Metrics for sqrt A (should all be same)

analyze0.0ms (0%)

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 10 to 5 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

Operation ival-sqrt, time spent: 0.0ms, 0.0% of total-time

Operation ival-add, time spent: 0.0ms, 0.0% of total-time

Operation ival-mult, time spent: 0.0ms, 0.0% of total-time

Operation const, time spent: 0.0ms, 0.0% of total-time

sample1.2s (29.4%)

Results

1.2s	8251×	256	valid
0.0ms	4×	256	infinite
0.0ms	1×	256	valid

Precisions

Click to see histograms. Total time spent on operations: 319.0ms

Operation ival-sqrt, time spent: 178.0ms, 56.0% of total-time

Operation ival-mult, time spent: 75.0ms, 24.0% of total-time

Operation ival-add, time spent: 57.0ms, 18.0% of total-time

Operation const, time spent: 8.0ms, 3.0% of total-time

Bogosity

preprocess119.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

112×	`fma-define`
80×	`fma-neg`
40×	`associate-r`
30×	`distribute-lft-neg-in`
26×	`sub-neg`

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
134	-	2	(3.484050276567062e-157)	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
0	-	0	-	`x`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`(+.f64 (.f64 x x) (.f64 x x))`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	56
1	36	56
2	82	56
3	197	56
4	302	56
5	362	56
6	364	56

Stop Event

1×

saturated

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(sqrt.f64 (+.f64 (.f64 (neg.f64 x) (neg.f64 x)) (.f64 (neg.f64 x) (neg.f64 x))))
(neg.f64 (sqrt.f64 (+.f64 (.f64 (neg.f64 x) (neg.f64 x)) (.f64 (neg.f64 x) (neg.f64 x)))))

Outputs
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(hypot.f64 x x)
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(hypot.f64 x x)
(sqrt.f64 (+.f64 (.f64 (neg.f64 x) (neg.f64 x)) (.f64 (neg.f64 x) (neg.f64 x))))
(hypot.f64 x x)
(neg.f64 (sqrt.f64 (+.f64 (.f64 (neg.f64 x) (neg.f64 x)) (.f64 (neg.f64 x) (neg.f64 x)))))
(neg.f64 (hypot.f64 x x))

Symmetry

(abs x)

Compiler

Compiled 51 to 14 computations (72.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

Operation ival-sqrt, time spent: 7.0ms, 48.0% of total-time

Operation ival-mult, time spent: 4.0ms, 28.0% of total-time

Operation ival-add, time spent: 3.0ms, 21.0% of total-time

Operation const, time spent: 1.0ms, 7.0% of total-time

eval0.0ms (0%)

Compiler: Compiled 4 to 2 computations (50% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)

Compiler

Compiled 4 to 2 computations (50% saved)

localize162.0ms (3.8%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	100.0%	(hypot.f64 x x)

Compiler

Compiled 6 to 3 computations (50% saved)

Precisions

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

Operation composed, time spent: 10.0ms, 54.0% of total-time

Operation ival-mult, time spent: 4.0ms, 22.0% of total-time

Operation ival-sqrt, time spent: 4.0ms, 22.0% of total-time

Operation ival-add, time spent: 1.0ms, 5.0% of total-time

Operation const, time spent: 0.0ms, 0.0% of total-time

series4.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(hypot.f64 x x)
1.0ms	x	@	0	(hypot.f64 x x)
1.0ms	x	@	-inf	(hypot.f64 x x)

rewrite252.0ms (5.9%)

Algorithm

1×	batch-egg-rewrite

Rules

801×	`log1p-expm1-u`
801×	`expm1-log1p-u`
402×	`associate-r`
340×	`associate-l`
288×	`unpow-prod-down`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	46	13
2	482	7
3	5560	7

Stop Event

1×	node limit

Counts

1 → 104

Calls

Call 1

Inputs
(hypot.f64 x x)

Outputs
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
(+.f64 (+.f64 (/.f64 0 0) 1) -1)
(+.f64 0 (/.f64 0 0))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 0 0))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 0 0)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))))
(+.f64 (.f64 (/.f64 0 0) (pow.f64 x 2)) (.f64 (/.f64 0 0) (pow.f64 x 2)))
(+.f64 (.f64 (pow.f64 x 2) (/.f64 0 0)) (.f64 (pow.f64 x 2) (/.f64 0 0)))
(-.f64 (+.f64 (/.f64 0 0) 1) 1)
(-.f64 (/.f64 (pow.f64 x 4) 0) (/.f64 (pow.f64 x 4) 0))
(.f64 x (.f64 x 2))
(.f64 x (.f64 (*.f64 x 2) 1))
(.f64 x (.f64 (*.f64 x 2) (/.f64 0 0)))
(*.f64 (pow.f64 x 2) 2)
(.f64 (pow.f64 x 2) (.f64 (.f64 x 2) (.f64 x 2)))
(*.f64 (/.f64 0 0) (/.f64 0 0))
(*.f64 (/.f64 0 0) 1)
(*.f64 (/.f64 0 0) (log.f64 (E.f64)))
(*.f64 (/.f64 0 0) (pow.f64 1 1/3))
(*.f64 (/.f64 0 0) (pow.f64 1 1/2))
(*.f64 1 (/.f64 0 0))
(.f64 (cbrt.f64 x) (cbrt.f64 (.f64 x 2)))
(*.f64 (cbrt.f64 x) (+.f64 (pow.f64 (cbrt.f64 x) 5) (pow.f64 (cbrt.f64 x) 5)))
(.f64 (cbrt.f64 x) (.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 x 2)))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (+.f64 (pow.f64 (cbrt.f64 x) 4) (pow.f64 (cbrt.f64 x) 4)))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (*.f64 x 2)))
(.f64 (sqrt.f64 x) (pow.f64 (.f64 x 2) 1/2))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 2)))
(*.f64 (sqrt.f64 x) (+.f64 (pow.f64 x 3/2) (pow.f64 x 3/2)))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (*.f64 x 2)))
(*.f64 0 (/.f64 1 0))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 (pow.f64 x 2) (/.f64 0 0)))
(*.f64 (pow.f64 (cbrt.f64 x) 4) (+.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (pow.f64 x 3/2) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))
(.f64 (.f64 2 (pow.f64 x 6)) (/.f64 1 (+.f64 0 (pow.f64 x 4))))
(.f64 (.f64 x 2) x)
(*.f64 (pow.f64 (cbrt.f64 x) 5) (+.f64 (cbrt.f64 x) (cbrt.f64 x)))
(*.f64 (pow.f64 1 1/3) (/.f64 0 0))
(*.f64 (pow.f64 1 1/2) (/.f64 0 0))
(*.f64 (pow.f64 2 1/2) x)
(*.f64 4 (pow.f64 x 4))
(*.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 x) 2))
(*.f64 (sqrt.f64 2) x)
(.f64 (.f64 2 (sqrt.f64 x)) (pow.f64 x 3/2))
(.f64 (.f64 (/.f64 0 0) x) (*.f64 x 2))
(.f64 (.f64 (/.f64 0 0) 2) (pow.f64 x 2))
(.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (cbrt.f64 x) 4))
(.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 4)) (pow.f64 (cbrt.f64 x) 2))
(.f64 (.f64 2 (pow.f64 x 3/2)) (sqrt.f64 x))
(.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 5)) (cbrt.f64 x))
(/.f64 1 (/.f64 0 0))
(/.f64 1 (/.f64 (+.f64 0 (pow.f64 x 4)) (*.f64 2 (pow.f64 x 6))))
(/.f64 0 0)
(/.f64 (*.f64 2 (pow.f64 x 6)) (+.f64 0 (pow.f64 x 4)))
(/.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 6))) (cbrt.f64 (+.f64 0 (pow.f64 x 4))))
(/.f64 (.f64 (.f64 2 (pow.f64 x 6)) (.f64 2 (pow.f64 x 6))) (.f64 (+.f64 0 (pow.f64 x 4)) (+.f64 0 (pow.f64 x 4))))
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 0 (pow.f64 x 4))))
(/.f64 (sqrt.f64 0) (sqrt.f64 0))
(/.f64 (.f64 (.f64 2 (pow.f64 x 6)) 0) (*.f64 (+.f64 0 (pow.f64 x 4)) 0))
(/.f64 (.f64 0 (.f64 2 (pow.f64 x 6))) (*.f64 0 (+.f64 0 (pow.f64 x 4))))
(/.f64 (neg.f64 (*.f64 2 (pow.f64 x 6))) (neg.f64 (+.f64 0 (pow.f64 x 4))))
(/.f64 (-.f64 (pow.f64 (+.f64 (/.f64 0 0) 1) 3) 1) (+.f64 (*.f64 (+.f64 (/.f64 0 0) 1) (+.f64 (/.f64 0 0) 1)) (+.f64 1 (+.f64 (/.f64 0 0) 1))))
(/.f64 (-.f64 (*.f64 (+.f64 (/.f64 0 0) 1) (+.f64 (/.f64 0 0) 1)) 1) (+.f64 (+.f64 (/.f64 0 0) 1) 1))
(/.f64 (.f64 (/.f64 0 0) (.f64 2 (pow.f64 x 6))) (+.f64 0 (pow.f64 x 4)))
(/.f64 (.f64 (.f64 2 (pow.f64 x 6)) 1) (+.f64 0 (pow.f64 x 4)))
(/.f64 (.f64 (.f64 2 (pow.f64 x 6)) (/.f64 0 0)) (+.f64 0 (pow.f64 x 4)))
(/.f64 (*.f64 0 (/.f64 0 0)) 0)
(pow.f64 (/.f64 0 0) 1)
(pow.f64 (/.f64 0 0) 1/2)
(pow.f64 (/.f64 0 0) 2)
(pow.f64 (/.f64 0 0) 1/3)
(pow.f64 (/.f64 0 0) 3)
(pow.f64 (/.f64 0 0) 1/9)
(pow.f64 (/.f64 0 0) 2/3)
(pow.f64 (/.f64 0 0) 1/6)
(pow.f64 (/.f64 0 0) 1/4)
(pow.f64 (/.f64 0 0) 3/2)
(pow.f64 (/.f64 0 0) 6)
(pow.f64 (/.f64 0 0) 4)
(pow.f64 (/.f64 0 0) 9)
(pow.f64 (/.f64 0 0) 4/3)
(pow.f64 (/.f64 0 0) 5/2)
(pow.f64 (/.f64 0 0) 5)
(pow.f64 (E.f64) (log.f64 (/.f64 0 0)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 0 0))) 2)) (cbrt.f64 (log.f64 (/.f64 0 0))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 0 0)))) (sqrt.f64 (log.f64 (/.f64 0 0))))
(sqrt.f64 (/.f64 0 0))
(fabs.f64 (/.f64 0 0))
(fabs.f64 (neg.f64 (/.f64 0 0)))
(log.f64 (exp.f64 (/.f64 0 0)))
(cbrt.f64 (/.f64 0 0))
(expm1.f64 (log1p.f64 (/.f64 0 0)))
(log1p.f64 (expm1.f64 (/.f64 0 0)))
(exp.f64 (log.f64 (/.f64 0 0)))
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/2))
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 3))
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/3))
(fma.f64 x x (pow.f64 x 2))
(fma.f64 1 (pow.f64 x 2) (pow.f64 x 2))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 4) (pow.f64 x 2))
(fma.f64 (sqrt.f64 x) (pow.f64 x 3/2) (pow.f64 x 2))
(fma.f64 (pow.f64 (cbrt.f64 x) 4) (pow.f64 (cbrt.f64 x) 2) (pow.f64 x 2))
(fma.f64 (pow.f64 x 3/2) (sqrt.f64 x) (pow.f64 x 2))
(fma.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x) (pow.f64 x 2))

simplify20.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

84×	`*-commutative`
64×	`sqr-pow`
32×	`associate-r`
28×	`associate-l`
20×	`count-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	222	946
1	658	946

Stop Event

1×

unsound

Counts

116 → 123

Calls

Call 1

Inputs
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
(+.f64 (+.f64 (/.f64 0 0) 1) -1)
(+.f64 0 (/.f64 0 0))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 0 0))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 0 0)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))))
(+.f64 (.f64 (/.f64 0 0) (pow.f64 x 2)) (.f64 (/.f64 0 0) (pow.f64 x 2)))
(+.f64 (.f64 (pow.f64 x 2) (/.f64 0 0)) (.f64 (pow.f64 x 2) (/.f64 0 0)))
(-.f64 (+.f64 (/.f64 0 0) 1) 1)
(-.f64 (/.f64 (pow.f64 x 4) 0) (/.f64 (pow.f64 x 4) 0))
(.f64 x (.f64 x 2))
(.f64 x (.f64 (*.f64 x 2) 1))
(.f64 x (.f64 (*.f64 x 2) (/.f64 0 0)))
(*.f64 (pow.f64 x 2) 2)
(.f64 (pow.f64 x 2) (.f64 (.f64 x 2) (.f64 x 2)))
(*.f64 (/.f64 0 0) (/.f64 0 0))
(*.f64 (/.f64 0 0) 1)
(*.f64 (/.f64 0 0) (log.f64 (E.f64)))
(*.f64 (/.f64 0 0) (pow.f64 1 1/3))
(*.f64 (/.f64 0 0) (pow.f64 1 1/2))
(*.f64 1 (/.f64 0 0))
(.f64 (cbrt.f64 x) (cbrt.f64 (.f64 x 2)))
(*.f64 (cbrt.f64 x) (+.f64 (pow.f64 (cbrt.f64 x) 5) (pow.f64 (cbrt.f64 x) 5)))
(.f64 (cbrt.f64 x) (.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 x 2)))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (+.f64 (pow.f64 (cbrt.f64 x) 4) (pow.f64 (cbrt.f64 x) 4)))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (*.f64 x 2)))
(.f64 (sqrt.f64 x) (pow.f64 (.f64 x 2) 1/2))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 2)))
(*.f64 (sqrt.f64 x) (+.f64 (pow.f64 x 3/2) (pow.f64 x 3/2)))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (*.f64 x 2)))
(*.f64 0 (/.f64 1 0))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 (pow.f64 x 2) (/.f64 0 0)))
(*.f64 (pow.f64 (cbrt.f64 x) 4) (+.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (pow.f64 x 3/2) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))
(.f64 (.f64 2 (pow.f64 x 6)) (/.f64 1 (+.f64 0 (pow.f64 x 4))))
(.f64 (.f64 x 2) x)
(*.f64 (pow.f64 (cbrt.f64 x) 5) (+.f64 (cbrt.f64 x) (cbrt.f64 x)))
(*.f64 (pow.f64 1 1/3) (/.f64 0 0))
(*.f64 (pow.f64 1 1/2) (/.f64 0 0))
(*.f64 (pow.f64 2 1/2) x)
(*.f64 4 (pow.f64 x 4))
(*.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 x) 2))
(*.f64 (sqrt.f64 2) x)
(.f64 (.f64 2 (sqrt.f64 x)) (pow.f64 x 3/2))
(.f64 (.f64 (/.f64 0 0) x) (*.f64 x 2))
(.f64 (.f64 (/.f64 0 0) 2) (pow.f64 x 2))
(.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (cbrt.f64 x) 4))
(.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 4)) (pow.f64 (cbrt.f64 x) 2))
(.f64 (.f64 2 (pow.f64 x 3/2)) (sqrt.f64 x))
(.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 5)) (cbrt.f64 x))
(/.f64 1 (/.f64 0 0))
(/.f64 1 (/.f64 (+.f64 0 (pow.f64 x 4)) (*.f64 2 (pow.f64 x 6))))
(/.f64 0 0)
(/.f64 (*.f64 2 (pow.f64 x 6)) (+.f64 0 (pow.f64 x 4)))
(/.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 6))) (cbrt.f64 (+.f64 0 (pow.f64 x 4))))
(/.f64 (.f64 (.f64 2 (pow.f64 x 6)) (.f64 2 (pow.f64 x 6))) (.f64 (+.f64 0 (pow.f64 x 4)) (+.f64 0 (pow.f64 x 4))))
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 0 (pow.f64 x 4))))
(/.f64 (sqrt.f64 0) (sqrt.f64 0))
(/.f64 (.f64 (.f64 2 (pow.f64 x 6)) 0) (*.f64 (+.f64 0 (pow.f64 x 4)) 0))
(/.f64 (.f64 0 (.f64 2 (pow.f64 x 6))) (*.f64 0 (+.f64 0 (pow.f64 x 4))))
(/.f64 (neg.f64 (*.f64 2 (pow.f64 x 6))) (neg.f64 (+.f64 0 (pow.f64 x 4))))
(/.f64 (-.f64 (pow.f64 (+.f64 (/.f64 0 0) 1) 3) 1) (+.f64 (*.f64 (+.f64 (/.f64 0 0) 1) (+.f64 (/.f64 0 0) 1)) (+.f64 1 (+.f64 (/.f64 0 0) 1))))
(/.f64 (-.f64 (*.f64 (+.f64 (/.f64 0 0) 1) (+.f64 (/.f64 0 0) 1)) 1) (+.f64 (+.f64 (/.f64 0 0) 1) 1))
(/.f64 (.f64 (/.f64 0 0) (.f64 2 (pow.f64 x 6))) (+.f64 0 (pow.f64 x 4)))
(/.f64 (.f64 (.f64 2 (pow.f64 x 6)) 1) (+.f64 0 (pow.f64 x 4)))
(/.f64 (.f64 (.f64 2 (pow.f64 x 6)) (/.f64 0 0)) (+.f64 0 (pow.f64 x 4)))
(/.f64 (*.f64 0 (/.f64 0 0)) 0)
(pow.f64 (/.f64 0 0) 1)
(pow.f64 (/.f64 0 0) 1/2)
(pow.f64 (/.f64 0 0) 2)
(pow.f64 (/.f64 0 0) 1/3)
(pow.f64 (/.f64 0 0) 3)
(pow.f64 (/.f64 0 0) 1/9)
(pow.f64 (/.f64 0 0) 2/3)
(pow.f64 (/.f64 0 0) 1/6)
(pow.f64 (/.f64 0 0) 1/4)
(pow.f64 (/.f64 0 0) 3/2)
(pow.f64 (/.f64 0 0) 6)
(pow.f64 (/.f64 0 0) 4)
(pow.f64 (/.f64 0 0) 9)
(pow.f64 (/.f64 0 0) 4/3)
(pow.f64 (/.f64 0 0) 5/2)
(pow.f64 (/.f64 0 0) 5)
(pow.f64 (E.f64) (log.f64 (/.f64 0 0)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 0 0))) 2)) (cbrt.f64 (log.f64 (/.f64 0 0))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 0 0)))) (sqrt.f64 (log.f64 (/.f64 0 0))))
(sqrt.f64 (/.f64 0 0))
(fabs.f64 (/.f64 0 0))
(fabs.f64 (neg.f64 (/.f64 0 0)))
(log.f64 (exp.f64 (/.f64 0 0)))
(cbrt.f64 (/.f64 0 0))
(expm1.f64 (log1p.f64 (/.f64 0 0)))
(log1p.f64 (expm1.f64 (/.f64 0 0)))
(exp.f64 (log.f64 (/.f64 0 0)))
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/2))
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 3))
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/3))
(fma.f64 x x (pow.f64 x 2))
(fma.f64 1 (pow.f64 x 2) (pow.f64 x 2))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 4) (pow.f64 x 2))
(fma.f64 (sqrt.f64 x) (pow.f64 x 3/2) (pow.f64 x 2))
(fma.f64 (pow.f64 (cbrt.f64 x) 4) (pow.f64 (cbrt.f64 x) 2) (pow.f64 x 2))
(fma.f64 (pow.f64 x 3/2) (sqrt.f64 x) (pow.f64 x 2))
(fma.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x) (pow.f64 x 2))

Outputs
(*.f64 x (sqrt.f64 2))
(*.f64 x -2)
(*.f64 x (sqrt.f64 2))
(*.f64 x -2)
(*.f64 x (sqrt.f64 2))
(*.f64 x -2)
(*.f64 x (sqrt.f64 2))
(*.f64 x -2)
(*.f64 x (sqrt.f64 2))
(*.f64 x -2)
(*.f64 x (sqrt.f64 2))
(*.f64 x -2)
(*.f64 x (sqrt.f64 2))
(*.f64 x -2)
(*.f64 x (sqrt.f64 2))
(*.f64 x -2)
(.f64 -1 (.f64 x (sqrt.f64 2)))
(*.f64 x -2)
(.f64 -1 (.f64 x (sqrt.f64 2)))
(*.f64 x -2)
(.f64 -1 (.f64 x (sqrt.f64 2)))
(*.f64 x -2)
(.f64 -1 (.f64 x (sqrt.f64 2)))
(*.f64 x -2)
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
-2
(+.f64 (+.f64 (/.f64 0 0) 1) -1)
-2
(+.f64 0 (/.f64 0 0))
-2
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 0 0))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 0 0)))))
-2
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))))
-2
(+.f64 (.f64 (/.f64 0 0) (pow.f64 x 2)) (.f64 (/.f64 0 0) (pow.f64 x 2)))
-2
(+.f64 (.f64 (pow.f64 x 2) (/.f64 0 0)) (.f64 (pow.f64 x 2) (/.f64 0 0)))
-2
(-.f64 (+.f64 (/.f64 0 0) 1) 1)
-2
(-.f64 (/.f64 (pow.f64 x 4) 0) (/.f64 (pow.f64 x 4) 0))
-2
(.f64 x (.f64 x 2))
-2
(.f64 x (.f64 (*.f64 x 2) 1))
-2
(.f64 x (.f64 (*.f64 x 2) (/.f64 0 0)))
-2
(*.f64 (pow.f64 x 2) 2)
-2
(.f64 (pow.f64 x 2) (.f64 (.f64 x 2) (.f64 x 2)))
-2
(*.f64 (/.f64 0 0) (/.f64 0 0))
-2
(*.f64 (/.f64 0 0) 1)
-2
(*.f64 (/.f64 0 0) (log.f64 (E.f64)))
-2
(*.f64 (/.f64 0 0) (pow.f64 1 1/3))
-2
(*.f64 (/.f64 0 0) (pow.f64 1 1/2))
-2
(*.f64 1 (/.f64 0 0))
-2
(.f64 (cbrt.f64 x) (cbrt.f64 (.f64 x 2)))
(.f64 (cbrt.f64 x) (cbrt.f64 (.f64 x -2)))
(*.f64 (cbrt.f64 x) (+.f64 (pow.f64 (cbrt.f64 x) 5) (pow.f64 (cbrt.f64 x) 5)))
(.f64 -2 (.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x)))
(.f64 (cbrt.f64 x) (.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 x 2)))
(.f64 (cbrt.f64 x) (.f64 (*.f64 x -2) (pow.f64 (cbrt.f64 x) -2)))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (+.f64 (pow.f64 (cbrt.f64 x) 4) (pow.f64 (cbrt.f64 x) 4)))
(*.f64 -2 (pow.f64 (cbrt.f64 x) -2))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (*.f64 x 2)))
(.f64 (pow.f64 (cbrt.f64 x) -2) (.f64 (*.f64 x -2) (cbrt.f64 x)))
(.f64 (sqrt.f64 x) (pow.f64 (.f64 x 2) 1/2))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x -2)))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 2)))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x -2)))
(*.f64 (sqrt.f64 x) (+.f64 (pow.f64 x 3/2) (pow.f64 x 3/2)))
(.f64 (sqrt.f64 x) (.f64 -2 (pow.f64 x 3/2)))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (*.f64 x 2)))
(.f64 (sqrt.f64 x) (.f64 (*.f64 x -2) (sqrt.f64 x)))
(*.f64 0 (/.f64 1 0))
-2
(*.f64 2 (pow.f64 x 2))
-2
(.f64 2 (.f64 (pow.f64 x 2) (/.f64 0 0)))
-2
(*.f64 (pow.f64 (cbrt.f64 x) 4) (+.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 2)))
(*.f64 -2 (pow.f64 (cbrt.f64 x) -2))
(*.f64 (pow.f64 x 3/2) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))
(.f64 (sqrt.f64 x) (.f64 -2 (pow.f64 x 3/2)))
(.f64 (.f64 2 (pow.f64 x 6)) (/.f64 1 (+.f64 0 (pow.f64 x 4))))
-2
(.f64 (.f64 x 2) x)
-2
(*.f64 (pow.f64 (cbrt.f64 x) 5) (+.f64 (cbrt.f64 x) (cbrt.f64 x)))
(.f64 -2 (.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x)))
(*.f64 (pow.f64 1 1/3) (/.f64 0 0))
-2
(*.f64 (pow.f64 1 1/2) (/.f64 0 0))
-2
(*.f64 (pow.f64 2 1/2) x)
(*.f64 x -2)
(*.f64 4 (pow.f64 x 4))
-2
(*.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 x) 2))
(*.f64 -2 (pow.f64 (cbrt.f64 x) -2))
(*.f64 (sqrt.f64 2) x)
(*.f64 x -2)
(.f64 (.f64 2 (sqrt.f64 x)) (pow.f64 x 3/2))
(.f64 (sqrt.f64 x) (.f64 -2 (pow.f64 x 3/2)))
(.f64 (.f64 (/.f64 0 0) x) (*.f64 x 2))
-2
(.f64 (.f64 (/.f64 0 0) 2) (pow.f64 x 2))
-2
(.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (cbrt.f64 x) 4))
(*.f64 -2 (pow.f64 (cbrt.f64 x) -2))
(.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 4)) (pow.f64 (cbrt.f64 x) 2))
(*.f64 -2 (pow.f64 (cbrt.f64 x) -2))
(.f64 (.f64 2 (pow.f64 x 3/2)) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (.f64 -2 (pow.f64 x 3/2)))
(.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 5)) (cbrt.f64 x))
(.f64 -2 (.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x)))
(/.f64 1 (/.f64 0 0))
-2
(/.f64 1 (/.f64 (+.f64 0 (pow.f64 x 4)) (*.f64 2 (pow.f64 x 6))))
-2
(/.f64 0 0)
-2
(/.f64 (*.f64 2 (pow.f64 x 6)) (+.f64 0 (pow.f64 x 4)))
-2
(/.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 6))) (cbrt.f64 (+.f64 0 (pow.f64 x 4))))
(/.f64 -2 (cbrt.f64 (pow.f64 x -2)))
(/.f64 (.f64 (.f64 2 (pow.f64 x 6)) (.f64 2 (pow.f64 x 6))) (.f64 (+.f64 0 (pow.f64 x 4)) (+.f64 0 (pow.f64 x 4))))
-2
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 0 (pow.f64 x 4))))
(/.f64 -2 (sqrt.f64 (pow.f64 x -2)))
(/.f64 (sqrt.f64 0) (sqrt.f64 0))
-2
(/.f64 (.f64 (.f64 2 (pow.f64 x 6)) 0) (*.f64 (+.f64 0 (pow.f64 x 4)) 0))
-2
(/.f64 (.f64 0 (.f64 2 (pow.f64 x 6))) (*.f64 0 (+.f64 0 (pow.f64 x 4))))
-2
(/.f64 (neg.f64 (*.f64 2 (pow.f64 x 6))) (neg.f64 (+.f64 0 (pow.f64 x 4))))
-2
(/.f64 (-.f64 (pow.f64 (+.f64 (/.f64 0 0) 1) 3) 1) (+.f64 (*.f64 (+.f64 (/.f64 0 0) 1) (+.f64 (/.f64 0 0) 1)) (+.f64 1 (+.f64 (/.f64 0 0) 1))))
-2
(/.f64 (-.f64 (*.f64 (+.f64 (/.f64 0 0) 1) (+.f64 (/.f64 0 0) 1)) 1) (+.f64 (+.f64 (/.f64 0 0) 1) 1))
-2
(/.f64 (.f64 (/.f64 0 0) (.f64 2 (pow.f64 x 6))) (+.f64 0 (pow.f64 x 4)))
-2
(/.f64 (.f64 (.f64 2 (pow.f64 x 6)) 1) (+.f64 0 (pow.f64 x 4)))
-2
(/.f64 (.f64 (.f64 2 (pow.f64 x 6)) (/.f64 0 0)) (+.f64 0 (pow.f64 x 4)))
-2
(/.f64 (*.f64 0 (/.f64 0 0)) 0)
-2
(pow.f64 (/.f64 0 0) 1)
-2
(pow.f64 (/.f64 0 0) 1/2)
-2
(pow.f64 (/.f64 0 0) 2)
-2
(pow.f64 (/.f64 0 0) 1/3)
-2
(pow.f64 (/.f64 0 0) 3)
-2
(pow.f64 (/.f64 0 0) 1/9)
-2
(pow.f64 (/.f64 0 0) 2/3)
-2
(pow.f64 (/.f64 0 0) 1/6)
-2
(pow.f64 (/.f64 0 0) 1/4)
-2
(pow.f64 (/.f64 0 0) 3/2)
-2
(pow.f64 (/.f64 0 0) 6)
-2
(pow.f64 (/.f64 0 0) 4)
-2
(pow.f64 (/.f64 0 0) 9)
-2
(pow.f64 (/.f64 0 0) 4/3)
-2
(pow.f64 (/.f64 0 0) 5/2)
-2
(pow.f64 (/.f64 0 0) 5)
-2
(pow.f64 (E.f64) (log.f64 (/.f64 0 0)))
-2
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 0 0))) 2)) (cbrt.f64 (log.f64 (/.f64 0 0))))
-2
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 0 0)))) (sqrt.f64 (log.f64 (/.f64 0 0))))
-2
(sqrt.f64 (/.f64 0 0))
-2
(fabs.f64 (/.f64 0 0))
-2
(fabs.f64 (neg.f64 (/.f64 0 0)))
-2
(log.f64 (exp.f64 (/.f64 0 0)))
-2
(cbrt.f64 (/.f64 0 0))
-2
(expm1.f64 (log1p.f64 (/.f64 0 0)))
-2
(log1p.f64 (expm1.f64 (/.f64 0 0)))
-2
(exp.f64 (log.f64 (/.f64 0 0)))
-2
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/2))
-2
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 3))
-2
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/3))
-2
(fma.f64 x x (pow.f64 x 2))
-2
(fma.f64 1 (pow.f64 x 2) (pow.f64 x 2))
(pow.f64 x -2)
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 4) (pow.f64 x 2))
(+.f64 (pow.f64 (cbrt.f64 x) -2) (pow.f64 x -2))
(fma.f64 (sqrt.f64 x) (pow.f64 x 3/2) (pow.f64 x 2))
(fma.f64 (sqrt.f64 x) (pow.f64 x 3/2) (pow.f64 x -2))
(fma.f64 (pow.f64 (cbrt.f64 x) 4) (pow.f64 (cbrt.f64 x) 2) (pow.f64 x 2))
(+.f64 (pow.f64 (cbrt.f64 x) -2) (pow.f64 x -2))
(fma.f64 (pow.f64 x 3/2) (sqrt.f64 x) (pow.f64 x 2))
(fma.f64 (pow.f64 x 3/2) (sqrt.f64 x) (pow.f64 x -2))
(fma.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x) (pow.f64 x 2))
(fma.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x) (pow.f64 x -2))

eval64.0ms (1.5%)

Compiler: Compiled 1027 to 817 computations (20.4% saved)

prune19.0ms (0.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	118	5	123
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	118	6	124

Accuracy

100.0%

Counts

124 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	6.9%	(.f64 (.f64 x 2) x)
▶	99.5%	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 2)))
▶	99.3%	(*.f64 (sqrt.f64 2) x)
▶	2.2%	(*.f64 x -2)
▶	1.7%	-2

Compiler

Compiled 54 to 40 computations (25.9% saved)

localize90.0ms (2.1%)

Localize:

Found 2 expressions with local error:

New	Accuracy	Program
✓	99.3%	(*.f64 (sqrt.f64 2) x)
✓	99.5%	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 2)))

Compiler

Compiled 44 to 29 computations (34.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

Operation ival-sqrt, time spent: 18.0ms, 50.0% of total-time

Operation ival-mult, time spent: 16.0ms, 44.0% of total-time

Operation const, time spent: 2.0ms, 6.0% of total-time

series5.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 2)))
1.0ms	x	@	-inf	(*.f64 (sqrt.f64 2) x)
1.0ms	x	@	0	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 2)))
1.0ms	x	@	inf	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 2)))
1.0ms	x	@	inf	(*.f64 (sqrt.f64 2) x)

rewrite80.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1320×	`unpow-prod-down`
744×	`prod-exp`
642×	`log-prod`
552×	`pow-prod-down`
489×	`log1p-expm1-u`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	46
1	148	28
2	1688	28

Stop Event

1×	node limit

Counts

2 → 94

Calls

Call 1

Inputs
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 2)))
(*.f64 (sqrt.f64 2) x)

Outputs
(+.f64 0 (*.f64 x (sqrt.f64 2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (.f64 x (sqrt.f64 2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (.f64 x (sqrt.f64 2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (.f64 x (sqrt.f64 2))))) (log.f64 (sqrt.f64 (exp.f64 (.f64 x (sqrt.f64 2))))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 x (sqrt.f64 2)))) 1)
(pow.f64 (*.f64 x (sqrt.f64 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1/2)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(log.f64 (exp.f64 (*.f64 x (sqrt.f64 2))))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))
(exp.f64 (.f64 (log.f64 (.f64 x (sqrt.f64 2))) 1))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) 3))
(exp.f64 (.f64 (.f64 3 (log.f64 (*.f64 x (sqrt.f64 2)))) 1/3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x (sqrt.f64 2)))) 2))
(exp.f64 (.f64 (log.f64 (.f64 2 (pow.f64 x 2))) 1/2))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 x (sqrt.f64 2))) 1) 1))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 2) 1/2)))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 (sqrt.f64 2)) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (log.f64 (sqrt.f64 2))))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1) (.f64 (log.f64 2) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1) (.f64 (log.f64 (sqrt.f64 2)) 1)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (.f64 (log.f64 (.f64 x 2)) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (.f64 (log.f64 (sqrt.f64 (.f64 x 2))) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (log.f64 (sqrt.f64 (.f64 x 2)))))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (.f64 (log.f64 (*.f64 x 2)) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (.f64 (log.f64 (sqrt.f64 (*.f64 x 2))) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (log.f64 (sqrt.f64 (.f64 x 2)))))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (.f64 (log.f64 (*.f64 x 2)) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (.f64 (log.f64 (sqrt.f64 (*.f64 x 2))) 1)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (.f64 x 2))) (.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (.f64 x 2))) (.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 x 2)) 1/2) (log.f64 (sqrt.f64 x))))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 x 2)) 1/2) (*.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 x 2)) 1/2) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x 2))) 1) (log.f64 (sqrt.f64 x))))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x 2))) 1) (*.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x 2))) 1) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 2)) (*.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 2) 1/2) (log.f64 x)))
(exp.f64 (+.f64 (.f64 (log.f64 2) 1/2) (.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 2)) 1) (log.f64 x)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 2)) 1) (.f64 (log.f64 x) 1)))
(+.f64 0 (*.f64 x (sqrt.f64 2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (.f64 x (sqrt.f64 2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (.f64 x (sqrt.f64 2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (.f64 x (sqrt.f64 2))))) (log.f64 (sqrt.f64 (exp.f64 (.f64 x (sqrt.f64 2))))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 x (sqrt.f64 2)))) 1)
(pow.f64 (*.f64 x (sqrt.f64 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1/2)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(log.f64 (exp.f64 (*.f64 x (sqrt.f64 2))))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))
(exp.f64 (.f64 (log.f64 (.f64 x (sqrt.f64 2))) 1))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) 3))
(exp.f64 (.f64 (.f64 3 (log.f64 (*.f64 x (sqrt.f64 2)))) 1/3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x (sqrt.f64 2)))) 2))
(exp.f64 (.f64 (log.f64 (.f64 2 (pow.f64 x 2))) 1/2))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 x (sqrt.f64 2))) 1) 1))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 2) 1/2)))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 (sqrt.f64 2)) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (log.f64 (sqrt.f64 2))))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1) (.f64 (log.f64 2) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1) (.f64 (log.f64 (sqrt.f64 2)) 1)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (.f64 (log.f64 (.f64 x 2)) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (.f64 (log.f64 (sqrt.f64 (.f64 x 2))) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (log.f64 (sqrt.f64 (.f64 x 2)))))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (.f64 (log.f64 (*.f64 x 2)) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (.f64 (log.f64 (sqrt.f64 (*.f64 x 2))) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (log.f64 (sqrt.f64 (.f64 x 2)))))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (.f64 (log.f64 (*.f64 x 2)) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (.f64 (log.f64 (sqrt.f64 (*.f64 x 2))) 1)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (.f64 x 2))) (.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (.f64 x 2))) (.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 x 2)) 1/2) (log.f64 (sqrt.f64 x))))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 x 2)) 1/2) (*.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 x 2)) 1/2) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x 2))) 1) (log.f64 (sqrt.f64 x))))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x 2))) 1) (*.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x 2))) 1) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 2)) (*.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 2) 1/2) (log.f64 x)))
(exp.f64 (+.f64 (.f64 (log.f64 2) 1/2) (.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 2)) 1) (log.f64 x)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 2)) 1) (.f64 (log.f64 x) 1)))

simplify93.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

1262×	`log-prod`
1070×	`distribute-lft-in`
926×	`distribute-rgt-in`
604×	`associate-r`
546×	`*-commutative`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	136	1806
1	298	1744
2	662	1744
3	2935	1744
4	7773	1744

Stop Event

1×	node limit

Counts

118 → 56

Calls

Call 1

Inputs
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(.f64 -1 (.f64 x (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(.f64 -1 (.f64 x (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(.f64 -1 (.f64 x (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(.f64 -1 (.f64 x (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(+.f64 0 (*.f64 x (sqrt.f64 2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (.f64 x (sqrt.f64 2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (.f64 x (sqrt.f64 2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (.f64 x (sqrt.f64 2))))) (log.f64 (sqrt.f64 (exp.f64 (.f64 x (sqrt.f64 2))))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 x (sqrt.f64 2)))) 1)
(pow.f64 (*.f64 x (sqrt.f64 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1/2)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(log.f64 (exp.f64 (*.f64 x (sqrt.f64 2))))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))
(exp.f64 (.f64 (log.f64 (.f64 x (sqrt.f64 2))) 1))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) 3))
(exp.f64 (.f64 (.f64 3 (log.f64 (*.f64 x (sqrt.f64 2)))) 1/3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x (sqrt.f64 2)))) 2))
(exp.f64 (.f64 (log.f64 (.f64 2 (pow.f64 x 2))) 1/2))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 x (sqrt.f64 2))) 1) 1))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 2) 1/2)))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 (sqrt.f64 2)) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (log.f64 (sqrt.f64 2))))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1) (.f64 (log.f64 2) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1) (.f64 (log.f64 (sqrt.f64 2)) 1)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (.f64 (log.f64 (.f64 x 2)) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (.f64 (log.f64 (sqrt.f64 (.f64 x 2))) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (log.f64 (sqrt.f64 (.f64 x 2)))))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (.f64 (log.f64 (*.f64 x 2)) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (.f64 (log.f64 (sqrt.f64 (*.f64 x 2))) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (log.f64 (sqrt.f64 (.f64 x 2)))))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (.f64 (log.f64 (*.f64 x 2)) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (.f64 (log.f64 (sqrt.f64 (*.f64 x 2))) 1)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (.f64 x 2))) (.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (.f64 x 2))) (.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 x 2)) 1/2) (log.f64 (sqrt.f64 x))))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 x 2)) 1/2) (*.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 x 2)) 1/2) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x 2))) 1) (log.f64 (sqrt.f64 x))))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x 2))) 1) (*.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x 2))) 1) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 2)) (*.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 2) 1/2) (log.f64 x)))
(exp.f64 (+.f64 (.f64 (log.f64 2) 1/2) (.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 2)) 1) (log.f64 x)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 2)) 1) (.f64 (log.f64 x) 1)))
(+.f64 0 (*.f64 x (sqrt.f64 2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (.f64 x (sqrt.f64 2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (.f64 x (sqrt.f64 2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (.f64 x (sqrt.f64 2))))) (log.f64 (sqrt.f64 (exp.f64 (.f64 x (sqrt.f64 2))))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 x (sqrt.f64 2)))) 1)
(pow.f64 (*.f64 x (sqrt.f64 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1/2)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(log.f64 (exp.f64 (*.f64 x (sqrt.f64 2))))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))
(exp.f64 (.f64 (log.f64 (.f64 x (sqrt.f64 2))) 1))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) 3))
(exp.f64 (.f64 (.f64 3 (log.f64 (*.f64 x (sqrt.f64 2)))) 1/3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x (sqrt.f64 2)))) 2))
(exp.f64 (.f64 (log.f64 (.f64 2 (pow.f64 x 2))) 1/2))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 x (sqrt.f64 2))) 1) 1))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 2) 1/2)))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 (sqrt.f64 2)) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (log.f64 (sqrt.f64 2))))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1) (.f64 (log.f64 2) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1) (.f64 (log.f64 (sqrt.f64 2)) 1)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (.f64 (log.f64 (.f64 x 2)) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (.f64 (log.f64 (sqrt.f64 (.f64 x 2))) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (log.f64 (sqrt.f64 (.f64 x 2)))))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (.f64 (log.f64 (*.f64 x 2)) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (.f64 (log.f64 (sqrt.f64 (*.f64 x 2))) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (log.f64 (sqrt.f64 (.f64 x 2)))))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (.f64 (log.f64 (*.f64 x 2)) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (.f64 (log.f64 (sqrt.f64 (*.f64 x 2))) 1)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (.f64 x 2))) (.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (.f64 x 2))) (.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 x 2)) 1/2) (log.f64 (sqrt.f64 x))))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 x 2)) 1/2) (*.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 x 2)) 1/2) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x 2))) 1) (log.f64 (sqrt.f64 x))))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x 2))) 1) (*.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x 2))) 1) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 2)) (*.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 2) 1/2) (log.f64 x)))
(exp.f64 (+.f64 (.f64 (log.f64 2) 1/2) (.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 2)) 1) (log.f64 x)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 2)) 1) (.f64 (log.f64 x) 1)))

Outputs
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(.f64 -1 (.f64 x (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(neg.f64 (.f64 x (.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(.f64 (.f64 (sqrt.f64 -2) (sqrt.f64 -1)) (neg.f64 x))
(.f64 (sqrt.f64 -2) (.f64 x (neg.f64 (sqrt.f64 -1))))
(.f64 x (.f64 (sqrt.f64 -2) (neg.f64 (sqrt.f64 -1))))
(.f64 -1 (.f64 x (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(neg.f64 (.f64 x (.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(.f64 (.f64 (sqrt.f64 -2) (sqrt.f64 -1)) (neg.f64 x))
(.f64 (sqrt.f64 -2) (.f64 x (neg.f64 (sqrt.f64 -1))))
(.f64 x (.f64 (sqrt.f64 -2) (neg.f64 (sqrt.f64 -1))))
(.f64 -1 (.f64 x (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(neg.f64 (.f64 x (.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(.f64 (.f64 (sqrt.f64 -2) (sqrt.f64 -1)) (neg.f64 x))
(.f64 (sqrt.f64 -2) (.f64 x (neg.f64 (sqrt.f64 -1))))
(.f64 x (.f64 (sqrt.f64 -2) (neg.f64 (sqrt.f64 -1))))
(.f64 -1 (.f64 x (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(neg.f64 (.f64 x (.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(.f64 (.f64 (sqrt.f64 -2) (sqrt.f64 -1)) (neg.f64 x))
(.f64 (sqrt.f64 -2) (.f64 x (neg.f64 (sqrt.f64 -1))))
(.f64 x (.f64 (sqrt.f64 -2) (neg.f64 (sqrt.f64 -1))))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(+.f64 0 (*.f64 x (sqrt.f64 2)))
(*.f64 x (sqrt.f64 2))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (.f64 x (sqrt.f64 2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (.f64 x (sqrt.f64 2))))))
(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))))
(*.f64 3 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))))
(*.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))) 3)
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (.f64 x (sqrt.f64 2))))) (log.f64 (sqrt.f64 (exp.f64 (.f64 x (sqrt.f64 2))))))
(*.f64 x (sqrt.f64 2))
(-.f64 (exp.f64 (log1p.f64 (*.f64 x (sqrt.f64 2)))) 1)
(*.f64 x (sqrt.f64 2))
(pow.f64 (*.f64 x (sqrt.f64 2)) 1)
(*.f64 x (sqrt.f64 2))
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(*.f64 x (sqrt.f64 2))
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 1/3)
(*.f64 x (sqrt.f64 2))
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(*.f64 x (sqrt.f64 2))
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1/2)
(*.f64 x (sqrt.f64 2))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(*.f64 x (sqrt.f64 2))
(log.f64 (exp.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 x (sqrt.f64 2))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3))
(*.f64 x (sqrt.f64 2))
(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 x (sqrt.f64 2))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (.f64 (log.f64 (.f64 x (sqrt.f64 2))) 1))
(*.f64 x (sqrt.f64 2))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) 3))
(*.f64 x (sqrt.f64 2))
(exp.f64 (.f64 (.f64 3 (log.f64 (*.f64 x (sqrt.f64 2)))) 1/3))
(*.f64 x (sqrt.f64 2))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x (sqrt.f64 2)))) 2))
(*.f64 x (sqrt.f64 2))
(exp.f64 (.f64 (log.f64 (.f64 2 (pow.f64 x 2))) 1/2))
(*.f64 x (sqrt.f64 2))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 x (sqrt.f64 2))) 1) 1))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 2) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 (sqrt.f64 2)) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (log.f64 (sqrt.f64 2))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1) (.f64 (log.f64 2) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1) (.f64 (log.f64 (sqrt.f64 2)) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (.f64 (log.f64 (.f64 x 2)) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (.f64 (log.f64 (sqrt.f64 (.f64 x 2))) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (log.f64 (sqrt.f64 (.f64 x 2)))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (.f64 (log.f64 (*.f64 x 2)) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (.f64 (log.f64 (sqrt.f64 (*.f64 x 2))) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (log.f64 (sqrt.f64 (.f64 x 2)))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (.f64 (log.f64 (*.f64 x 2)) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (.f64 (log.f64 (sqrt.f64 (*.f64 x 2))) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (.f64 x 2))) (.f64 (log.f64 x) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (.f64 x 2))) (.f64 (log.f64 (sqrt.f64 x)) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 x 2)) 1/2) (log.f64 (sqrt.f64 x))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 x 2)) 1/2) (*.f64 (log.f64 x) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 x 2)) 1/2) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x 2))) 1) (log.f64 (sqrt.f64 x))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x 2))) 1) (*.f64 (log.f64 x) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x 2))) 1) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 2)) (*.f64 (log.f64 x) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 2) 1/2) (log.f64 x)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 2) 1/2) (.f64 (log.f64 x) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 2)) 1) (log.f64 x)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 2)) 1) (.f64 (log.f64 x) 1)))
(*.f64 x (sqrt.f64 2))
(+.f64 0 (*.f64 x (sqrt.f64 2)))
(*.f64 x (sqrt.f64 2))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (.f64 x (sqrt.f64 2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (.f64 x (sqrt.f64 2))))))
(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))))
(*.f64 3 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))))
(*.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))) 3)
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (.f64 x (sqrt.f64 2))))) (log.f64 (sqrt.f64 (exp.f64 (.f64 x (sqrt.f64 2))))))
(*.f64 x (sqrt.f64 2))
(-.f64 (exp.f64 (log1p.f64 (*.f64 x (sqrt.f64 2)))) 1)
(*.f64 x (sqrt.f64 2))
(pow.f64 (*.f64 x (sqrt.f64 2)) 1)
(*.f64 x (sqrt.f64 2))
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(*.f64 x (sqrt.f64 2))
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 1/3)
(*.f64 x (sqrt.f64 2))
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(*.f64 x (sqrt.f64 2))
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1/2)
(*.f64 x (sqrt.f64 2))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(*.f64 x (sqrt.f64 2))
(log.f64 (exp.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 x (sqrt.f64 2))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3))
(*.f64 x (sqrt.f64 2))
(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 x (sqrt.f64 2))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (.f64 (log.f64 (.f64 x (sqrt.f64 2))) 1))
(*.f64 x (sqrt.f64 2))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) 3))
(*.f64 x (sqrt.f64 2))
(exp.f64 (.f64 (.f64 3 (log.f64 (*.f64 x (sqrt.f64 2)))) 1/3))
(*.f64 x (sqrt.f64 2))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x (sqrt.f64 2)))) 2))
(*.f64 x (sqrt.f64 2))
(exp.f64 (.f64 (log.f64 (.f64 2 (pow.f64 x 2))) 1/2))
(*.f64 x (sqrt.f64 2))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 x (sqrt.f64 2))) 1) 1))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 2) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 (sqrt.f64 2)) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (log.f64 (sqrt.f64 2))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1) (.f64 (log.f64 2) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1) (.f64 (log.f64 (sqrt.f64 2)) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (.f64 (log.f64 (.f64 x 2)) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (.f64 (log.f64 (sqrt.f64 (.f64 x 2))) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (log.f64 (sqrt.f64 (.f64 x 2)))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (.f64 (log.f64 (*.f64 x 2)) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (.f64 (log.f64 (sqrt.f64 (*.f64 x 2))) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (log.f64 (sqrt.f64 (.f64 x 2)))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (.f64 (log.f64 (*.f64 x 2)) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (.f64 (log.f64 (sqrt.f64 (*.f64 x 2))) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (.f64 x 2))) (.f64 (log.f64 x) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (.f64 x 2))) (.f64 (log.f64 (sqrt.f64 x)) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 x 2)) 1/2) (log.f64 (sqrt.f64 x))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 x 2)) 1/2) (*.f64 (log.f64 x) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 x 2)) 1/2) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x 2))) 1) (log.f64 (sqrt.f64 x))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x 2))) 1) (*.f64 (log.f64 x) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x 2))) 1) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 2)) (*.f64 (log.f64 x) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 2) 1/2) (log.f64 x)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 2) 1/2) (.f64 (log.f64 x) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 2)) 1) (log.f64 x)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 2)) 1) (.f64 (log.f64 x) 1)))
(*.f64 x (sqrt.f64 2))

eval13.0ms (0.3%)

Compiler: Compiled 544 to 434 computations (20.2% saved)

prune11.0ms (0.3%)

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	0	0
Picked	0	5	5
Done	0	1	1
Total	56	6	62

Accuracy

100.0%

Counts

62 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	6.9%	(.f64 (.f64 x 2) x)
✓	99.5%	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 2)))
✓	99.3%	(*.f64 (sqrt.f64 2) x)
✓	2.2%	(*.f64 x -2)
✓	1.7%	-2

Compiler

Compiled 61 to 40 computations (34.4% saved)

regimes18.0ms (0.4%)

Counts

7 → 1

Calls

Call 1

Inputs
-2
(*.f64 x -2)
(.f64 (.f64 x 2) x)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 2)))

Outputs
(hypot.f64 x x)

Calls

4 calls:

5.0ms	x
5.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
4.0ms	(+.f64 (.f64 x x) (.f64 x x))
4.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
100.0%	1	`(+.f64 (.f64 x x) (.f64 x x))`
100.0%	1	`(*.f64 x x)`

Compiler

Compiled 23 to 10 computations (56.5% saved)

regimes4.0ms (0.1%)

Counts

3 → 1

Calls

Call 1

Inputs
-2
(*.f64 x -2)
(.f64 (.f64 x 2) x)

Outputs
(.f64 (.f64 x 2) x)

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
6.9%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes38.0ms (0.9%)

Counts

2 → 1

Calls

Call 1

Inputs
-2
(*.f64 x -2)

Outputs
(*.f64 x -2)

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
2.2%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes10.0ms (0.2%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
-2

Outputs
-2

Calls

1 calls:

10.0ms

Results

Accuracy	Segments	Branch
1.7%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	43
1	14	43

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(hypot.f64 x x)
(.f64 (.f64 x 2) x)
(*.f64 x -2)
-2

Outputs
(hypot.f64 x x)
(.f64 (.f64 x 2) x)
(.f64 x (.f64 x 2))
(*.f64 x -2)
-2

Compiler

Compiled 16 to 11 computations (31.3% saved)

soundness1.9s (45.5%)

Rules

801×	`log1p-expm1-u`
801×	`expm1-log1p-u`
801×	`log1p-expm1-u`
801×	`expm1-log1p-u`
402×	`associate-r`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	56
1	36	56
2	82	56
3	197	56
4	302	56
5	362	56
6	364	56
0	6	13
1	46	13
2	482	7
3	5560	7
0	222	946
1	658	946
0	222	946
1	658	946
0	6	13
1	46	13
2	482	7
3	5560	7

Stop Event

1×	node limit
1×	unsound
1×	unsound
1×	node limit
1×	saturated

Compiler

Compiled 616 to 157 computations (74.5% saved)

end0.0ms (0%)

preprocess60.0ms (1.4%)

Remove: (abs x)
Compiler: Compiled 84 to 44 computations (47.6% saved)

analyze0.0ms (0%)

sample1.2s (29.4%)

preprocess119.0ms (2.8%)

eval0.0ms (0%)

prune1.0ms (0%)

localize162.0ms (3.8%)

series4.0ms (0.1%)

rewrite252.0ms (5.9%)

simplify20.0ms (0.5%)

eval64.0ms (1.5%)

prune19.0ms (0.4%)

localize90.0ms (2.1%)

series5.0ms (0.1%)

rewrite80.0ms (1.9%)

simplify93.0ms (2.2%)

eval13.0ms (0.3%)

prune11.0ms (0.3%)

regimes18.0ms (0.4%)

regimes4.0ms (0.1%)

regimes38.0ms (0.9%)

regimes10.0ms (0.2%)

simplify3.0ms (0.1%)

soundness1.9s (45.5%)

end0.0ms (0%)

preprocess60.0ms (1.4%)

Profiling