Metrics for sqrt E (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
100%	100%	0%	0%	0%	0%	0%	1

Compiler

Compiled 10 to 8 computations (20% saved)

Precisions

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

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

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

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

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

sample1.0s (9.5%)

Results

973.0ms	8251×	256	valid
0.0ms	4×	256	infinite
0.0ms	1×	256	valid

Precisions

Click to see histograms. Total time spent on operations: 422.0ms

Operation ival-pow, time spent: 246.0ms, 58.0% of total-time

Operation ival-sqrt, time spent: 115.0ms, 27.0% of total-time

Operation ival-add, time spent: 42.0ms, 10.0% of total-time

Operation const, time spent: 18.0ms, 4.0% of total-time

Bogosity

preprocess390.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

114×	`fma-define`
86×	`fma-neg`
56×	`associate-r`
52×	`unsub-neg`
28×	`distribute-rgt-neg-out`

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
136	-	6	(6.834554183376986e-161)	`(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))`
0	-	0	-	`(+.f64 (pow.f64 x 2) (pow.f64 x 2))`
0	-	0	-	`x`
0	-	0	-	`(pow.f64 x 2)`
0	-	0	-	`2`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	88
1	25	56
2	54	56
3	171	56
4	322	56
5	397	56
6	413	56

Stop Event

1×

saturated

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

Symmetry

(abs x)

Compiler

Compiled 53 to 39 computations (26.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 32.0ms

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

Operation ival-sqrt, time spent: 7.0ms, 22.0% of total-time

Operation ival-add, time spent: 5.0ms, 16.0% of total-time

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

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)

Compiler

Compiled 4 to 2 computations (50% saved)

localize27.0ms (0.2%)

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: 22.0ms

Operation composed, time spent: 11.0ms, 50.0% of total-time

Operation ival-mult, time spent: 6.0ms, 27.0% of total-time

Operation ival-sqrt, time spent: 3.0ms, 14.0% 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

series2.0ms (0%)

Counts

1 → 12

Calls

Call 1

Inputs
#<alt (hypot.f64 x x)>

Outputs
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (.f64 -1 (.f64 x (sqrt.f64 2)))>
#<alt (.f64 -1 (.f64 x (sqrt.f64 2)))>
#<alt (.f64 -1 (.f64 x (sqrt.f64 2)))>
#<alt (.f64 -1 (.f64 x (sqrt.f64 2)))>

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(sqrt (+ (* x x) (* x x)))
1.0ms	x	@	inf	(sqrt (+ (* x x) (* x x)))
0.0ms	x	@	-inf	(sqrt (+ (* x x) (* x x)))

rewrite354.0ms (3.2%)

Algorithm

1×	batch-egg-rewrite

Rules

801×	`log1p-expm1-u`
801×	`expm1-log1p-u`
404×	`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	5570	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 (/.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)) 3))
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/3))
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/2))
(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 (0.2%)

Algorithm

1×	egg-herbie

Rules

84×	`*-commutative`
32×	`associate-r`
28×	`associate-l`
20×	`count-2`
18×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	222	12884902958
1	581	12884902958

Stop Event

1×

unsound

Counts

116 → 134

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 (/.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)) 3))
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/3))
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/2))
(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 (.f64 (pow.f64 (cbrt.f64 x) -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 (.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 (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 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 (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 (.f64 (pow.f64 (cbrt.f64 x) -2) (pow.f64 (cbrt.f64 x) -2)))
(.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 4)) (pow.f64 (cbrt.f64 x) 2))
(.f64 -2 (.f64 (pow.f64 (cbrt.f64 x) -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)
(pow.f64 -2 1/9)
(pow.f64 (/.f64 0 0) 2/3)
(pow.f64 -2 2/3)
(pow.f64 (/.f64 0 0) 1/6)
(pow.f64 -2 1/6)
(pow.f64 (/.f64 0 0) 1/4)
(pow.f64 -2 1/4)
(pow.f64 (/.f64 0 0) 3/2)
(pow.f64 -2 3/2)
(pow.f64 (/.f64 0 0) 6)
64
(pow.f64 (/.f64 0 0) 4)
-2
(pow.f64 (/.f64 0 0) 9)
512
(pow.f64 (/.f64 0 0) 4/3)
(pow.f64 -2 4/3)
(pow.f64 (/.f64 0 0) 5/2)
(pow.f64 -2 5/2)
(pow.f64 (/.f64 0 0) 5)
32
(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)) 3))
-2
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/3))
-2
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/2))
-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))
(fma.f64 (pow.f64 (cbrt.f64 x) -2) (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))
(fma.f64 (pow.f64 (cbrt.f64 x) -2) (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))

eval26.0ms (0.2%)

Compiler: Compiled 1066 to 850 computations (20.3% saved)

prune24.0ms (0.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	128	6	134
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	128	7	135

Accuracy

100.0%

Counts

135 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	6.8%	(.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)
▶	5.2%	512
▶	5.2%	32

Compiler

Compiled 58 to 44 computations (24.1% saved)

localize149.0ms (1.4%)

Localize:

Found 1 expressions with local error:

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

Compiler

Compiled 37 to 24 computations (35.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

Operation ival-mult, time spent: 17.0ms, 60.0% of total-time

Operation ival-sqrt, time spent: 10.0ms, 35.0% of total-time

Operation const, time spent: 2.0ms, 7.0% of total-time

series2.0ms (0%)

Counts

1 → 12

Calls

Call 1

Inputs
#<alt (.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 2)))>

Outputs
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (.f64 -1 (.f64 x (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))>
#<alt (.f64 -1 (.f64 x (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))>
#<alt (.f64 -1 (.f64 x (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))>
#<alt (.f64 -1 (.f64 x (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))>

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(* (sqrt x) (sqrt (* x 2)))
0.0ms	x	@	0	(* (sqrt x) (sqrt (* x 2)))
0.0ms	x	@	inf	(* (sqrt x) (sqrt (* x 2)))

rewrite75.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1122×	`unpow-prod-down`
550×	`prod-exp`
530×	`log-prod`
492×	`cbrt-prod`
424×	`pow-prod-down`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	23
1	109	14
2	1194	14

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

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

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

simplify82.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1450×	`fma-neg`
1386×	`distribute-lft-in`
1172×	`distribute-rgt-in`
1150×	`associate-r`
996×	`prod-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	74	695
1	130	695
2	310	695
3	1066	695
4	5427	695
5	7495	695

Stop Event

1×	node limit

Counts

34 → 29

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 0 (*.f64 x (sqrt.f64 2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2))) 2)) (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 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 (pow.f64 x 2) 2) 1/2)
(pow.f64 (E.f64) (log.f64 (*.f64 x (sqrt.f64 2))))
(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 x (sqrt.f64 2))))) (sqrt.f64 (log.f64 (.f64 x (sqrt.f64 2)))))
(sqrt.f64 (*.f64 (pow.f64 x 2) 2))
(log.f64 (pow.f64 (exp.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 (cbrt.f64 (.f64 x (sqrt.f64 2)))) 3))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 3)) 1/3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x (sqrt.f64 2)))) 2))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 x 2) 2)) 1/2))

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

eval7.0ms (0.1%)

Compiler: Compiled 247 to 208 computations (15.8% saved)

prune7.0ms (0.1%)

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	29	0	29
Fresh	0	1	1
Picked	0	5	5
Done	0	1	1
Total	29	7	36

Accuracy

100.0%

Counts

36 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	6.8%	(.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)
✓	5.2%	512
✓	5.2%	32

Compiler

Compiled 31 to 23 computations (25.8% saved)

localize52.0ms (0.5%)

Localize:

Found 1 expressions with local error:

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

Compiler

Compiled 10 to 8 computations (20% saved)

Precisions

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

Operation ival-sqrt, time spent: 8.0ms, 72.0% of total-time

Operation ival-mult, time spent: 2.0ms, 18.0% of total-time

Operation const, time spent: 1.0ms, 9.0% of total-time

series1.0ms (0%)

Counts

1 → 12

Calls

Call 1

Inputs
#<alt (*.f64 (sqrt.f64 2) x)>

Outputs
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>

Calls

3 calls:

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

rewrite61.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

946×	`associate-r`
804×	`associate-l`
488×	`unpow-prod-down`
296×	`log-prod`
286×	`cbrt-prod`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	67	14
2	729	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 (sqrt.f64 2)) x))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))
(-.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 (*.f64 (sqrt.f64 8) (pow.f64 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 (sqrt.f64 2)) x))
(cbrt.f64 (*.f64 (sqrt.f64 8) (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))
(log1p.f64 (expm1.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 (.f64 3 (log.f64 (*.f64 (sqrt.f64 2) x))) 1/3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (sqrt.f64 2) x))) 2))

simplify62.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1406×	`cancel-sign-sub-inv`
1112×	`distribute-lft-out`
852×	`sub-neg`
758×	`times-frac`
598×	`div-sub`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	83	778
1	161	760
2	401	745
3	1618	745
4	3913	745

Stop Event

1×	node limit

Counts

37 → 34

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

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 (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 (sqrt.f64 2)) x))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))
(*.f64 2 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))
(*.f64 2 (log.f64 (sqrt.f64 (pow.f64 (exp.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 (*.f64 (sqrt.f64 8) (pow.f64 x 3)) 1/3)
(cbrt.f64 (*.f64 (sqrt.f64 8) (pow.f64 x 3)))
(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 (sqrt.f64 2)) x))
(*.f64 x (sqrt.f64 2))
(cbrt.f64 (*.f64 (sqrt.f64 8) (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))
(*.f64 x (sqrt.f64 2))
(log1p.f64 (expm1.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 (.f64 3 (log.f64 (*.f64 (sqrt.f64 2) x))) 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))

eval19.0ms (0.2%)

Compiler: Compiled 403 to 346 computations (14.1% saved)

prune7.0ms (0.1%)

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	34	0	34
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	34	7	41

Accuracy

100.0%

Counts

41 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	6.8%	(.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)
✓	5.2%	512
✓	5.2%	32

Compiler

Compiled 64 to 46 computations (28.1% saved)

regimes21.0ms (0.2%)

Counts

8 → 1

Calls

Call 1

Inputs
32
512
(*.f64 x -2)
(.f64 (.f64 x 2) x)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 2)))
(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))

Outputs
(hypot.f64 x x)

Calls

4 calls:

7.0ms	x
5.0ms	(pow.f64 x 2)
4.0ms	(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
4.0ms	(+.f64 (pow.f64 x 2) (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 23 to 17 computations (26.1% saved)

regimes4.0ms (0%)

Counts

4 → 1

Calls

Call 1

Inputs
32
512
(*.f64 x -2)
(.f64 (.f64 x 2) x)

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

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
6.8%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes4.0ms (0%)

Counts

3 → 1

Calls

Call 1

Inputs
32
512
(*.f64 x -2)

Outputs
512

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
5.2%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
32

Outputs
32

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
5.2%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	34
1	13	34

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(hypot.f64 x x)
(.f64 (.f64 x 2) x)
512
32

Outputs
(hypot.f64 x x)
(.f64 (.f64 x 2) x)
(.f64 x (.f64 x 2))
512
32

Compiler

Compiled 14 to 10 computations (28.6% saved)

soundness8.5s (77.2%)

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	222	12884902958
1	581	12884902958
0	6	13
1	46	13
2	482	7
3	5570	7
0	15	88
1	25	56
2	54	56
3	171	56
4	322	56
5	397	56
6	413	56

Stop Event

1×	saturated
1×	node limit
1×	unsound

Compiler

Compiled 342 to 97 computations (71.6% saved)

end0.0ms (0%)

preprocess66.0ms (0.6%)

Remove: (abs x)
Compiler: Compiled 80 to 48 computations (40% saved)

analyze0.0ms (0%)

sample1.0s (9.5%)

preprocess390.0ms (3.5%)

eval0.0ms (0%)

prune1.0ms (0%)

localize27.0ms (0.2%)

series2.0ms (0%)

rewrite354.0ms (3.2%)

simplify20.0ms (0.2%)

eval26.0ms (0.2%)

prune24.0ms (0.2%)

localize149.0ms (1.4%)

series2.0ms (0%)

rewrite75.0ms (0.7%)

simplify82.0ms (0.7%)

eval7.0ms (0.1%)

prune7.0ms (0.1%)

localize52.0ms (0.5%)

series1.0ms (0%)

rewrite61.0ms (0.6%)

simplify62.0ms (0.6%)

eval19.0ms (0.2%)

prune7.0ms (0.1%)

regimes21.0ms (0.2%)

regimes4.0ms (0%)

regimes4.0ms (0%)

regimes3.0ms (0%)

simplify4.0ms (0%)

soundness8.5s (77.2%)

end0.0ms (0%)

preprocess66.0ms (0.6%)

Profiling