Metrics for sqrt E (should all be same)

analyze1.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 10 to 8 computations (20% saved)

sample1.0s (25.4%)

Results

1.0s	8254×	body	256	valid
0.0ms	2×	body	256	infinite

Bogosity

preprocess183.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

1064×	`fma-neg`
980×	`distribute-lft-out`
896×	`fma-def`
886×	`hypot-def`
738×	`distribute-lft-neg-in`

Problems

134×	`(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))`
122×	No Errors

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	60
1	28	39
2	70	39
3	239	39
4	1034	39
5	2786	39
6	5774	39
7	7854	39

Stop Event

1×	node limit

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
(sqrt.f64 (+.f64 (pow.f64 (neg.f64 x) 2) (pow.f64 (neg.f64 x) 2)))

Outputs
(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(hypot.f64 x x)
(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(hypot.f64 x x)
(sqrt.f64 (+.f64 (pow.f64 (neg.f64 x) 2) (pow.f64 (neg.f64 x) 2)))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(hypot.f64 x x)

Symmetry

(abs x)

Compiler

Compiled 31 to 23 computations (25.8% saved)

eval0.0ms (0%)

Compiler: Compiled 10 to 7 computations (30% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

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

Compiler

Compiled 8 to 4 computations (50% saved)

localize15.0ms (0.4%)

Localize:

Found 1 expressions with local error:

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

Compiler

Compiled 6 to 3 computations (50% saved)

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite126.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

801×	`log1p-expm1-u`
486×	`expm1-log1p-u`
434×	`expm1-udef`
434×	`log1p-udef`
408×	`associate-r`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	46	13
2	478	7
3	5496	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 4 (pow.f64 x 4))
(*.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 (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 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 (.f64 (/.f64 0 0) x) (*.f64 x 2))
(.f64 (.f64 (/.f64 0 0) 2) (pow.f64 x 2))
(/.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 (sqrt.f64 0) (sqrt.f64 0))
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.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 (.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) 2)
(pow.f64 (/.f64 0 0) 1/2)
(pow.f64 (/.f64 0 0) 1/3)
(pow.f64 (/.f64 0 0) 3)
(pow.f64 (/.f64 0 0) 6)
(pow.f64 (/.f64 0 0) 5/2)
(pow.f64 (/.f64 0 0) 5)
(pow.f64 (/.f64 0 0) 3/2)
(pow.f64 (/.f64 0 0) 4/3)
(pow.f64 (/.f64 0 0) 4)
(pow.f64 (/.f64 0 0) 2/3)
(pow.f64 (/.f64 0 0) 1/6)
(pow.f64 (/.f64 0 0) 1/9)
(pow.f64 (/.f64 0 0) 1/4)
(pow.f64 (/.f64 0 0) 9)
(pow.f64 (E.f64) (log.f64 (/.f64 0 0)))
(pow.f64 (exp.f64 (cbrt.f64 (pow.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)))
(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))
(log1p.f64 (expm1.f64 (/.f64 0 0)))
(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))

simplify14.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

78×	`*-commutative`
60×	`sqr-pow`
30×	`associate-r`
26×	`associate-l`
20×	`count-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	223	916
1	678	916

Stop Event

1×

unsound

Counts

116 → 126

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 4 (pow.f64 x 4))
(*.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 (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 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 (.f64 (/.f64 0 0) x) (*.f64 x 2))
(.f64 (.f64 (/.f64 0 0) 2) (pow.f64 x 2))
(/.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 (sqrt.f64 0) (sqrt.f64 0))
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.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 (.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) 2)
(pow.f64 (/.f64 0 0) 1/2)
(pow.f64 (/.f64 0 0) 1/3)
(pow.f64 (/.f64 0 0) 3)
(pow.f64 (/.f64 0 0) 6)
(pow.f64 (/.f64 0 0) 5/2)
(pow.f64 (/.f64 0 0) 5)
(pow.f64 (/.f64 0 0) 3/2)
(pow.f64 (/.f64 0 0) 4/3)
(pow.f64 (/.f64 0 0) 4)
(pow.f64 (/.f64 0 0) 2/3)
(pow.f64 (/.f64 0 0) 1/6)
(pow.f64 (/.f64 0 0) 1/9)
(pow.f64 (/.f64 0 0) 1/4)
(pow.f64 (/.f64 0 0) 9)
(pow.f64 (E.f64) (log.f64 (/.f64 0 0)))
(pow.f64 (exp.f64 (cbrt.f64 (pow.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)))
(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))
(log1p.f64 (expm1.f64 (/.f64 0 0)))
(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 -2 (sqrt.f64 x))
(.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 -2 (sqrt.f64 x))
(.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 4 (pow.f64 x 4))
-2
(*.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 (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 -2 (sqrt.f64 x))
(.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 -2 (sqrt.f64 x))
(.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 (.f64 (/.f64 0 0) x) (*.f64 x 2))
-2
(.f64 (.f64 (/.f64 0 0) 2) (pow.f64 x 2))
-2
(/.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 (sqrt.f64 0) (sqrt.f64 0))
-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 (.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 (.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) 2)
-2
(pow.f64 (/.f64 0 0) 1/2)
-2
(pow.f64 (/.f64 0 0) 1/3)
-2
(pow.f64 (/.f64 0 0) 3)
-2
(pow.f64 (/.f64 0 0) 6)
-2
(pow.f64 (/.f64 0 0) 5/2)
(pow.f64 -2 5/2)
(pow.f64 (/.f64 0 0) 5)
-2
(pow.f64 (/.f64 0 0) 3/2)
-2
(pow.f64 (/.f64 0 0) 4/3)
-2
(pow.f64 (/.f64 0 0) 4)
-2
(pow.f64 (/.f64 0 0) 2/3)
-2
(pow.f64 (/.f64 0 0) 1/6)
(pow.f64 -2 1/6)
(pow.f64 (/.f64 0 0) 1/9)
(*.f64 (pow.f64 -2 1/18) (pow.f64 -2 1/18))
(pow.f64 (/.f64 0 0) 1/4)
-2
(pow.f64 (/.f64 0 0) 9)
-2
(pow.f64 (E.f64) (log.f64 (/.f64 0 0)))
-2
(pow.f64 (exp.f64 (cbrt.f64 (pow.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
(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
(log1p.f64 (expm1.f64 (/.f64 0 0)))
-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 -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 -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))

eval68.0ms (1.7%)

Compiler: Compiled 1036 to 827 computations (20.2% saved)

prune18.0ms (0.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	122	4	126
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	122	5	127

Accuracy

100.0%

Counts

127 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	7.1%	(.f64 (.f64 x 2) x)
▶	99.4%	(*.f64 (sqrt.f64 2) x)
▶	2.4%	(*.f64 x -2)
	1.7%	-2
✓	100.0%	(hypot.f64 x x)
▶	7.1%	(.f64 (.f64 x 2) x)
▶	99.4%	(*.f64 (sqrt.f64 2) x)
▶	2.4%	(*.f64 x -2)
	1.7%	-2

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize65.0ms (1.6%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	99.4%	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 25 to 17 computations (32% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(*.f64 (sqrt.f64 2) x)
0.0ms	x	@	inf	(*.f64 (sqrt.f64 2) x)
0.0ms	x	@	-inf	(*.f64 (sqrt.f64 2) x)

rewrite45.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

938×	`associate-r`
810×	`associate-l`
396×	`unpow-prod-down`
296×	`log-prod`
288×	`cbrt-prod`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	67	14
2	723	14

Stop Event

1×	node limit

Counts

1 → 25

Calls

Call 1

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

Outputs
(+.f64 (+.f64 1 (*.f64 (sqrt.f64 2) x)) -1)
(+.f64 0 (*.f64 (sqrt.f64 2) x))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (sqrt.f64 8)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))))
(-.f64 (+.f64 1 (*.f64 (sqrt.f64 2) x)) 1)
(/.f64 (-.f64 (pow.f64 (+.f64 1 (.f64 (sqrt.f64 2) x)) 3) 1) (+.f64 (.f64 (+.f64 1 (.f64 (sqrt.f64 2) x)) (+.f64 1 (.f64 (sqrt.f64 2) x))) (+.f64 1 (.f64 (+.f64 1 (.f64 (sqrt.f64 2) x)) 1))))
(/.f64 (-.f64 (.f64 (+.f64 1 (.f64 (sqrt.f64 2) x)) (+.f64 1 (.f64 (sqrt.f64 2) x))) 1) (+.f64 (+.f64 1 (.f64 (sqrt.f64 2) x)) 1))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1/2)
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(pow.f64 (E.f64) (log.f64 (*.f64 (sqrt.f64 2) x)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 (sqrt.f64 2) x))) 2)) (cbrt.f64 (log.f64 (.f64 (sqrt.f64 2) x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 (sqrt.f64 2) x)))) (sqrt.f64 (log.f64 (.f64 (sqrt.f64 2) x))))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(fabs.f64 (*.f64 (sqrt.f64 2) x))
(log.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))
(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (sqrt.f64 2) x))) 3))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (sqrt.f64 2) x) 3)) 1/3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (sqrt.f64 2) x))) 2))
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))

simplify50.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

952×	`log-prod`
910×	`times-frac`
898×	`fma-def`
816×	`associate-r`
792×	`distribute-lft-out`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	81	740
1	196	722
2	665	707
3	4409	707

Stop Event

1×	node limit

Counts

37 → 31

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 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(+.f64 (+.f64 1 (*.f64 (sqrt.f64 2) x)) -1)
(+.f64 0 (*.f64 (sqrt.f64 2) x))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (sqrt.f64 8)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))))
(-.f64 (+.f64 1 (*.f64 (sqrt.f64 2) x)) 1)
(/.f64 (-.f64 (pow.f64 (+.f64 1 (.f64 (sqrt.f64 2) x)) 3) 1) (+.f64 (.f64 (+.f64 1 (.f64 (sqrt.f64 2) x)) (+.f64 1 (.f64 (sqrt.f64 2) x))) (+.f64 1 (.f64 (+.f64 1 (.f64 (sqrt.f64 2) x)) 1))))
(/.f64 (-.f64 (.f64 (+.f64 1 (.f64 (sqrt.f64 2) x)) (+.f64 1 (.f64 (sqrt.f64 2) x))) 1) (+.f64 (+.f64 1 (.f64 (sqrt.f64 2) x)) 1))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1/2)
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(pow.f64 (E.f64) (log.f64 (*.f64 (sqrt.f64 2) x)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 (sqrt.f64 2) x))) 2)) (cbrt.f64 (log.f64 (.f64 (sqrt.f64 2) x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 (sqrt.f64 2) x)))) (sqrt.f64 (log.f64 (.f64 (sqrt.f64 2) x))))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(fabs.f64 (*.f64 (sqrt.f64 2) x))
(log.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))
(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (sqrt.f64 2) x))) 3))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (sqrt.f64 2) x) 3)) 1/3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (sqrt.f64 2) x))) 2))
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))

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 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(+.f64 (+.f64 1 (*.f64 (sqrt.f64 2) x)) -1)
(*.f64 x (sqrt.f64 2))
(+.f64 0 (*.f64 (sqrt.f64 2) x))
(*.f64 x (sqrt.f64 2))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (sqrt.f64 8)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))))
(*.f64 x (sqrt.f64 2))
(-.f64 (+.f64 1 (*.f64 (sqrt.f64 2) x)) 1)
(*.f64 x (sqrt.f64 2))
(/.f64 (-.f64 (pow.f64 (+.f64 1 (.f64 (sqrt.f64 2) x)) 3) 1) (+.f64 (.f64 (+.f64 1 (.f64 (sqrt.f64 2) x)) (+.f64 1 (.f64 (sqrt.f64 2) x))) (+.f64 1 (.f64 (+.f64 1 (.f64 (sqrt.f64 2) x)) 1))))
(/.f64 (+.f64 (pow.f64 (+.f64 1 (.f64 x (sqrt.f64 2))) 3) -1) (fma.f64 (+.f64 1 (.f64 x (sqrt.f64 2))) (+.f64 1 (.f64 x (sqrt.f64 2))) (+.f64 1 (+.f64 1 (.f64 x (sqrt.f64 2))))))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 x (sqrt.f64 2) 1) 3)) (fma.f64 (fma.f64 x (sqrt.f64 2) 1) (fma.f64 x (sqrt.f64 2) 1) (+.f64 2 (*.f64 x (sqrt.f64 2)))))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 x (sqrt.f64 2) 1) 3)) (+.f64 1 (*.f64 (fma.f64 x (sqrt.f64 2) 1) (fma.f64 x (sqrt.f64 2) 2))))
(/.f64 (-.f64 (.f64 (+.f64 1 (.f64 (sqrt.f64 2) x)) (+.f64 1 (.f64 (sqrt.f64 2) x))) 1) (+.f64 (+.f64 1 (.f64 (sqrt.f64 2) x)) 1))
(*.f64 x (sqrt.f64 2))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(*.f64 x (sqrt.f64 2))
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(*.f64 x (sqrt.f64 2))
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1/2)
(*.f64 x (sqrt.f64 2))
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3) 1/3)
(*.f64 x (sqrt.f64 2))
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(*.f64 x (sqrt.f64 2))
(pow.f64 (E.f64) (log.f64 (*.f64 (sqrt.f64 2) x)))
(*.f64 x (sqrt.f64 2))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 (sqrt.f64 2) x))) 2)) (cbrt.f64 (log.f64 (.f64 (sqrt.f64 2) x))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 x (sqrt.f64 2)))) 2)) (cbrt.f64 (log.f64 (.f64 x (sqrt.f64 2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 (sqrt.f64 2) x)))) (sqrt.f64 (log.f64 (.f64 (sqrt.f64 2) x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 x (sqrt.f64 2))))) (sqrt.f64 (log.f64 (.f64 x (sqrt.f64 2)))))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(*.f64 x (sqrt.f64 2))
(fabs.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 x (sqrt.f64 2))
(log.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))
(*.f64 x (sqrt.f64 2))
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
(*.f64 x (sqrt.f64 2))
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (sqrt.f64 2) x))) 3))
(*.f64 x (sqrt.f64 2))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (sqrt.f64 2) x) 3)) 1/3))
(*.f64 x (sqrt.f64 2))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (sqrt.f64 2) x))) 2))
(*.f64 x (sqrt.f64 2))
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))
(*.f64 x (sqrt.f64 2))

eval9.0ms (0.2%)

Compiler: Compiled 370 to 316 computations (14.6% saved)

prune7.0ms (0.2%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	31	0	31
Fresh	0	1	1
Picked	0	3	3
Done	0	1	1
Total	31	5	36

Accuracy

100.0%

Counts

36 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	7.1%	(.f64 (.f64 x 2) x)
✓	99.4%	(*.f64 (sqrt.f64 2) x)
✓	2.4%	(*.f64 x -2)
	1.7%	-2
✓	100.0%	(hypot.f64 x x)
✓	7.1%	(.f64 (.f64 x 2) x)
✓	99.4%	(*.f64 (sqrt.f64 2) x)
✓	2.4%	(*.f64 x -2)
	1.7%	-2

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize0.0ms (0%)

eval0.0ms (0%)

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

prune3.0ms (0.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	4	4
Total	5	5

Accuracy

100.0%

Counts

5 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	7.1%	(.f64 (.f64 x 2) x)
✓	99.4%	(*.f64 (sqrt.f64 2) x)
✓	2.4%	(*.f64 x -2)
	1.7%	-2
✓	100.0%	(hypot.f64 x x)
✓	7.1%	(.f64 (.f64 x 2) x)
✓	99.4%	(*.f64 (sqrt.f64 2) x)
✓	2.4%	(*.f64 x -2)
	1.7%	-2

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize0.0ms (0%)

eval0.0ms (0%)

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

prune3.0ms (0.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	4	4
Total	5	5

Accuracy

100.0%

Counts

5 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	7.1%	(.f64 (.f64 x 2) x)
✓	99.4%	(*.f64 (sqrt.f64 2) x)
✓	2.4%	(*.f64 x -2)
	1.7%	-2

Compiler

Compiled 46 to 32 computations (30.4% saved)

regimes18.0ms (0.4%)

Counts

6 → 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 (pow.f64 x 2) (pow.f64 x 2)))

Outputs
(hypot.f64 x x)

Calls

4 calls:

5.0ms	x
4.0ms	(+.f64 (pow.f64 x 2) (pow.f64 x 2))
4.0ms	(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
3.0ms	(pow.f64 x 2)

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))`
100.0%	1	`(+.f64 (pow.f64 x 2) (pow.f64 x 2))`
100.0%	1	`(pow.f64 x 2)`

Compiler

Compiled 48 to 34 computations (29.2% saved)

regimes5.0ms (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
7.1%	1	`x`

Compiler

Compiled 12 to 8 computations (33.3% saved)

regimes4.0ms (0.1%)

Counts

2 → 1

Calls

Call 1

Inputs
-2
(*.f64 x -2)

Outputs
(*.f64 x -2)

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
2.4%	1	`x`

Compiler

Compiled 7 to 5 computations (28.6% saved)

regimes3.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
-2

Outputs
-2

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
1.7%	1	`x`

Compiler

Compiled 4 to 3 computations (25% saved)

simplify2.0ms (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×	fuel
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)

soundness2.3s (57.5%)

Rules

1064×	`fma-neg`
980×	`distribute-lft-out`
896×	`fma-def`
886×	`hypot-def`
801×	`log1p-expm1-u`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	60
1	28	39
2	70	39
3	239	39
4	1034	39
5	2786	39
6	5774	39
7	7854	39
0	6	13
1	46	13
2	478	7
3	5496	7
0	223	916
1	678	916
0	223	916
1	678	916
0	6	13
1	46	13
2	478	7
3	5496	7

Stop Event

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

Compiler

Compiled 632 to 167 computations (73.6% saved)

end0.0ms (0%)

preprocess41.0ms (1%)

Remove: (abs x)
Compiler: Compiled 52 to 34 computations (34.6% saved)

analyze1.0ms (0%)

sample1.0s (25.4%)

preprocess183.0ms (4.6%)

eval0.0ms (0%)

prune1.0ms (0%)

localize15.0ms (0.4%)

series2.0ms (0.1%)

rewrite126.0ms (3.1%)

simplify14.0ms (0.4%)

eval68.0ms (1.7%)

prune18.0ms (0.5%)

localize65.0ms (1.6%)

series1.0ms (0%)

rewrite45.0ms (1.1%)

simplify50.0ms (1.2%)

eval9.0ms (0.2%)

prune7.0ms (0.2%)

localize0.0ms (0%)

eval0.0ms (0%)

prune3.0ms (0.1%)

localize0.0ms (0%)

eval0.0ms (0%)

prune3.0ms (0.1%)

regimes18.0ms (0.4%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

regimes3.0ms (0.1%)

simplify2.0ms (0.1%)

soundness2.3s (57.5%)

end0.0ms (0%)

preprocess41.0ms (1%)

Profiling