #s(literal 1 binary64) x)
(/.f64 (/.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 x))) (sqrt.f64 x))
(/.f64 x (sqrt.f64 x))
(/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 x))) (sqrt.f64 x)) (neg.f64 x))
(/.f64 #s(literal -1 binary64) (/.f64 x (sqrt.f64 x)))

Outputs
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eval42.0ms (1.9%)

Memory: 0.4MiB live, 75.8MiB allocated
Compiler: Compiled 4 346 to 848 computations (80.5% saved)

prune15.0ms (0.7%)

Memory

-4.1MiB live, 34.9MiB allocated

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	402	2	404
Fresh	0	0	0
Picked	1	1	2
Done	0	4	4
Total	403	7	410

Accuracy

100.0%

Counts

410 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(pow.f64 x #s(literal -2 binary64))
	99.7%	(/.f64 (/.f64 (/.f64 (sqrt.f64 x) (neg.f64 x)) (sqrt.f64 x)) (neg.f64 x))
✓	99.6%	(/.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (neg.f64 x))
✓	98.6%	(/.f64 #s(literal 1 binary64) (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x)))
✓	98.9%	(/.f64 #s(literal 1 binary64) (*.f64 x x))
✓	99.8%	#s(approx (/ (/ (/ -1 (sqrt x)) (sqrt x)) (neg x)) (/.f64 (/.f64 #s(literal 1 binary64) x) x))
	99.5%	#s(approx (/ (/ (/ -1 (sqrt x)) (sqrt x)) (neg x)) (/.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) x))

Compiler

Compiled 130 to 68 computations (47.7% saved)

regimes9.0ms (0.4%)

Memory

16.5MiB live, 16.5MiB allocated

Counts

9 → 1

Calls

Call 1

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

Outputs
(pow.f64 x #s(literal -2 binary64))

Calls

3 calls:

3.0ms	x
3.0ms	(*.f64 x x)
3.0ms	(/.f64 #s(literal 1 binary64) (*.f64 x x))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(/.f64 #s(literal 1 binary64) (*.f64 x x))`
100.0%	1	`(*.f64 x x)`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes9.0ms (0.4%)

Memory

15.6MiB live, 15.6MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

3 calls:

3.0ms	x
3.0ms	(*.f64 x x)
3.0ms	(/.f64 #s(literal 1 binary64) (*.f64 x x))

Results

Accuracy	Segments	Branch
99.8%	1	`x`
99.8%	1	`(/.f64 #s(literal 1 binary64) (*.f64 x x))`
99.8%	1	`(*.f64 x x)`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes6.0ms (0.3%)

Memory

-36.3MiB live, 8.2MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (*.f64 x x))

Outputs
(/.f64 #s(literal 1 binary64) (*.f64 x x))

Calls

3 calls:

4.0ms	x
1.0ms	(/.f64 #s(literal 1 binary64) (*.f64 x x))
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
98.9%	1	`x`
98.9%	1	`(/.f64 #s(literal 1 binary64) (*.f64 x x))`
98.9%	1	`(*.f64 x x)`

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify23.0ms (1.1%)

Memory

4.2MiB live, 42.8MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`1-exp-binary32-exp.f32`
2×	`1-exp-binary64-exp.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	18	24

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness328.0ms (15.1%)

Memory

31.1MiB live, 224.9MiB allocated

Rules

426×	`lower-*.f32`
424×	`lower-*.f64`
420×	`lower-*.f64`
420×	`lower-fma.f64`
420×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	204
1	38	204
2	87	204
3	156	204
4	315	204
5	556	204
6	954	204
7	1260	204
8	1414	204
9	1434	204
10	1434	204
11	1434	204
0	1434	204
0	12	36
0	20	45
1	62	22
2	268	21
0	1155	21
0	4	8
0	6	8
1	20	6
2	72	6
3	260	6
0	1092	6

Stop Event

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

Compiler

Compiled 54 to 36 computations (33.3% saved)

preprocess46.0ms (2.1%)

Memory: 5.2MiB live, 86.7MiB allocated
Remove: (abs x)
Compiler: Compiled 60 to 46 computations (23.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	12	42
0	20	45
1	34	33
2	56	33
3	109	33
4	180	33
5	218	33
6	252	33
7	275	33
8	297	33
9	322	33
10	336	33
11	422	33
12	566	33
13	605	33
14	607	33
15	608	33
0	608	33

Iter	Nodes	Cost
0	7	27
0	12	27
1	21	19
2	43	18
3	106	18
4	177	18
5	211	18
6	243	18
7	266	18
8	293	18
9	319	18
10	327	18
11	406	18
12	550	18
13	589	18
14	591	18
15	592	18
0	592	18

Iter	Nodes	Cost
0	16	336
1	26	336
2	53	336
3	86	336
4	110	336
5	120	336
6	137	336
7	156	336
8	170	336
9	192	336
10	211	336
11	233	336
12	235	336
0	235	336

Iter	Nodes	Cost
0	12	42
0	20	45
1	34	33
2	56	33
3	109	33
4	180	33
5	218	33
6	252	33
7	275	33
8	297	33
9	322	33
10	336	33
11	422	33
12	566	33
13	605	33
14	607	33
15	608	33
0	608	33

Iter	Nodes	Cost
0	7	27
0	12	27
1	21	19
2	43	18
3	106	18
4	177	18
5	211	18
6	243	18
7	266	18
8	293	18
9	319	18
10	327	18
11	406	18
12	550	18
13	589	18
14	591	18
15	592	18
0	592	18

Iter	Nodes	Cost
0	16	336
1	26	336
2	53	336
3	86	336
4	110	336
5	120	336
6	137	336
7	156	336
8	170	336
9	192	336
10	211	336
11	233	336
12	235	336
0	235	336

start0.0ms (0%)

analyze1.0ms (0.1%)

sample457.0ms (21.1%)

explain44.0ms (2%)

preprocess17.0ms (0.8%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize14.0ms (0.6%)

series2.0ms (0.1%)

simplify3.0ms (0.1%)

rewrite69.0ms (3.2%)

eval14.0ms (0.6%)

prune4.0ms (0.2%)

simplify25.0ms (1.2%)

localize39.0ms (1.8%)

series8.0ms (0.4%)

simplify64.0ms (2.9%)

rewrite86.0ms (4%)

eval55.0ms (2.5%)

prune24.0ms (1.1%)

simplify25.0ms (1.2%)

localize25.0ms (1.2%)

series9.0ms (0.4%)

simplify50.0ms (2.3%)

rewrite64.0ms (2.9%)

eval119.0ms (5.5%)

prune17.0ms (0.8%)

simplify286.0ms (13.2%)

localize57.0ms (2.6%)

series5.0ms (0.2%)

simplify17.0ms (0.8%)

rewrite86.0ms (4%)

eval42.0ms (1.9%)

prune15.0ms (0.7%)

regimes9.0ms (0.4%)

regimes9.0ms (0.4%)

regimes6.0ms (0.3%)

simplify23.0ms (1.1%)

soundness328.0ms (15.1%)

preprocess46.0ms (2.1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	12	42
0	20	45
1	34	33
2	56	33
3	109	33
4	180	33
5	218	33
6	252	33
7	275	33
8	297	33
9	322	33
10	336	33
11	422	33
12	566	33
13	605	33
14	607	33
15	608	33
0	608	33

Iter	Nodes	Cost
0	7	27
0	12	27
1	21	19
2	43	18
3	106	18
4	177	18
5	211	18
6	243	18
7	266	18
8	293	18
9	319	18
10	327	18
11	406	18
12	550	18
13	589	18
14	591	18
15	592	18
0	592	18

Iter	Nodes	Cost
0	16	336
1	26	336
2	53	336
3	86	336
4	110	336
5	120	336
6	137	336
7	156	336
8	170	336
9	192	336
10	211	336
11	233	336
12	235	336
0	235	336