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)

sample1.1s (33.7%)

Results

1.1s

8256×

body

256

valid

Bogosity

preprocess92.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

1068×	`fma-neg`
982×	`distribute-lft-out`
896×	`fma-def`
886×	`hypot-def`
744×	`distribute-lft-neg-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	34
1	26	14
2	68	14
3	235	14
4	1047	14
5	2829	14
6	5830	14
7	7894	14

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

Symmetry

(abs x)

Compiler

Compiled 10 to 8 computations (20% saved)

simplify112.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

2556×	`fma-def`
1482×	`distribute-lft-out`
1118×	`hypot-def`
988×	`count-2`
868×	`unswap-sqr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	14	7
2	33	7
3	56	7
4	121	7
5	380	7
6	1381	7
7	2589	7
8	3932	7
9	4860	7
10	5626	7
11	6637	7
12	7494	7

Stop Event

1×	node limit

Counts

1 → 3

Calls

Call 1

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

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

eval1.0ms (0%)

Compiler: Compiled 18 to 12 computations (33.3% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	2	1	3
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	3	1	4

Accurracy

100.0%

Counts

4 → 1

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)

localize14.0ms (0.4%)

Local Accuracy

Found 1 expressions with local accuracy:

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)

rewrite51.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

738×	`pow1`
704×	`add-sqr-sqrt`
696×	`*-un-lft-identity`
674×	`add-exp-log`
674×	`log1p-expm1-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7
1	80	7
2	933	7

Stop Event

1×	node limit

Counts

1 → 41

Calls

Call 1

Inputs
(hypot.f64 x x)

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

simplify70.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

924×	`associate-r`
884×	`log-prod`
766×	`associate-l`
738×	`associate-+r+`
718×	`associate-+l+`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	116	717
1	249	681
2	686	669
3	4006	669

Stop Event

1×	node limit

Counts

53 → 55

Calls

Call 1

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

Outputs
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(+.f64 0 (hypot.f64 x x))
(hypot.f64 x x)
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))))
(hypot.f64 x x)
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x)))))
(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x))))) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x)))))
(*.f64 3 (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x)))))
(*.f64 (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x)))) 3)
(-.f64 (+.f64 1 (hypot.f64 x x)) 1)
(hypot.f64 x x)
(*.f64 (hypot.f64 x x) 1)
(hypot.f64 x x)
(*.f64 1 (hypot.f64 x x))
(hypot.f64 x x)
(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
(hypot.f64 x x)
(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4) 1/2))
(hypot.f64 x x)
(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (pow.f64 (hypot.f64 x x) 3/2) 1/2))
(hypot.f64 x x)
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 5/2)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
(*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (hypot.f64 x x) 5/2)))
(.f64 (cbrt.f64 (pow.f64 (.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x))) 2)) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x))) 2)))
(*.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4) 2)))
(*.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 8)))
(*.f64 (pow.f64 1 1/3) (hypot.f64 x x))
(hypot.f64 x x)
(*.f64 (pow.f64 1 1/2) (hypot.f64 x x))
(hypot.f64 x x)
(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3))
(hypot.f64 x x)
(.f64 (pow.f64 (pow.f64 (.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x))) 2) 1/3) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x))) 2)))
(*.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4) 2)))
(*.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 8)))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
(*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (hypot.f64 x x) 5/2)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4) 1/2) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))
(hypot.f64 x x)
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 3/2) 1/2) (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))
(hypot.f64 x x)
(*.f64 (pow.f64 2 1/2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5) 1/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
(hypot.f64 x x)
(pow.f64 (hypot.f64 x x) 1)
(hypot.f64 x x)
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)
(hypot.f64 x x)
(pow.f64 (pow.f64 (hypot.f64 x x) 3) 1/3)
(hypot.f64 x x)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
(hypot.f64 x x)
(pow.f64 (*.f64 x (+.f64 x x)) 1/2)
(hypot.f64 x x)
(pow.f64 (E.f64) (log.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 x x))) 2)) (cbrt.f64 (log.f64 (hypot.f64 x x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (hypot.f64 x x)))) (sqrt.f64 (log.f64 (hypot.f64 x x))))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(hypot.f64 x x)
(log.f64 (exp.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
(hypot.f64 x x)
(expm1.f64 (log1p.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(exp.f64 (log.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (hypot.f64 x x))) 3))
(hypot.f64 x x)
(exp.f64 (.f64 (.f64 3 (log.f64 (hypot.f64 x x))) 1/3))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (hypot.f64 x x))) 2))
(hypot.f64 x x)
(exp.f64 (.f64 (.f64 2 (log.f64 (hypot.f64 x x))) 1/2))
(hypot.f64 x x)
(log1p.f64 (expm1.f64 (hypot.f64 x x)))
(hypot.f64 x x)

eval9.0ms (0.3%)

Compiler: Compiled 507 to 205 computations (59.6% saved)

prune7.0ms (0.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	54	1	55
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	54	2	56

Accurracy

100.0%

Counts

56 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	99.4%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	100.0%	(hypot.f64 x x)
▶	99.4%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))

Compiler

Compiled 24 to 14 computations (41.7% saved)

localize69.0ms (2.1%)

Local Accuracy

Found 1 expressions with local accuracy:

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

Compiler

Compiled 19 to 6 computations (68.4% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
0.0ms	x	@	0	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
0.0ms	x	@	inf	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))

rewrite50.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1184×	`pow1`
1102×	`add-exp-log`
1100×	`log1p-expm1-u`
1100×	`expm1-log1p-u`
1076×	`add-log-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	167	7
2	2257	7

Stop Event

1×	node limit

Counts

1 → 38

Calls

Call 1

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

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

simplify16.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

18×	`associate-/l*`
18×	`sqr-pow`
16×	`*-commutative`
12×	`associate-r`
8×	`fma-udef`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	92	504
1	253	504

Stop Event

1×

unsound

Counts

50 → 50

Calls

Call 1

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

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

eval10.0ms (0.3%)

Compiler: Compiled 384 to 233 computations (39.3% saved)

prune8.0ms (0.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	47	3	50
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	47	5	52

Accurracy

100.0%

Counts

52 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	13.3%	(-.f64 (+.f64 1 (+.f64 x x)) 1)
▶	20.3%	(+.f64 x x)
✓	99.4%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
	3.9%	0
✓	100.0%	(hypot.f64 x x)
▶	13.3%	(-.f64 (+.f64 1 (+.f64 x x)) 1)
▶	20.3%	(+.f64 x x)
✓	99.4%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
	3.9%	0

Compiler

Compiled 52 to 34 computations (34.6% saved)

localize38.0ms (1.2%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	52.4%	(-.f64 (+.f64 1 (+.f64 x x)) 1)

Compiler

Compiled 23 to 10 computations (56.5% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(-.f64 (+.f64 1 (+.f64 x x)) 1)
0.0ms	x	@	0	(-.f64 (+.f64 1 (+.f64 x x)) 1)
0.0ms	x	@	-inf	(-.f64 (+.f64 1 (+.f64 x x)) 1)

rewrite55.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1506×	`pow1`
1420×	`add-exp-log`
1416×	`log1p-expm1-u`
1416×	`expm1-log1p-u`
1404×	`add-log-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	165	7
2	2610	7

Stop Event

1×	node limit

Counts

1 → 93

Calls

Call 1

Inputs
(-.f64 (+.f64 1 (+.f64 x x)) 1)

Outputs
(+.f64 1 (fma.f64 2 x -1))
(+.f64 1 (*.f64 (fma.f64 2 x -1) 1))
(+.f64 x x)
(+.f64 (+.f64 x x) 0)
(+.f64 (+.f64 x x) (+.f64 (+.f64 x x) (*.f64 -2 x)))
(+.f64 (+.f64 x x) (*.f64 (fma.f64 2 x -1) (+.f64 x x)))
(+.f64 (fma.f64 2 x 1) -1)
(+.f64 -1 (fma.f64 2 x 1))
(+.f64 (+.f64 1 x) (+.f64 x -1))
(+.f64 (+.f64 1 x) (-.f64 x 1))
(+.f64 (fma.f64 2 x -1) 1)
(+.f64 (.f64 (+.f64 x x) x) (.f64 (+.f64 x x) x))
(+.f64 (.f64 (fma.f64 2 x 1) (+.f64 x x)) (.f64 -1 (+.f64 x x)))
(+.f64 (.f64 x (+.f64 x x)) (.f64 x (+.f64 x x)))
(+.f64 (.f64 (+.f64 x x) (fma.f64 2 x 1)) (.f64 (+.f64 x x) -1))
(*.f64 1 (+.f64 x x))
(*.f64 x 2)
(*.f64 (+.f64 x x) 1)
(*.f64 (+.f64 x x) (+.f64 x x))
(*.f64 (cbrt.f64 x) (+.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (+.f64 (cbrt.f64 x) (cbrt.f64 x)))
(*.f64 (sqrt.f64 x) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))
(.f64 (.f64 2 (pow.f64 x 3)) (/.f64 1 (fma.f64 x x 0)))
(*.f64 0 (/.f64 1 0))
(*.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1) (/.f64 1 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2))))
(*.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (/.f64 1 (+.f64 (+.f64 x x) 2)))
(*.f64 2 x)
(.f64 2 (.f64 x (+.f64 x x)))
(*.f64 (cbrt.f64 2) (cbrt.f64 x))
(.f64 4 (.f64 x x))
(*.f64 8 (pow.f64 x 3))
(*.f64 (sqrt.f64 2) (sqrt.f64 x))
(*.f64 (+.f64 (sqrt.f64 (fma.f64 2 x 1)) 1) (-.f64 (sqrt.f64 (fma.f64 2 x 1)) 1))
(*.f64 (pow.f64 (+.f64 x x) 3/2) (pow.f64 (+.f64 x x) 3/2))
(.f64 (.f64 (+.f64 x x) 2) x)
(.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(.f64 (.f64 2 (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 1 (+.f64 x x))
(/.f64 1 (/.f64 (fma.f64 x x 0) (*.f64 2 (pow.f64 x 3))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2)) (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)))
(/.f64 1 (/.f64 (+.f64 (+.f64 x x) 2) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)))
(/.f64 (*.f64 2 (pow.f64 x 3)) (fma.f64 x x 0))
(/.f64 0 0)
(/.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2)))
(/.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (-.f64 1 (*.f64 (fma.f64 2 x 1) -1))))
(/.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (+.f64 (+.f64 x x) 2))
(/.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (-.f64 (fma.f64 2 x 1) -1))
(/.f64 (cbrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)) (cbrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2))))
(/.f64 (cbrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (cbrt.f64 (+.f64 (+.f64 x x) 2)))
(/.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 3))) (cbrt.f64 (fma.f64 x x 0)))
(/.f64 (.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1) (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)) (.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2)) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2))))
(/.f64 (.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (.f64 (+.f64 (+.f64 x x) 2) (+.f64 (+.f64 x x) 2)))
(/.f64 (.f64 (.f64 2 (pow.f64 x 3)) (.f64 2 (pow.f64 x 3))) (.f64 (fma.f64 x x 0) (fma.f64 x x 0)))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)) (sqrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (sqrt.f64 (+.f64 (+.f64 x x) 2)))
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 3))) (sqrt.f64 (fma.f64 x x 0)))
(/.f64 (sqrt.f64 0) (sqrt.f64 0))
(/.f64 (pow.f64 (*.f64 2 (pow.f64 x 3)) 3) (pow.f64 (fma.f64 x x 0) 3))
(/.f64 (.f64 (.f64 2 (pow.f64 x 3)) 0) (*.f64 (fma.f64 x x 0) 0))
(/.f64 (.f64 0 (.f64 2 (pow.f64 x 3))) (*.f64 0 (fma.f64 x x 0)))
(/.f64 (.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2)) (+.f64 (+.f64 x x) 2)))
(/.f64 (.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)) (.f64 (+.f64 (+.f64 x x) 2) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2))))
(/.f64 (neg.f64 (*.f64 2 (pow.f64 x 3))) (neg.f64 (fma.f64 x x 0)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)) (neg.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (neg.f64 (+.f64 (+.f64 x x) 2)))
(/.f64 (+.f64 1 (pow.f64 (fma.f64 2 x -1) 3)) (+.f64 1 (-.f64 (*.f64 (fma.f64 2 x -1) (fma.f64 2 x -1)) (fma.f64 2 x -1))))
(/.f64 (-.f64 1 (*.f64 (fma.f64 2 x -1) (fma.f64 2 x -1))) (-.f64 1 (fma.f64 2 x -1)))
(/.f64 (.f64 (+.f64 x x) (.f64 2 (pow.f64 x 3))) (fma.f64 x x 0))
(/.f64 (*.f64 (+.f64 x x) (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2)))
(/.f64 (*.f64 (+.f64 x x) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (+.f64 (+.f64 x x) 2))
(/.f64 (.f64 (.f64 2 (pow.f64 x 3)) (+.f64 x x)) (fma.f64 x x 0))
(/.f64 (*.f64 0 (+.f64 x x)) 0)
(/.f64 (*.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1) (+.f64 x x)) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2)))
(/.f64 (*.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (+.f64 x x)) (+.f64 (+.f64 x x) 2))
(pow.f64 (+.f64 x x) 1)
(pow.f64 (+.f64 x x) 3)
(pow.f64 (+.f64 x x) 2)
(pow.f64 (+.f64 x x) 1/2)
(pow.f64 (+.f64 x x) 1/3)
(sqrt.f64 (+.f64 x x))
(fabs.f64 (+.f64 x x))
(log.f64 (pow.f64 (exp.f64 2) x))
(cbrt.f64 (+.f64 x x))
(expm1.f64 (log1p.f64 (+.f64 x x)))
(hypot.f64 (sqrt.f64 x) (sqrt.f64 x))
(exp.f64 (log.f64 (+.f64 x x)))
(log1p.f64 (expm1.f64 (+.f64 x x)))
(fma.f64 1 x x)
(fma.f64 1 (fma.f64 2 x 1) -1)
(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 2 x 1)) 2) (cbrt.f64 (fma.f64 2 x 1)) -1)
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) x)
(fma.f64 (sqrt.f64 (fma.f64 2 x 1)) (sqrt.f64 (fma.f64 2 x 1)) -1)
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) x)

simplify26.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

60×	`*-commutative`
44×	`distribute-lft-in`
38×	`distribute-rgt-in`
38×	`+-commutative`
30×	`associate-/l*`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	216	357
1	790	357

Stop Event

1×

unsound

Counts

105 → 103

Calls

Call 1

Inputs
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(+.f64 1 (fma.f64 2 x -1))
(+.f64 1 (*.f64 (fma.f64 2 x -1) 1))
(+.f64 x x)
(+.f64 (+.f64 x x) 0)
(+.f64 (+.f64 x x) (+.f64 (+.f64 x x) (*.f64 -2 x)))
(+.f64 (+.f64 x x) (*.f64 (fma.f64 2 x -1) (+.f64 x x)))
(+.f64 (fma.f64 2 x 1) -1)
(+.f64 -1 (fma.f64 2 x 1))
(+.f64 (+.f64 1 x) (+.f64 x -1))
(+.f64 (+.f64 1 x) (-.f64 x 1))
(+.f64 (fma.f64 2 x -1) 1)
(+.f64 (.f64 (+.f64 x x) x) (.f64 (+.f64 x x) x))
(+.f64 (.f64 (fma.f64 2 x 1) (+.f64 x x)) (.f64 -1 (+.f64 x x)))
(+.f64 (.f64 x (+.f64 x x)) (.f64 x (+.f64 x x)))
(+.f64 (.f64 (+.f64 x x) (fma.f64 2 x 1)) (.f64 (+.f64 x x) -1))
(*.f64 1 (+.f64 x x))
(*.f64 x 2)
(*.f64 (+.f64 x x) 1)
(*.f64 (+.f64 x x) (+.f64 x x))
(*.f64 (cbrt.f64 x) (+.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (+.f64 (cbrt.f64 x) (cbrt.f64 x)))
(*.f64 (sqrt.f64 x) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))
(.f64 (.f64 2 (pow.f64 x 3)) (/.f64 1 (fma.f64 x x 0)))
(*.f64 0 (/.f64 1 0))
(*.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1) (/.f64 1 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2))))
(*.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (/.f64 1 (+.f64 (+.f64 x x) 2)))
(*.f64 2 x)
(.f64 2 (.f64 x (+.f64 x x)))
(*.f64 (cbrt.f64 2) (cbrt.f64 x))
(.f64 4 (.f64 x x))
(*.f64 8 (pow.f64 x 3))
(*.f64 (sqrt.f64 2) (sqrt.f64 x))
(*.f64 (+.f64 (sqrt.f64 (fma.f64 2 x 1)) 1) (-.f64 (sqrt.f64 (fma.f64 2 x 1)) 1))
(*.f64 (pow.f64 (+.f64 x x) 3/2) (pow.f64 (+.f64 x x) 3/2))
(.f64 (.f64 (+.f64 x x) 2) x)
(.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(.f64 (.f64 2 (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 1 (+.f64 x x))
(/.f64 1 (/.f64 (fma.f64 x x 0) (*.f64 2 (pow.f64 x 3))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2)) (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)))
(/.f64 1 (/.f64 (+.f64 (+.f64 x x) 2) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)))
(/.f64 (*.f64 2 (pow.f64 x 3)) (fma.f64 x x 0))
(/.f64 0 0)
(/.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2)))
(/.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (-.f64 1 (*.f64 (fma.f64 2 x 1) -1))))
(/.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (+.f64 (+.f64 x x) 2))
(/.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (-.f64 (fma.f64 2 x 1) -1))
(/.f64 (cbrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)) (cbrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2))))
(/.f64 (cbrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (cbrt.f64 (+.f64 (+.f64 x x) 2)))
(/.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 3))) (cbrt.f64 (fma.f64 x x 0)))
(/.f64 (.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1) (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)) (.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2)) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2))))
(/.f64 (.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (.f64 (+.f64 (+.f64 x x) 2) (+.f64 (+.f64 x x) 2)))
(/.f64 (.f64 (.f64 2 (pow.f64 x 3)) (.f64 2 (pow.f64 x 3))) (.f64 (fma.f64 x x 0) (fma.f64 x x 0)))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)) (sqrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (sqrt.f64 (+.f64 (+.f64 x x) 2)))
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 3))) (sqrt.f64 (fma.f64 x x 0)))
(/.f64 (sqrt.f64 0) (sqrt.f64 0))
(/.f64 (pow.f64 (*.f64 2 (pow.f64 x 3)) 3) (pow.f64 (fma.f64 x x 0) 3))
(/.f64 (.f64 (.f64 2 (pow.f64 x 3)) 0) (*.f64 (fma.f64 x x 0) 0))
(/.f64 (.f64 0 (.f64 2 (pow.f64 x 3))) (*.f64 0 (fma.f64 x x 0)))
(/.f64 (.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2)) (+.f64 (+.f64 x x) 2)))
(/.f64 (.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)) (.f64 (+.f64 (+.f64 x x) 2) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2))))
(/.f64 (neg.f64 (*.f64 2 (pow.f64 x 3))) (neg.f64 (fma.f64 x x 0)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)) (neg.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (neg.f64 (+.f64 (+.f64 x x) 2)))
(/.f64 (+.f64 1 (pow.f64 (fma.f64 2 x -1) 3)) (+.f64 1 (-.f64 (*.f64 (fma.f64 2 x -1) (fma.f64 2 x -1)) (fma.f64 2 x -1))))
(/.f64 (-.f64 1 (*.f64 (fma.f64 2 x -1) (fma.f64 2 x -1))) (-.f64 1 (fma.f64 2 x -1)))
(/.f64 (.f64 (+.f64 x x) (.f64 2 (pow.f64 x 3))) (fma.f64 x x 0))
(/.f64 (*.f64 (+.f64 x x) (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2)))
(/.f64 (*.f64 (+.f64 x x) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (+.f64 (+.f64 x x) 2))
(/.f64 (.f64 (.f64 2 (pow.f64 x 3)) (+.f64 x x)) (fma.f64 x x 0))
(/.f64 (*.f64 0 (+.f64 x x)) 0)
(/.f64 (*.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1) (+.f64 x x)) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2)))
(/.f64 (*.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (+.f64 x x)) (+.f64 (+.f64 x x) 2))
(pow.f64 (+.f64 x x) 1)
(pow.f64 (+.f64 x x) 3)
(pow.f64 (+.f64 x x) 2)
(pow.f64 (+.f64 x x) 1/2)
(pow.f64 (+.f64 x x) 1/3)
(sqrt.f64 (+.f64 x x))
(fabs.f64 (+.f64 x x))
(log.f64 (pow.f64 (exp.f64 2) x))
(cbrt.f64 (+.f64 x x))
(expm1.f64 (log1p.f64 (+.f64 x x)))
(hypot.f64 (sqrt.f64 x) (sqrt.f64 x))
(exp.f64 (log.f64 (+.f64 x x)))
(log1p.f64 (expm1.f64 (+.f64 x x)))
(fma.f64 1 x x)
(fma.f64 1 (fma.f64 2 x 1) -1)
(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 2 x 1)) 2) (cbrt.f64 (fma.f64 2 x 1)) -1)
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) x)
(fma.f64 (sqrt.f64 (fma.f64 2 x 1)) (sqrt.f64 (fma.f64 2 x 1)) -1)
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) x)

Outputs
(*.f64 2 x)
-2
(*.f64 2 x)
-2
(*.f64 2 x)
-2
(*.f64 2 x)
-2
(*.f64 2 x)
-2
(*.f64 2 x)
-2
(*.f64 2 x)
-2
(*.f64 2 x)
-2
(*.f64 2 x)
-2
(*.f64 2 x)
-2
(*.f64 2 x)
-2
(*.f64 2 x)
-2
(+.f64 1 (fma.f64 2 x -1))
-2
(+.f64 1 (*.f64 (fma.f64 2 x -1) 1))
-2
(+.f64 x x)
-2
(+.f64 (+.f64 x x) 0)
-2
(+.f64 (+.f64 x x) (+.f64 (+.f64 x x) (*.f64 -2 x)))
-2
(+.f64 (+.f64 x x) (*.f64 (fma.f64 2 x -1) (+.f64 x x)))
-2
(+.f64 (fma.f64 2 x 1) -1)
-2
(+.f64 -1 (fma.f64 2 x 1))
-2
(+.f64 (+.f64 1 x) (+.f64 x -1))
-2
(+.f64 (+.f64 1 x) (-.f64 x 1))
-2
(+.f64 (fma.f64 2 x -1) 1)
-2
(+.f64 (.f64 (+.f64 x x) x) (.f64 (+.f64 x x) x))
-2
(+.f64 (.f64 (fma.f64 2 x 1) (+.f64 x x)) (.f64 -1 (+.f64 x x)))
-2
(+.f64 (.f64 x (+.f64 x x)) (.f64 x (+.f64 x x)))
-2
(+.f64 (.f64 (+.f64 x x) (fma.f64 2 x 1)) (.f64 (+.f64 x x) -1))
-2
(*.f64 1 (+.f64 x x))
-2
(*.f64 x 2)
-2
(*.f64 (+.f64 x x) 1)
-2
(*.f64 (+.f64 x x) (+.f64 x x))
-2
(*.f64 (cbrt.f64 x) (+.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 2)))
(.f64 -2 (.f64 (pow.f64 (cbrt.f64 x) -2) (cbrt.f64 x)))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (+.f64 (cbrt.f64 x) (cbrt.f64 x)))
(.f64 -2 (.f64 (pow.f64 (cbrt.f64 x) -2) (cbrt.f64 x)))
(*.f64 (sqrt.f64 x) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))
(.f64 (sqrt.f64 x) (.f64 -2 (sqrt.f64 x)))
(.f64 (.f64 2 (pow.f64 x 3)) (/.f64 1 (fma.f64 x x 0)))
-2
(*.f64 0 (/.f64 1 0))
-2
(*.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1) (/.f64 1 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2))))
-2
(*.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (/.f64 1 (+.f64 (+.f64 x x) 2)))
-2
(*.f64 2 x)
-2
(.f64 2 (.f64 x (+.f64 x x)))
-2
(*.f64 (cbrt.f64 2) (cbrt.f64 x))
(*.f64 -2 (cbrt.f64 x))
(.f64 4 (.f64 x x))
-2
(*.f64 8 (pow.f64 x 3))
-2
(*.f64 (sqrt.f64 2) (sqrt.f64 x))
(*.f64 -2 (sqrt.f64 x))
(*.f64 (+.f64 (sqrt.f64 (fma.f64 2 x 1)) 1) (-.f64 (sqrt.f64 (fma.f64 2 x 1)) 1))
-2
(*.f64 (pow.f64 (+.f64 x x) 3/2) (pow.f64 (+.f64 x x) 3/2))
-2
(.f64 (.f64 (+.f64 x x) 2) x)
-2
(.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(.f64 -2 (.f64 (pow.f64 (cbrt.f64 x) -2) (cbrt.f64 x)))
(.f64 (.f64 2 (sqrt.f64 x)) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (.f64 -2 (sqrt.f64 x)))
(/.f64 1 (+.f64 x x))
-2
(/.f64 1 (/.f64 (fma.f64 x x 0) (*.f64 2 (pow.f64 x 3))))
-2
(/.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2)) (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)))
-2
(/.f64 1 (/.f64 (+.f64 (+.f64 x x) 2) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)))
-2
(/.f64 (*.f64 2 (pow.f64 x 3)) (fma.f64 x x 0))
-2
(/.f64 0 0)
-2
(/.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2)))
-2
(/.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (-.f64 1 (*.f64 (fma.f64 2 x 1) -1))))
-2
(/.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (+.f64 (+.f64 x x) 2))
-2
(/.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (-.f64 (fma.f64 2 x 1) -1))
-2
(/.f64 (cbrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)) (cbrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2))))
-2
(/.f64 (cbrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (cbrt.f64 (+.f64 (+.f64 x x) 2)))
-2
(/.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 3))) (cbrt.f64 (fma.f64 x x 0)))
(/.f64 -2 (cbrt.f64 (fma.f64 x x -2)))
(/.f64 (.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1) (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)) (.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2)) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2))))
-2
(/.f64 (.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (.f64 (+.f64 (+.f64 x x) 2) (+.f64 (+.f64 x x) 2)))
-2
(/.f64 (.f64 (.f64 2 (pow.f64 x 3)) (.f64 2 (pow.f64 x 3))) (.f64 (fma.f64 x x 0) (fma.f64 x x 0)))
-2
(/.f64 (sqrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)) (sqrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2))))
-2
(/.f64 (sqrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (sqrt.f64 (+.f64 (+.f64 x x) 2)))
-2
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 3))) (sqrt.f64 (fma.f64 x x 0)))
(/.f64 -2 (sqrt.f64 (fma.f64 x x -2)))
(/.f64 (sqrt.f64 0) (sqrt.f64 0))
-2
(/.f64 (pow.f64 (*.f64 2 (pow.f64 x 3)) 3) (pow.f64 (fma.f64 x x 0) 3))
(/.f64 -2 (pow.f64 (fma.f64 x x -2) 3))
(/.f64 (.f64 (.f64 2 (pow.f64 x 3)) 0) (*.f64 (fma.f64 x x 0) 0))
-2
(/.f64 (.f64 0 (.f64 2 (pow.f64 x 3))) (*.f64 0 (fma.f64 x x 0)))
-2
(/.f64 (.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2)) (+.f64 (+.f64 x x) 2)))
-2
(/.f64 (.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)) (.f64 (+.f64 (+.f64 x x) 2) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2))))
-2
(/.f64 (neg.f64 (*.f64 2 (pow.f64 x 3))) (neg.f64 (fma.f64 x x 0)))
-2
(/.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)) (neg.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2))))
-2
(/.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (neg.f64 (+.f64 (+.f64 x x) 2)))
-2
(/.f64 (+.f64 1 (pow.f64 (fma.f64 2 x -1) 3)) (+.f64 1 (-.f64 (*.f64 (fma.f64 2 x -1) (fma.f64 2 x -1)) (fma.f64 2 x -1))))
-2
(/.f64 (-.f64 1 (*.f64 (fma.f64 2 x -1) (fma.f64 2 x -1))) (-.f64 1 (fma.f64 2 x -1)))
-2
(/.f64 (.f64 (+.f64 x x) (.f64 2 (pow.f64 x 3))) (fma.f64 x x 0))
-2
(/.f64 (*.f64 (+.f64 x x) (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2)))
-2
(/.f64 (*.f64 (+.f64 x x) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (+.f64 (+.f64 x x) 2))
-2
(/.f64 (.f64 (.f64 2 (pow.f64 x 3)) (+.f64 x x)) (fma.f64 x x 0))
-2
(/.f64 (*.f64 0 (+.f64 x x)) 0)
-2
(/.f64 (*.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1) (+.f64 x x)) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2)))
-2
(/.f64 (*.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (+.f64 x x)) (+.f64 (+.f64 x x) 2))
-2
(pow.f64 (+.f64 x x) 1)
-2
(pow.f64 (+.f64 x x) 3)
-2
(pow.f64 (+.f64 x x) 2)
-2
(pow.f64 (+.f64 x x) 1/2)
-2
(pow.f64 (+.f64 x x) 1/3)
-2
(sqrt.f64 (+.f64 x x))
-2
(fabs.f64 (+.f64 x x))
-2
(log.f64 (pow.f64 (exp.f64 2) x))
-2
(cbrt.f64 (+.f64 x x))
-2
(expm1.f64 (log1p.f64 (+.f64 x x)))
-2
(hypot.f64 (sqrt.f64 x) (sqrt.f64 x))
(exp.f64 (log.f64 (+.f64 x x)))
-2
(log1p.f64 (expm1.f64 (+.f64 x x)))
-2
(fma.f64 1 x x)
(+.f64 x -2)
(fma.f64 1 (fma.f64 2 x 1) -1)
-2
(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 2 x 1)) 2) (cbrt.f64 (fma.f64 2 x 1)) -1)
-2
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) x)
(fma.f64 (pow.f64 (cbrt.f64 x) -2) (cbrt.f64 x) x)
(fma.f64 (sqrt.f64 (fma.f64 2 x 1)) (sqrt.f64 (fma.f64 2 x 1)) -1)
-2
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) x)

eval26.0ms (0.8%)

Compiler: Compiled 1156 to 772 computations (33.2% saved)

prune15.0ms (0.5%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	0	1	1
Picked	0	2	2
Done	0	2	2
Total	101	7	108

Accurracy

100.0%

Counts

108 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	13.3%	(-.f64 (+.f64 1 (+.f64 x x)) 1)
▶	13.3%	(+.f64 (+.f64 1 x) (-.f64 x 1))
✓	20.3%	(+.f64 x x)
▶	10.8%	(+.f64 x -2)
✓	99.4%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
	3.9%	0
✓	100.0%	(hypot.f64 x x)
✓	13.3%	(-.f64 (+.f64 1 (+.f64 x x)) 1)
▶	13.3%	(+.f64 (+.f64 1 x) (-.f64 x 1))
✓	20.3%	(+.f64 x x)
▶	10.8%	(+.f64 x -2)
✓	99.4%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
	3.9%	0

Compiler

Compiled 76 to 52 computations (31.6% saved)

localize40.0ms (1.2%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	52.4%	(+.f64 (+.f64 1 x) (-.f64 x 1))

Compiler

Compiled 22 to 15 computations (31.8% saved)

series0.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(+.f64 (+.f64 1 x) (-.f64 x 1))
0.0ms	x	@	-inf	(+.f64 (+.f64 1 x) (-.f64 x 1))
0.0ms	x	@	inf	(+.f64 (+.f64 1 x) (-.f64 x 1))

rewrite146.0ms (4.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1948×	`prod-diff`
1074×	`unpow-prod-down`
1046×	`fma-def`
688×	`log-prod`
578×	`pow-prod-down`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	166	19
2	2536	15

Stop Event

1×	node limit

Counts

1 → 115

Calls

Call 1

Inputs
(+.f64 (+.f64 1 x) (-.f64 x 1))

Outputs
(-.f64 x (-.f64 1 (+.f64 1 x)))
(-.f64 (+.f64 1 (+.f64 x x)) 1)
(-.f64 (exp.f64 (log1p.f64 (expm1.f64 (log1p.f64 (+.f64 x x))))) 1)
(-.f64 (/.f64 (pow.f64 (+.f64 1 x) 2) (+.f64 1 (-.f64 x (+.f64 x -1)))) (/.f64 (pow.f64 (+.f64 x -1) 2) (+.f64 1 (-.f64 x (+.f64 x -1)))))
(*.f64 1 (expm1.f64 (log1p.f64 (+.f64 x x))))
(*.f64 (expm1.f64 (log1p.f64 (+.f64 x x))) 1)
(*.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))) (pow.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))) 2))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))) 2) (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))) 2) (pow.f64 (cbrt.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x))))) 2))
(*.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))) (sqrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))))
(*.f64 (+.f64 (pow.f64 (+.f64 x -1) 3) (pow.f64 (+.f64 1 x) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 2) (-.f64 (pow.f64 (+.f64 x -1) 2) (fma.f64 x x -1)))))
(*.f64 (+.f64 (pow.f64 (+.f64 x -1) 3) (pow.f64 (+.f64 1 x) 3)) (pow.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 2) (-.f64 (pow.f64 (+.f64 x -1) 2) (fma.f64 x x -1)))) 1))
(*.f64 (-.f64 (pow.f64 (+.f64 1 x) 2) (pow.f64 (+.f64 x -1) 2)) (/.f64 1 (+.f64 1 (-.f64 x (+.f64 x -1)))))
(*.f64 (-.f64 (pow.f64 (+.f64 1 x) 2) (pow.f64 (+.f64 x -1) 2)) (pow.f64 (/.f64 1 (+.f64 1 (-.f64 x (+.f64 x -1)))) 1))
(*.f64 (pow.f64 1 1/3) (expm1.f64 (log1p.f64 (+.f64 x x))))
(*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x))))) 3) (pow.f64 (cbrt.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x))))) 3))
(.f64 (pow.f64 (.f64 (cbrt.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x))))) (cbrt.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))))) 3) (pow.f64 (cbrt.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x))))) 3))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))) 2)) 3) (pow.f64 (cbrt.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x))))) 3))
(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x))))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x))))) 3))
(*.f64 (pow.f64 (pow.f64 (expm1.f64 (log1p.f64 (+.f64 x x))) 3/2) 1/3) (pow.f64 (pow.f64 (expm1.f64 (log1p.f64 (+.f64 x x))) 3/2) 1/3))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (expm1.f64 (log1p.f64 (+.f64 x x))) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (expm1.f64 (log1p.f64 (+.f64 x x))) 3)) 1/3))
(.f64 (pow.f64 (pow.f64 (.f64 (expm1.f64 (log1p.f64 (+.f64 x x))) (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x))))) 2) 1/3) (pow.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))) 1/3))
(*.f64 (pow.f64 (pow.f64 (expm1.f64 (log1p.f64 (+.f64 x x))) 5/2) 1/3) (pow.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))) 1/3))
(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x))))) 2) (pow.f64 (sqrt.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x))))) 2))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))) 2)) 2) (pow.f64 (sqrt.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x))))) 2))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 1 x) 2) (-.f64 (pow.f64 (+.f64 x -1) 2) (fma.f64 x x -1))) (+.f64 (pow.f64 (+.f64 x -1) 3) (pow.f64 (+.f64 1 x) 3))))
(/.f64 1 (/.f64 (+.f64 1 (-.f64 x (+.f64 x -1))) (-.f64 (pow.f64 (+.f64 1 x) 2) (pow.f64 (+.f64 x -1) 2))))
(/.f64 (+.f64 (pow.f64 (+.f64 x -1) 3) (pow.f64 (+.f64 1 x) 3)) (+.f64 (pow.f64 (+.f64 1 x) 2) (-.f64 (pow.f64 (+.f64 x -1) 2) (fma.f64 x x -1))))
(/.f64 (+.f64 (pow.f64 (+.f64 x -1) 3) (pow.f64 (+.f64 1 x) 3)) (+.f64 (pow.f64 (+.f64 x -1) 2) (-.f64 (pow.f64 (+.f64 1 x) 2) (fma.f64 x x -1))))
(/.f64 (-.f64 (pow.f64 (+.f64 1 x) 2) (pow.f64 (+.f64 x -1) 2)) (+.f64 1 (-.f64 x (+.f64 x -1))))
(/.f64 (fma.f64 (+.f64 1 (pow.f64 x 3)) (+.f64 (fma.f64 x x 1) x) (.f64 (fma.f64 x (+.f64 x -1) 1) (+.f64 (pow.f64 x 3) -1))) (.f64 (fma.f64 x (+.f64 x -1) 1) (+.f64 (fma.f64 x x 1) x)))
(/.f64 (fma.f64 (+.f64 1 (pow.f64 x 3)) (+.f64 1 x) (.f64 (fma.f64 x (+.f64 x -1) 1) (fma.f64 x x -1))) (.f64 (fma.f64 x (+.f64 x -1) 1) (+.f64 1 x)))
(/.f64 (fma.f64 (-.f64 1 (.f64 x x)) (+.f64 (fma.f64 x x 1) x) (.f64 (-.f64 1 x) (+.f64 (pow.f64 x 3) -1))) (*.f64 (-.f64 1 x) (+.f64 (fma.f64 x x 1) x)))
(/.f64 (fma.f64 (-.f64 1 (.f64 x x)) (+.f64 1 x) (.f64 (-.f64 1 x) (fma.f64 x x -1))) (*.f64 (-.f64 1 x) (+.f64 1 x)))
(/.f64 (fma.f64 (+.f64 (pow.f64 x 3) -1) (fma.f64 x (+.f64 x -1) 1) (.f64 (+.f64 (fma.f64 x x 1) x) (+.f64 1 (pow.f64 x 3)))) (.f64 (+.f64 (fma.f64 x x 1) x) (fma.f64 x (+.f64 x -1) 1)))
(/.f64 (fma.f64 (+.f64 (pow.f64 x 3) -1) (-.f64 1 x) (.f64 (+.f64 (fma.f64 x x 1) x) (-.f64 1 (.f64 x x)))) (*.f64 (+.f64 (fma.f64 x x 1) x) (-.f64 1 x)))
(/.f64 (fma.f64 (fma.f64 x x -1) (fma.f64 x (+.f64 x -1) 1) (.f64 (+.f64 1 x) (+.f64 1 (pow.f64 x 3)))) (.f64 (+.f64 1 x) (fma.f64 x (+.f64 x -1) 1)))
(/.f64 (fma.f64 (fma.f64 x x -1) (-.f64 1 x) (.f64 (+.f64 1 x) (-.f64 1 (.f64 x x)))) (*.f64 (+.f64 1 x) (-.f64 1 x)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 x -1) 3) (pow.f64 (+.f64 1 x) 3))) (neg.f64 (+.f64 (pow.f64 (+.f64 1 x) 2) (-.f64 (pow.f64 (+.f64 x -1) 2) (fma.f64 x x -1)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (+.f64 1 x) 2) (pow.f64 (+.f64 x -1) 2))) (neg.f64 (+.f64 1 (-.f64 x (+.f64 x -1)))))
(/.f64 (+.f64 1 (pow.f64 (+.f64 x (+.f64 x -1)) 3)) (+.f64 1 (-.f64 (pow.f64 (+.f64 x (+.f64 x -1)) 2) (+.f64 x (+.f64 x -1)))))
(/.f64 (-.f64 (pow.f64 (+.f64 1 (+.f64 x x)) 3) 1) (+.f64 (pow.f64 (+.f64 1 (+.f64 x x)) 2) (+.f64 1 (*.f64 (+.f64 1 (+.f64 x x)) 1))))
(/.f64 (-.f64 1 (pow.f64 (+.f64 x (+.f64 x -1)) 2)) (-.f64 1 (+.f64 x (+.f64 x -1))))
(/.f64 (-.f64 (pow.f64 (+.f64 x -1) 2) (pow.f64 (+.f64 1 x) 2)) (-.f64 (+.f64 x -1) (+.f64 1 x)))
(/.f64 (-.f64 (pow.f64 (+.f64 1 (+.f64 x x)) 2) 1) (+.f64 (+.f64 1 (+.f64 x x)) 1))
(pow.f64 (expm1.f64 (log1p.f64 (+.f64 x x))) 1)
(pow.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))) 3)
(pow.f64 (pow.f64 (expm1.f64 (log1p.f64 (+.f64 x x))) 2) 1/2)
(pow.f64 (pow.f64 (expm1.f64 (log1p.f64 (+.f64 x x))) 3) 1/3)
(pow.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))) 2)
(pow.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 x) 2) (-.f64 (pow.f64 (+.f64 x -1) 2) (fma.f64 x x -1))) (+.f64 (pow.f64 (+.f64 x -1) 3) (pow.f64 (+.f64 1 x) 3))) -1)
(pow.f64 (/.f64 (+.f64 1 (-.f64 x (+.f64 x -1))) (-.f64 (pow.f64 (+.f64 1 x) 2) (pow.f64 (+.f64 x -1) 2))) -1)
(sqrt.f64 (pow.f64 (expm1.f64 (log1p.f64 (+.f64 x x))) 2))
(log.f64 (exp.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))))
(log.f64 (+.f64 1 (expm1.f64 (expm1.f64 (log1p.f64 (+.f64 x x))))))
(log.f64 (*.f64 (exp.f64 (+.f64 1 x)) (+.f64 1 (expm1.f64 (+.f64 x -1)))))
(log.f64 (*.f64 (+.f64 1 (expm1.f64 (+.f64 1 x))) (exp.f64 (+.f64 x -1))))
(log.f64 (*.f64 (+.f64 1 (expm1.f64 (+.f64 1 x))) (+.f64 1 (expm1.f64 (+.f64 x -1)))))
(log.f64 (*.f64 (exp.f64 (+.f64 x -1)) (+.f64 1 (expm1.f64 (+.f64 1 x)))))
(log.f64 (*.f64 (+.f64 1 (expm1.f64 (+.f64 x -1))) (exp.f64 (+.f64 1 x))))
(log.f64 (*.f64 (+.f64 1 (expm1.f64 (+.f64 x -1))) (+.f64 1 (expm1.f64 (+.f64 1 x)))))
(cbrt.f64 (pow.f64 (expm1.f64 (log1p.f64 (+.f64 x x))) 3))
(expm1.f64 (log1p.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))))
(expm1.f64 (log1p.f64 (+.f64 x x)))
(exp.f64 (log1p.f64 (+.f64 x (+.f64 x -1))))
(exp.f64 (*.f64 (log1p.f64 (+.f64 x (+.f64 x -1))) 1))
(exp.f64 (.f64 (.f64 (log1p.f64 (+.f64 x (+.f64 x -1))) 1) 1))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x))))) 3))
(exp.f64 (.f64 (.f64 3 (log1p.f64 (+.f64 x (+.f64 x -1)))) 1/3))
(exp.f64 (.f64 (.f64 1/2 (log1p.f64 (+.f64 x (+.f64 x -1)))) 2))
(log1p.f64 (expm1.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))))
(fma.f64 1 x (+.f64 1 (+.f64 x -1)))
(fma.f64 1 x (+.f64 -1 (+.f64 1 x)))
(fma.f64 1 x (neg.f64 (-.f64 1 (+.f64 1 x))))
(fma.f64 1 (+.f64 1 x) (+.f64 x -1))
(fma.f64 1 (+.f64 x -1) (+.f64 1 x))
(fma.f64 1 (+.f64 x (+.f64 x -1)) 1)
(fma.f64 1 (+.f64 1 (+.f64 x x)) -1)
(fma.f64 x 1 (+.f64 1 (+.f64 x -1)))
(fma.f64 x 1 (+.f64 -1 (+.f64 1 x)))
(fma.f64 x 1 (neg.f64 (-.f64 1 (+.f64 1 x))))
(fma.f64 (+.f64 1 x) 1 (+.f64 x -1))
(fma.f64 (+.f64 x -1) 1 (+.f64 1 x))
(fma.f64 (cbrt.f64 (+.f64 x -1)) (pow.f64 (cbrt.f64 (+.f64 x -1)) 2) (+.f64 1 x))
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 x -1)) 2) (cbrt.f64 (+.f64 x -1)) (+.f64 1 x))
(fma.f64 (cbrt.f64 (+.f64 1 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) 2) (+.f64 x -1))
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2) (cbrt.f64 (+.f64 1 x)) (+.f64 x -1))
(fma.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 x) 2) (+.f64 1 (+.f64 x -1)))
(fma.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 x) 2) (+.f64 -1 (+.f64 1 x)))
(fma.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 x) 2) (neg.f64 (-.f64 1 (+.f64 1 x))))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (+.f64 1 (+.f64 x -1)))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (+.f64 -1 (+.f64 1 x)))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (neg.f64 (-.f64 1 (+.f64 1 x))))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) 1) (+.f64 1 (+.f64 x -1)))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) 1) (+.f64 -1 (+.f64 1 x)))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) 1) (neg.f64 (-.f64 1 (+.f64 1 x))))
(fma.f64 (sqrt.f64 (+.f64 x -1)) (sqrt.f64 (+.f64 x -1)) (+.f64 1 x))
(fma.f64 (hypot.f64 1 (sqrt.f64 x)) (hypot.f64 1 (sqrt.f64 x)) (+.f64 x -1))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (+.f64 1 (+.f64 x -1)))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (+.f64 -1 (+.f64 1 x)))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (-.f64 1 (+.f64 1 x))))
(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 1) (+.f64 1 (+.f64 x -1)))
(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 1) (+.f64 -1 (+.f64 1 x)))
(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 1) (neg.f64 (-.f64 1 (+.f64 1 x))))
(fma.f64 (+.f64 1 (pow.f64 x 3)) (/.f64 1 (fma.f64 x (+.f64 x -1) 1)) (+.f64 x -1))
(fma.f64 (+.f64 (pow.f64 x 3) -1) (/.f64 1 (+.f64 (fma.f64 x x 1) x)) (+.f64 1 x))
(fma.f64 (-.f64 1 (*.f64 x x)) (/.f64 1 (-.f64 1 x)) (+.f64 x -1))
(fma.f64 (fma.f64 x x -1) (/.f64 1 (+.f64 1 x)) (+.f64 1 x))
(fma.f64 (*.f64 (cbrt.f64 (+.f64 x (+.f64 x -1))) (cbrt.f64 (+.f64 x (+.f64 x -1)))) (cbrt.f64 (+.f64 x (+.f64 x -1))) 1)
(fma.f64 (*.f64 (cbrt.f64 (+.f64 1 (+.f64 x x))) (cbrt.f64 (+.f64 1 (+.f64 x x)))) (cbrt.f64 (+.f64 1 (+.f64 x x))) -1)
(fma.f64 (sqrt.f64 (+.f64 x (+.f64 x -1))) (sqrt.f64 (+.f64 x (+.f64 x -1))) 1)
(fma.f64 (sqrt.f64 (+.f64 1 (+.f64 x x))) (sqrt.f64 (+.f64 1 (+.f64 x x))) -1)
(fma.f64 (+.f64 (sqrt.f64 x) 1) (-.f64 (sqrt.f64 x) 1) (+.f64 1 x))
(fma.f64 (/.f64 (fma.f64 x x -1) (+.f64 1 (pow.f64 x 3))) (fma.f64 x (+.f64 x -1) 1) (+.f64 1 x))
(fma.f64 (/.f64 (fma.f64 x x -1) (-.f64 1 (*.f64 x x))) (-.f64 1 x) (+.f64 1 x))

simplify238.0ms (7.3%)

Algorithm

1×	egg-herbie

Rules

1052×	`associate-+r+`
836×	`associate-+l+`
634×	`*-commutative`
524×	`cancel-sign-sub-inv`
388×	`+-commutative`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	298	3137
1	816	2755
2	2516	2581

Stop Event

1×	node limit

Counts

127 → 158

Calls

Call 1

Inputs
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(*.f64 2 x)
(-.f64 x (-.f64 1 (+.f64 1 x)))
(-.f64 (+.f64 1 (+.f64 x x)) 1)
(-.f64 (exp.f64 (log1p.f64 (expm1.f64 (log1p.f64 (+.f64 x x))))) 1)
(-.f64 (/.f64 (pow.f64 (+.f64 1 x) 2) (+.f64 1 (-.f64 x (+.f64 x -1)))) (/.f64 (pow.f64 (+.f64 x -1) 2) (+.f64 1 (-.f64 x (+.f64 x -1)))))
(*.f64 1 (expm1.f64 (log1p.f64 (+.f64 x x))))
(*.f64 (expm1.f64 (log1p.f64 (+.f64 x x))) 1)
(*.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))) (pow.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))) 2))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))) 2) (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))) 2) (pow.f64 (cbrt.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x))))) 2))
(*.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))) (sqrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))))
(*.f64 (+.f64 (pow.f64 (+.f64 x -1) 3) (pow.f64 (+.f64 1 x) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 2) (-.f64 (pow.f64 (+.f64 x -1) 2) (fma.f64 x x -1)))))
(*.f64 (+.f64 (pow.f64 (+.f64 x -1) 3) (pow.f64 (+.f64 1 x) 3)) (pow.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 2) (-.f64 (pow.f64 (+.f64 x -1) 2) (fma.f64 x x -1)))) 1))
(*.f64 (-.f64 (pow.f64 (+.f64 1 x) 2) (pow.f64 (+.f64 x -1) 2)) (/.f64 1 (+.f64 1 (-.f64 x (+.f64 x -1)))))
(*.f64 (-.f64 (pow.f64 (+.f64 1 x) 2) (pow.f64 (+.f64 x -1) 2)) (pow.f64 (/.f64 1 (+.f64 1 (-.f64 x (+.f64 x -1)))) 1))
(*.f64 (pow.f64 1 1/3) (expm1.f64 (log1p.f64 (+.f64 x x))))
(*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x))))) 3) (pow.f64 (cbrt.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x))))) 3))
(.f64 (pow.f64 (.f64 (cbrt.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x))))) (cbrt.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))))) 3) (pow.f64 (cbrt.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x))))) 3))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))) 2)) 3) (pow.f64 (cbrt.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x))))) 3))
(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x))))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x))))) 3))
(*.f64 (pow.f64 (pow.f64 (expm1.f64 (log1p.f64 (+.f64 x x))) 3/2) 1/3) (pow.f64 (pow.f64 (expm1.f64 (log1p.f64 (+.f64 x x))) 3/2) 1/3))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (expm1.f64 (log1p.f64 (+.f64 x x))) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (expm1.f64 (log1p.f64 (+.f64 x x))) 3)) 1/3))
(.f64 (pow.f64 (pow.f64 (.f64 (expm1.f64 (log1p.f64 (+.f64 x x))) (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x))))) 2) 1/3) (pow.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))) 1/3))
(*.f64 (pow.f64 (pow.f64 (expm1.f64 (log1p.f64 (+.f64 x x))) 5/2) 1/3) (pow.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))) 1/3))
(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x))))) 2) (pow.f64 (sqrt.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x))))) 2))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))) 2)) 2) (pow.f64 (sqrt.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x))))) 2))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 1 x) 2) (-.f64 (pow.f64 (+.f64 x -1) 2) (fma.f64 x x -1))) (+.f64 (pow.f64 (+.f64 x -1) 3) (pow.f64 (+.f64 1 x) 3))))
(/.f64 1 (/.f64 (+.f64 1 (-.f64 x (+.f64 x -1))) (-.f64 (pow.f64 (+.f64 1 x) 2) (pow.f64 (+.f64 x -1) 2))))
(/.f64 (+.f64 (pow.f64 (+.f64 x -1) 3) (pow.f64 (+.f64 1 x) 3)) (+.f64 (pow.f64 (+.f64 1 x) 2) (-.f64 (pow.f64 (+.f64 x -1) 2) (fma.f64 x x -1))))
(/.f64 (+.f64 (pow.f64 (+.f64 x -1) 3) (pow.f64 (+.f64 1 x) 3)) (+.f64 (pow.f64 (+.f64 x -1) 2) (-.f64 (pow.f64 (+.f64 1 x) 2) (fma.f64 x x -1))))
(/.f64 (-.f64 (pow.f64 (+.f64 1 x) 2) (pow.f64 (+.f64 x -1) 2)) (+.f64 1 (-.f64 x (+.f64 x -1))))
(/.f64 (fma.f64 (+.f64 1 (pow.f64 x 3)) (+.f64 (fma.f64 x x 1) x) (.f64 (fma.f64 x (+.f64 x -1) 1) (+.f64 (pow.f64 x 3) -1))) (.f64 (fma.f64 x (+.f64 x -1) 1) (+.f64 (fma.f64 x x 1) x)))
(/.f64 (fma.f64 (+.f64 1 (pow.f64 x 3)) (+.f64 1 x) (.f64 (fma.f64 x (+.f64 x -1) 1) (fma.f64 x x -1))) (.f64 (fma.f64 x (+.f64 x -1) 1) (+.f64 1 x)))
(/.f64 (fma.f64 (-.f64 1 (.f64 x x)) (+.f64 (fma.f64 x x 1) x) (.f64 (-.f64 1 x) (+.f64 (pow.f64 x 3) -1))) (*.f64 (-.f64 1 x) (+.f64 (fma.f64 x x 1) x)))
(/.f64 (fma.f64 (-.f64 1 (.f64 x x)) (+.f64 1 x) (.f64 (-.f64 1 x) (fma.f64 x x -1))) (*.f64 (-.f64 1 x) (+.f64 1 x)))
(/.f64 (fma.f64 (+.f64 (pow.f64 x 3) -1) (fma.f64 x (+.f64 x -1) 1) (.f64 (+.f64 (fma.f64 x x 1) x) (+.f64 1 (pow.f64 x 3)))) (.f64 (+.f64 (fma.f64 x x 1) x) (fma.f64 x (+.f64 x -1) 1)))
(/.f64 (fma.f64 (+.f64 (pow.f64 x 3) -1) (-.f64 1 x) (.f64 (+.f64 (fma.f64 x x 1) x) (-.f64 1 (.f64 x x)))) (*.f64 (+.f64 (fma.f64 x x 1) x) (-.f64 1 x)))
(/.f64 (fma.f64 (fma.f64 x x -1) (fma.f64 x (+.f64 x -1) 1) (.f64 (+.f64 1 x) (+.f64 1 (pow.f64 x 3)))) (.f64 (+.f64 1 x) (fma.f64 x (+.f64 x -1) 1)))
(/.f64 (fma.f64 (fma.f64 x x -1) (-.f64 1 x) (.f64 (+.f64 1 x) (-.f64 1 (.f64 x x)))) (*.f64 (+.f64 1 x) (-.f64 1 x)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 x -1) 3) (pow.f64 (+.f64 1 x) 3))) (neg.f64 (+.f64 (pow.f64 (+.f64 1 x) 2) (-.f64 (pow.f64 (+.f64 x -1) 2) (fma.f64 x x -1)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (+.f64 1 x) 2) (pow.f64 (+.f64 x -1) 2))) (neg.f64 (+.f64 1 (-.f64 x (+.f64 x -1)))))
(/.f64 (+.f64 1 (pow.f64 (+.f64 x (+.f64 x -1)) 3)) (+.f64 1 (-.f64 (pow.f64 (+.f64 x (+.f64 x -1)) 2) (+.f64 x (+.f64 x -1)))))
(/.f64 (-.f64 (pow.f64 (+.f64 1 (+.f64 x x)) 3) 1) (+.f64 (pow.f64 (+.f64 1 (+.f64 x x)) 2) (+.f64 1 (*.f64 (+.f64 1 (+.f64 x x)) 1))))
(/.f64 (-.f64 1 (pow.f64 (+.f64 x (+.f64 x -1)) 2)) (-.f64 1 (+.f64 x (+.f64 x -1))))
(/.f64 (-.f64 (pow.f64 (+.f64 x -1) 2) (pow.f64 (+.f64 1 x) 2)) (-.f64 (+.f64 x -1) (+.f64 1 x)))
(/.f64 (-.f64 (pow.f64 (+.f64 1 (+.f64 x x)) 2) 1) (+.f64 (+.f64 1 (+.f64 x x)) 1))
(pow.f64 (expm1.f64 (log1p.f64 (+.f64 x x))) 1)
(pow.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))) 3)
(pow.f64 (pow.f64 (expm1.f64 (log1p.f64 (+.f64 x x))) 2) 1/2)
(pow.f64 (pow.f64 (expm1.f64 (log1p.f64 (+.f64 x x))) 3) 1/3)
(pow.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))) 2)
(pow.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 x) 2) (-.f64 (pow.f64 (+.f64 x -1) 2) (fma.f64 x x -1))) (+.f64 (pow.f64 (+.f64 x -1) 3) (pow.f64 (+.f64 1 x) 3))) -1)
(pow.f64 (/.f64 (+.f64 1 (-.f64 x (+.f64 x -1))) (-.f64 (pow.f64 (+.f64 1 x) 2) (pow.f64 (+.f64 x -1) 2))) -1)
(sqrt.f64 (pow.f64 (expm1.f64 (log1p.f64 (+.f64 x x))) 2))
(log.f64 (exp.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))))
(log.f64 (+.f64 1 (expm1.f64 (expm1.f64 (log1p.f64 (+.f64 x x))))))
(log.f64 (*.f64 (exp.f64 (+.f64 1 x)) (+.f64 1 (expm1.f64 (+.f64 x -1)))))
(log.f64 (*.f64 (+.f64 1 (expm1.f64 (+.f64 1 x))) (exp.f64 (+.f64 x -1))))
(log.f64 (*.f64 (+.f64 1 (expm1.f64 (+.f64 1 x))) (+.f64 1 (expm1.f64 (+.f64 x -1)))))
(log.f64 (*.f64 (exp.f64 (+.f64 x -1)) (+.f64 1 (expm1.f64 (+.f64 1 x)))))
(log.f64 (*.f64 (+.f64 1 (expm1.f64 (+.f64 x -1))) (exp.f64 (+.f64 1 x))))
(log.f64 (*.f64 (+.f64 1 (expm1.f64 (+.f64 x -1))) (+.f64 1 (expm1.f64 (+.f64 1 x)))))
(cbrt.f64 (pow.f64 (expm1.f64 (log1p.f64 (+.f64 x x))) 3))
(expm1.f64 (log1p.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))))
(expm1.f64 (log1p.f64 (+.f64 x x)))
(exp.f64 (log1p.f64 (+.f64 x (+.f64 x -1))))
(exp.f64 (*.f64 (log1p.f64 (+.f64 x (+.f64 x -1))) 1))
(exp.f64 (.f64 (.f64 (log1p.f64 (+.f64 x (+.f64 x -1))) 1) 1))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (+.f64 x x))))) 3))
(exp.f64 (.f64 (.f64 3 (log1p.f64 (+.f64 x (+.f64 x -1)))) 1/3))
(exp.f64 (.f64 (.f64 1/2 (log1p.f64 (+.f64 x (+.f64 x -1)))) 2))
(log1p.f64 (expm1.f64 (expm1.f64 (log1p.f64 (+.f64 x x)))))
(fma.f64 1 x (+.f64 1 (+.f64 x -1)))
(fma.f64 1 x (+.f64 -1 (+.f64 1 x)))
(fma.f64 1 x (neg.f64 (-.f64 1 (+.f64 1 x))))
(fma.f64 1 (+.f64 1 x) (+.f64 x -1))
(fma.f64 1 (+.f64 x -1) (+.f64 1 x))
(fma.f64 1 (+.f64 x (+.f64 x -1)) 1)
(fma.f64 1 (+.f64 1 (+.f64 x x)) -1)
(fma.f64 x 1 (+.f64 1 (+.f64 x -1)))
(fma.f64 x 1 (+.f64 -1 (+.f64 1 x)))
(fma.f64 x 1 (neg.f64 (-.f64 1 (+.f64 1 x))))
(fma.f64 (+.f64 1 x) 1 (+.f64 x -1))
(fma.f64 (+.f64 x -1) 1 (+.f64 1 x))
(fma.f64 (cbrt.f64 (+.f64 x -1)) (pow.f64 (cbrt.f64 (+.f64 x -1)) 2) (+.f64 1 x))
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 x -1)) 2) (cbrt.f64 (+.f64 x -1)) (+.f64 1 x))
(fma.f64 (cbrt.f64 (+.f64 1 x)) (pow.f64 (cbrt.f64 (+.f64 1 x)) 2) (+.f64 x -1))
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2) (cbrt.f64 (+.f64 1 x)) (+.f64 x -1))
(fma.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 x) 2) (+.f64 1 (+.f64 x -1)))
(fma.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 x) 2) (+.f64 -1 (+.f64 1 x)))
(fma.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 x) 2) (neg.f64 (-.f64 1 (+.f64 1 x))))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (+.f64 1 (+.f64 x -1)))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (+.f64 -1 (+.f64 1 x)))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (neg.f64 (-.f64 1 (+.f64 1 x))))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) 1) (+.f64 1 (+.f64 x -1)))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) 1) (+.f64 -1 (+.f64 1 x)))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) 1) (neg.f64 (-.f64 1 (+.f64 1 x))))
(fma.f64 (sqrt.f64 (+.f64 x -1)) (sqrt.f64 (+.f64 x -1)) (+.f64 1 x))
(fma.f64 (hypot.f64 1 (sqrt.f64 x)) (hypot.f64 1 (sqrt.f64 x)) (+.f64 x -1))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (+.f64 1 (+.f64 x -1)))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (+.f64 -1 (+.f64 1 x)))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (-.f64 1 (+.f64 1 x))))
(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 1) (+.f64 1 (+.f64 x -1)))
(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 1) (+.f64 -1 (+.f64 1 x)))
(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 1) (neg.f64 (-.f64 1 (+.f64 1 x))))
(fma.f64 (+.f64 1 (pow.f64 x 3)) (/.f64 1 (fma.f64 x (+.f64 x -1) 1)) (+.f64 x -1))
(fma.f64 (+.f64 (pow.f64 x 3) -1) (/.f64 1 (+.f64 (fma.f64 x x 1) x)) (+.f64 1 x))
(fma.f64 (-.f64 1 (*.f64 x x)) (/.f64 1 (-.f64 1 x)) (+.f64 x -1))
(fma.f64 (fma.f64 x x -1) (/.f64 1 (+.f64 1 x)) (+.f64 1 x))
(fma.f64 (*.f64 (cbrt.f64 (+.f64 x (+.f64 x -1))) (cbrt.f64 (+.f64 x (+.f64 x -1)))) (cbrt.f64 (+.f64 x (+.f64 x -1))) 1)
(fma.f64 (*.f64 (cbrt.f64 (+.f64 1 (+.f64 x x))) (cbrt.f64 (+.f64 1 (+.f64 x x)))) (cbrt.f64 (+.f64 1 (+.f64 x x))) -1)
(fma.f64 (sqrt.f64 (+.f64 x (+.f64 x -1))) (sqrt.f64 (+.f64 x (+.f64 x -1))) 1)
(fma.f64 (sqrt.f64 (+.f64 1 (+.f64 x x))) (sqrt.f64 (+.f64 1 (+.f64 x x))) -1)
(fma.f64 (+.f64 (sqrt.f64 x) 1) (-.f64 (sqrt.f64 x) 1) (+.f64 1 x))
(fma.f64 (/.f64 (fma.f64 x x -1) (+.f64 1 (pow.f64 x 3))) (fma.f64 x (+.f64 x -1) 1) (+.f64 1 x))
(fma.f64 (/.f64 (fma.f64 x x -1) (-.f64 1 (*.f64 x x))) (-.f64 1 x) (+.f64 1 x))

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

eval115.0ms (3.5%)

Compiler: Compiled 2642 to 1705 computations (35.5% saved)

prune21.0ms (0.7%)

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	156	2	158
Fresh	0	1	1
Picked	1	1	2
Done	0	4	4
Total	157	8	165

Accurracy

100.0%

Counts

165 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	13.3%	(-.f64 (+.f64 1 (+.f64 x x)) 1)
	20.3%	(-.f64 x (-.f64 1 (+.f64 1 x)))
	16.5%	(+.f64 x (+.f64 -1 (/.f64 (-.f64 1 (*.f64 x x)) (-.f64 1 x))))
✓	20.3%	(+.f64 x x)
✓	10.8%	(+.f64 x -2)
✓	99.4%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
	3.9%	0

Compiler

Compiled 112 to 74 computations (33.9% saved)

regimes20.0ms (0.6%)

Counts

10 → 1

Calls

Call 1

Inputs
0
(+.f64 x -2)
(+.f64 x x)
(+.f64 (+.f64 1 x) (-.f64 x 1))
(-.f64 x (-.f64 1 (+.f64 1 x)))
(-.f64 (+.f64 1 (+.f64 x x)) 1)
(+.f64 x (+.f64 -1 (/.f64 (-.f64 1 (*.f64 x x)) (-.f64 1 x))))
(hypot.f64 x x)
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))

Outputs
(hypot.f64 x x)

Calls

4 calls:

6.0ms	x
5.0ms	(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
4.0ms	(+.f64 (pow.f64 x 2) (pow.f64 x 2))
4.0ms	(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 83 to 55 computations (33.7% saved)

regimes6.0ms (0.2%)

Counts

7 → 1

Calls

Call 1

Inputs
0
(+.f64 x -2)
(+.f64 x x)
(+.f64 (+.f64 1 x) (-.f64 x 1))
(-.f64 x (-.f64 1 (+.f64 1 x)))
(-.f64 (+.f64 1 (+.f64 x x)) 1)
(+.f64 x (+.f64 -1 (/.f64 (-.f64 1 (*.f64 x x)) (-.f64 1 x))))

Outputs
(+.f64 x x)

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
20.3%	1	`x`

Compiler

Compiled 44 to 29 computations (34.1% saved)

regimes7.0ms (0.2%)

Counts

2 → 2

Calls

Call 1

Inputs
0
(+.f64 x -2)

Outputs
0
(+.f64 x -2)

Calls

1 calls:

6.0ms

Results

Accuracy	Segments	Branch
12.5%	2	`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
0

Outputs
0

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
3.9%	1	`x`

Compiler

Compiled 4 to 3 computations (25% saved)

bsearch16.0ms (0.5%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
16.0ms	0.000519058423105674	9706.977706622309

Results

13.0ms

144×

body

256

valid

Compiler

Compiled 85 to 73 computations (14.1% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	32
1	15	32

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(hypot.f64 x x)
(+.f64 x x)
(if (<=.f64 x 2) 0 (+.f64 x -2))
0

Outputs
(hypot.f64 x x)
(+.f64 x x)
(if (<=.f64 x 2) 0 (+.f64 x -2))
0

Compiler

Compiled 19 to 13 computations (31.6% saved)

soundness817.0ms (25.2%)

Rules

2556×	`fma-def`
1506×	`pow1`
1482×	`distribute-lft-out`
1420×	`add-exp-log`
1416×	`log1p-expm1-u`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	14	7
2	33	7
3	56	7
4	121	7
5	380	7
6	1381	7
7	2589	7
8	3932	7
9	4860	7
10	5626	7
11	6637	7
12	7494	7
0	4	7
1	80	7
2	933	7
0	116	717
1	249	681
2	686	669
3	4006	669
0	8	17
1	167	7
2	2257	7
0	92	504
1	253	504
0	8	17
1	167	7
2	2257	7
0	7	19
1	165	7
2	2610	7
0	216	357
1	790	357

Stop Event

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

Compiler

Compiled 268 to 103 computations (61.6% saved)

end0.0ms (0%)

preprocess37.0ms (1.1%)

Remove: (abs x)
Compiler: Compiled 58 to 38 computations (34.5% saved)

analyze1.0ms (0%)

sample1.1s (33.7%)

preprocess92.0ms (2.8%)

simplify112.0ms (3.5%)

eval1.0ms (0%)

prune1.0ms (0%)

localize14.0ms (0.4%)

series2.0ms (0.1%)

rewrite51.0ms (1.6%)

simplify70.0ms (2.2%)

eval9.0ms (0.3%)

prune7.0ms (0.2%)

localize69.0ms (2.1%)

series2.0ms (0%)

rewrite50.0ms (1.5%)

simplify16.0ms (0.5%)

eval10.0ms (0.3%)

prune8.0ms (0.3%)

localize38.0ms (1.2%)

series1.0ms (0%)

rewrite55.0ms (1.7%)

simplify26.0ms (0.8%)

eval26.0ms (0.8%)

prune15.0ms (0.5%)

localize40.0ms (1.2%)

series0.0ms (0%)

rewrite146.0ms (4.5%)

simplify238.0ms (7.3%)

eval115.0ms (3.5%)

prune21.0ms (0.7%)

regimes20.0ms (0.6%)

regimes6.0ms (0.2%)

regimes7.0ms (0.2%)

regimes3.0ms (0.1%)

bsearch16.0ms (0.5%)

simplify5.0ms (0.1%)

soundness817.0ms (25.2%)

end0.0ms (0%)

preprocess37.0ms (1.1%)

Profiling