Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	74.6%	25.4%	0%	0%	0%	0
0%	0%	74.6%	25.4%	0%	0%	0%	1
50%	37.3%	37.3%	25.4%	0%	0%	0%	2
66.7%	37.3%	18.7%	25.4%	18.7%	0%	0%	3
83.3%	46.7%	9.3%	25.4%	18.7%	0%	0%	4
90.9%	46.7%	4.7%	25.4%	23.3%	0%	0%	5
95.5%	49%	2.3%	25.4%	23.3%	0%	0%	6
97.7%	49%	1.2%	25.4%	24.5%	0%	0%	7
98.8%	49.6%	0.6%	25.4%	24.5%	0%	0%	8
99.4%	49.9%	0.3%	25.4%	24.5%	0%	0%	9
99.7%	49.9%	0.1%	25.4%	24.6%	0%	0%	10
99.9%	49.9%	0.1%	25.4%	24.7%	0%	0%	11
99.9%	49.9%	0%	25.4%	24.7%	0%	0%	12

Compiler

Compiled 8 to 6 computations (25% saved)

sample1.7s (74.1%)

Results

1.1s	4180×	body	1024	valid
356.0ms	2051×	body	512	valid
146.0ms	441×	body	2048	valid
145.0ms	1584×	body	256	valid
0.0ms	1×	body	256	infinite

Bogosity

preprocess52.0ms (2.3%)

Algorithm

2×	egg-herbie

Rules

2×	`1-exp`
2×	`expm1-def`
2×	`sub-neg`
2×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	5
1	13	5
2	14	5
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

Outputs
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify11.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

2×	`1-exp`
2×	`expm1-def`
2×	`sub-neg`
2×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	5
1	13	5
2	14	5

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

Outputs
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)

eval0.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

prune1.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Accurracy

100.0%

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	9.9%	(-.f64 (exp.f64 x) 1)
▶	100.0%	(expm1.f64 x)

Compiler

Compiled 8 to 6 computations (25% saved)

localize2.0ms (0.1%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	100.0%	(expm1.f64 x)

Compiler

Compiled 4 to 2 computations (50% saved)

series0.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(expm1.f64 x)
0.0ms	x	@	inf	(expm1.f64 x)
0.0ms	x	@	-inf	(expm1.f64 x)

rewrite47.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

698×	`pow1`
672×	`add-sqr-sqrt`
660×	`*-un-lft-identity`
640×	`add-exp-log`
640×	`log1p-expm1-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	5
1	76	5
2	876	5

Stop Event

1×	node limit

Counts

1 → 50

Calls

Call 1

Inputs
(expm1.f64 x)

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

simplify60.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

982×	`associate-r`
904×	`div-sub`
864×	`associate-l`
720×	`fma-def`
716×	`log-prod`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	148	1132
1	325	1102
2	932	894
3	5260	870

Stop Event

1×	node limit

Counts

62 → 74

Calls

Call 1

Inputs
x
(+.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 2)) x))
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/24 (pow.f64 x 4)) x)))
(-.f64 (exp.f64 x) 1)
(-.f64 (exp.f64 x) 1)
(-.f64 (exp.f64 x) 1)
(-.f64 (exp.f64 x) 1)
(-.f64 (exp.f64 x) 1)
(-.f64 (exp.f64 x) 1)
(-.f64 (exp.f64 x) 1)
(-.f64 (exp.f64 x) 1)
(+.f64 (exp.f64 x) -1)
(+.f64 0 (expm1.f64 x))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (expm1.f64 x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (expm1.f64 x)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 x)))) (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 x)))))
(-.f64 (exp.f64 x) 1)
(-.f64 (/.f64 (pow.f64 (exp.f64 x) 3) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x)))) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x)))))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1)) (/.f64 1 (+.f64 (exp.f64 x) 1)))
(*.f64 (expm1.f64 x) 1)
(*.f64 1 (expm1.f64 x))
(*.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (expm1.f64 x)))
(*.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 x)))
(*.f64 (pow.f64 (expm1.f64 x) 1/4) (sqrt.f64 (pow.f64 (expm1.f64 x) 3/2)))
(*.f64 (+.f64 (pow.f64 (exp.f64 x) 3) -1) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x)))))
(*.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (/.f64 1 (+.f64 (exp.f64 x) 1)))
(*.f64 (cbrt.f64 (pow.f64 (expm1.f64 x) 5/2)) (pow.f64 (expm1.f64 x) 1/6))
(.f64 (cbrt.f64 (pow.f64 (.f64 (expm1.f64 x) (cbrt.f64 (expm1.f64 x))) 2)) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))
(*.f64 (sqrt.f64 (pow.f64 (expm1.f64 x) 3/2)) (pow.f64 (expm1.f64 x) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 5)) (pow.f64 (expm1.f64 x) 1/6))
(*.f64 (pow.f64 1 1/3) (expm1.f64 x))
(.f64 (pow.f64 (pow.f64 (.f64 (expm1.f64 x) (cbrt.f64 (expm1.f64 x))) 2) 1/3) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))
(*.f64 (pow.f64 (pow.f64 (expm1.f64 x) 5/2) 1/3) (pow.f64 (expm1.f64 x) 1/6))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x))) (+.f64 (pow.f64 (exp.f64 x) 3) -1)))
(/.f64 1 (/.f64 (+.f64 (exp.f64 x) 1) (+.f64 (pow.f64 (exp.f64 x) 2) -1)))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) 3) -1) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x))))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) 3) -1) (+.f64 (pow.f64 (exp.f64 x) 2) (-.f64 1 (*.f64 (exp.f64 x) -1))))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (-.f64 (exp.f64 x) -1))
(/.f64 (neg.f64 (+.f64 (pow.f64 (exp.f64 x) 3) -1)) (neg.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1)) (neg.f64 (+.f64 (exp.f64 x) 1)))
(pow.f64 (expm1.f64 x) 1)
(pow.f64 (cbrt.f64 (expm1.f64 x)) 3)
(pow.f64 (pow.f64 (expm1.f64 x) 2) 1/2)
(pow.f64 (pow.f64 (expm1.f64 x) 3) 1/3)
(pow.f64 (sqrt.f64 (expm1.f64 x)) 2)
(pow.f64 (E.f64) (log.f64 (expm1.f64 x)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (expm1.f64 x))) 2)) (cbrt.f64 (log.f64 (expm1.f64 x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (expm1.f64 x)))) (sqrt.f64 (log.f64 (expm1.f64 x))))
(sqrt.f64 (pow.f64 (expm1.f64 x) 2))
(fabs.f64 (expm1.f64 x))
(log.f64 (exp.f64 (expm1.f64 x)))
(cbrt.f64 (pow.f64 (expm1.f64 x) 3))
(exp.f64 (log.f64 (expm1.f64 x)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (expm1.f64 x))) 3))
(exp.f64 (.f64 (.f64 3 (log.f64 (expm1.f64 x))) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (expm1.f64 x))) 2))
(log1p.f64 (expm1.f64 (expm1.f64 x)))
(fma.f64 1 (exp.f64 x) -1)
(fma.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 2)) (cbrt.f64 (exp.f64 x)) -1)
(fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) -1)

Outputs
x
(+.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(fma.f64 1/2 (*.f64 x x) x)
(fma.f64 x (*.f64 x 1/2) x)
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 2)) x))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) x))
(fma.f64 x (*.f64 x 1/2) (fma.f64 1/6 (pow.f64 x 3) x))
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/24 (pow.f64 x 4)) x)))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 4) x)))
(fma.f64 x (*.f64 x 1/2) (fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/24 (pow.f64 x 4) x)))
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(+.f64 (exp.f64 x) -1)
(expm1.f64 x)
(+.f64 0 (expm1.f64 x))
(expm1.f64 x)
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (expm1.f64 x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (expm1.f64 x)))))
(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (exp.f64 (expm1.f64 x))))) (log.f64 (cbrt.f64 (exp.f64 (expm1.f64 x)))))
(*.f64 3 (log.f64 (cbrt.f64 (exp.f64 (expm1.f64 x)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 x)))) (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 x)))))
(expm1.f64 x)
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(-.f64 (/.f64 (pow.f64 (exp.f64 x) 3) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x)))) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x)))))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) 3) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1))) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1))))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) 3) (+.f64 (exp.f64 x) (+.f64 1 (pow.f64 (exp.f64 x) 2)))) (/.f64 -1 (+.f64 (exp.f64 x) (+.f64 1 (pow.f64 (exp.f64 x) 2)))))
(/.f64 (+.f64 -1 (pow.f64 (exp.f64 x) 3)) (+.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (exp.f64 x) 1)))
(/.f64 (+.f64 -1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1) 1))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1)) (/.f64 1 (+.f64 (exp.f64 x) 1)))
(expm1.f64 x)
(*.f64 (expm1.f64 x) 1)
(expm1.f64 x)
(*.f64 1 (expm1.f64 x))
(expm1.f64 x)
(*.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))
(expm1.f64 x)
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (expm1.f64 x)))
(expm1.f64 x)
(*.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 x)))
(expm1.f64 x)
(*.f64 (pow.f64 (expm1.f64 x) 1/4) (sqrt.f64 (pow.f64 (expm1.f64 x) 3/2)))
(expm1.f64 x)
(*.f64 (+.f64 (pow.f64 (exp.f64 x) 3) -1) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x)))))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) 3) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1))) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1))))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) 3) (+.f64 (exp.f64 x) (+.f64 1 (pow.f64 (exp.f64 x) 2)))) (/.f64 -1 (+.f64 (exp.f64 x) (+.f64 1 (pow.f64 (exp.f64 x) 2)))))
(/.f64 (+.f64 -1 (pow.f64 (exp.f64 x) 3)) (+.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (exp.f64 x) 1)))
(/.f64 (+.f64 -1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1) 1))
(*.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (/.f64 1 (+.f64 (exp.f64 x) 1)))
(expm1.f64 x)
(*.f64 (cbrt.f64 (pow.f64 (expm1.f64 x) 5/2)) (pow.f64 (expm1.f64 x) 1/6))
(*.f64 (pow.f64 (expm1.f64 x) 1/6) (cbrt.f64 (pow.f64 (expm1.f64 x) 5/2)))
(.f64 (cbrt.f64 (pow.f64 (.f64 (expm1.f64 x) (cbrt.f64 (expm1.f64 x))) 2)) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))
(.f64 (cbrt.f64 (cbrt.f64 (expm1.f64 x))) (cbrt.f64 (pow.f64 (.f64 (expm1.f64 x) (cbrt.f64 (expm1.f64 x))) 2)))
(*.f64 (cbrt.f64 (cbrt.f64 (expm1.f64 x))) (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 4) 2)))
(*.f64 (cbrt.f64 (cbrt.f64 (expm1.f64 x))) (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 8)))
(*.f64 (sqrt.f64 (pow.f64 (expm1.f64 x) 3/2)) (pow.f64 (expm1.f64 x) 1/4))
(expm1.f64 x)
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 5)) (pow.f64 (expm1.f64 x) 1/6))
(*.f64 (pow.f64 (expm1.f64 x) 1/6) (sqrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 5)))
(*.f64 (pow.f64 (expm1.f64 x) 1/6) (pow.f64 (cbrt.f64 (expm1.f64 x)) 5/2))
(*.f64 (pow.f64 1 1/3) (expm1.f64 x))
(expm1.f64 x)
(.f64 (pow.f64 (pow.f64 (.f64 (expm1.f64 x) (cbrt.f64 (expm1.f64 x))) 2) 1/3) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))
(.f64 (cbrt.f64 (cbrt.f64 (expm1.f64 x))) (cbrt.f64 (pow.f64 (.f64 (expm1.f64 x) (cbrt.f64 (expm1.f64 x))) 2)))
(*.f64 (cbrt.f64 (cbrt.f64 (expm1.f64 x))) (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 4) 2)))
(*.f64 (cbrt.f64 (cbrt.f64 (expm1.f64 x))) (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 8)))
(*.f64 (pow.f64 (pow.f64 (expm1.f64 x) 5/2) 1/3) (pow.f64 (expm1.f64 x) 1/6))
(*.f64 (pow.f64 (expm1.f64 x) 1/6) (cbrt.f64 (pow.f64 (expm1.f64 x) 5/2)))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x))) (+.f64 (pow.f64 (exp.f64 x) 3) -1)))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) 3) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1))) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1))))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) 3) (+.f64 (exp.f64 x) (+.f64 1 (pow.f64 (exp.f64 x) 2)))) (/.f64 -1 (+.f64 (exp.f64 x) (+.f64 1 (pow.f64 (exp.f64 x) 2)))))
(/.f64 (+.f64 -1 (pow.f64 (exp.f64 x) 3)) (+.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (exp.f64 x) 1)))
(/.f64 (+.f64 -1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1) 1))
(/.f64 1 (/.f64 (+.f64 (exp.f64 x) 1) (+.f64 (pow.f64 (exp.f64 x) 2) -1)))
(expm1.f64 x)
(/.f64 (+.f64 (pow.f64 (exp.f64 x) 3) -1) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x))))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) 3) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1))) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1))))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) 3) (+.f64 (exp.f64 x) (+.f64 1 (pow.f64 (exp.f64 x) 2)))) (/.f64 -1 (+.f64 (exp.f64 x) (+.f64 1 (pow.f64 (exp.f64 x) 2)))))
(/.f64 (+.f64 -1 (pow.f64 (exp.f64 x) 3)) (+.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (exp.f64 x) 1)))
(/.f64 (+.f64 -1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1) 1))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) 3) -1) (+.f64 (pow.f64 (exp.f64 x) 2) (-.f64 1 (*.f64 (exp.f64 x) -1))))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) 3) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1))) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1))))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) 3) (+.f64 (exp.f64 x) (+.f64 1 (pow.f64 (exp.f64 x) 2)))) (/.f64 -1 (+.f64 (exp.f64 x) (+.f64 1 (pow.f64 (exp.f64 x) 2)))))
(/.f64 (+.f64 -1 (pow.f64 (exp.f64 x) 3)) (+.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (exp.f64 x) 1)))
(/.f64 (+.f64 -1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1) 1))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1))
(expm1.f64 x)
(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (-.f64 (exp.f64 x) -1))
(expm1.f64 x)
(/.f64 (neg.f64 (+.f64 (pow.f64 (exp.f64 x) 3) -1)) (neg.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x)))))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) 3) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1))) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1))))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) 3) (+.f64 (exp.f64 x) (+.f64 1 (pow.f64 (exp.f64 x) 2)))) (/.f64 -1 (+.f64 (exp.f64 x) (+.f64 1 (pow.f64 (exp.f64 x) 2)))))
(/.f64 (+.f64 -1 (pow.f64 (exp.f64 x) 3)) (+.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (exp.f64 x) 1)))
(/.f64 (+.f64 -1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1) 1))
(/.f64 (neg.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1)) (neg.f64 (+.f64 (exp.f64 x) 1)))
(expm1.f64 x)
(pow.f64 (expm1.f64 x) 1)
(expm1.f64 x)
(pow.f64 (cbrt.f64 (expm1.f64 x)) 3)
(expm1.f64 x)
(pow.f64 (pow.f64 (expm1.f64 x) 2) 1/2)
(expm1.f64 x)
(pow.f64 (pow.f64 (expm1.f64 x) 3) 1/3)
(expm1.f64 x)
(pow.f64 (sqrt.f64 (expm1.f64 x)) 2)
(expm1.f64 x)
(pow.f64 (E.f64) (log.f64 (expm1.f64 x)))
(expm1.f64 x)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (expm1.f64 x))) 2)) (cbrt.f64 (log.f64 (expm1.f64 x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (expm1.f64 x)))) (sqrt.f64 (log.f64 (expm1.f64 x))))
(sqrt.f64 (pow.f64 (expm1.f64 x) 2))
(expm1.f64 x)
(fabs.f64 (expm1.f64 x))
(expm1.f64 x)
(log.f64 (exp.f64 (expm1.f64 x)))
(expm1.f64 x)
(cbrt.f64 (pow.f64 (expm1.f64 x) 3))
(expm1.f64 x)
(exp.f64 (log.f64 (expm1.f64 x)))
(expm1.f64 x)
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (expm1.f64 x))) 3))
(expm1.f64 x)
(exp.f64 (.f64 (.f64 3 (log.f64 (expm1.f64 x))) 1/3))
(expm1.f64 x)
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (expm1.f64 x))) 2))
(expm1.f64 x)
(log1p.f64 (expm1.f64 (expm1.f64 x)))
(expm1.f64 x)
(fma.f64 1 (exp.f64 x) -1)
(expm1.f64 x)
(fma.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 2)) (cbrt.f64 (exp.f64 x)) -1)
(fma.f64 (cbrt.f64 (pow.f64 (exp.f64 2) x)) (cbrt.f64 (exp.f64 x)) -1)
(fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) -1)
(expm1.f64 x)

localize4.0ms (0.2%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	90.9%	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 9 to 5 computations (44.4% saved)

series0.0ms (0%)

Counts

1 → 4

Calls

3 calls:

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

rewrite49.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1270×	`pow1`
1172×	`add-exp-log`
1170×	`log1p-expm1-u`
1170×	`expm1-log1p-u`
1150×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	5
1	140	5
2	1642	5

Stop Event

1×	node limit

Counts

1 → 31

Calls

Call 1

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

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

simplify55.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1654×	`fma-def`
956×	`associate-/l*`
918×	`associate-/r*`
500×	`associate-r`
484×	`log-prod`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	89	649
1	196	619
2	572	463
3	2812	401

Stop Event

1×	node limit

Counts

35 → 48

Calls

Call 1

Inputs
x
(+.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 2)) x))
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/24 (pow.f64 x 4)) x)))
(+.f64 (exp.f64 x) -1)
(+.f64 -1 (exp.f64 x))
(*.f64 1 (expm1.f64 x))
(*.f64 (expm1.f64 x) 1)
(*.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (expm1.f64 x)))
(*.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 x)))
(.f64 (+.f64 (exp.f64 (.f64 x 3)) -1) (/.f64 1 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (exp.f64 x) 1))))
(*.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (/.f64 1 (+.f64 (exp.f64 x) 1)))
(*.f64 (+.f64 (sqrt.f64 (exp.f64 x)) 1) (-.f64 (sqrt.f64 (exp.f64 x)) 1))
(/.f64 1 (/.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (exp.f64 x) 1)) (+.f64 (exp.f64 (*.f64 x 3)) -1)))
(/.f64 1 (/.f64 (+.f64 (exp.f64 x) 1) (+.f64 (pow.f64 (exp.f64 x) 2) -1)))
(/.f64 (+.f64 (exp.f64 (*.f64 x 3)) -1) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (exp.f64 x) 1)))
(/.f64 (+.f64 (exp.f64 (.f64 x 3)) -1) (+.f64 (pow.f64 (exp.f64 x) 2) (-.f64 1 (.f64 (exp.f64 x) -1))))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (-.f64 (exp.f64 x) -1))
(/.f64 (neg.f64 (+.f64 (exp.f64 (*.f64 x 3)) -1)) (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (exp.f64 x) 1))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1)) (neg.f64 (+.f64 (exp.f64 x) 1)))
(pow.f64 (expm1.f64 x) 1)
(pow.f64 (cbrt.f64 (expm1.f64 x)) 3)
(pow.f64 (pow.f64 (expm1.f64 x) 3) 1/3)
(pow.f64 (sqrt.f64 (expm1.f64 x)) 2)
(sqrt.f64 (pow.f64 (expm1.f64 x) 2))
(log.f64 (exp.f64 (expm1.f64 x)))
(cbrt.f64 (pow.f64 (expm1.f64 x) 3))
(expm1.f64 x)
(exp.f64 (log.f64 (expm1.f64 x)))
(log1p.f64 (expm1.f64 (expm1.f64 x)))
(fma.f64 1 (exp.f64 x) -1)
(fma.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (cbrt.f64 (exp.f64 x)) -1)
(fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) -1)

Outputs
x
(+.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(fma.f64 1/2 (*.f64 x x) x)
(fma.f64 x (*.f64 x 1/2) x)
(*.f64 (fma.f64 x 1/2 1) x)
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 2)) x))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) x))
(fma.f64 x (*.f64 x 1/2) (fma.f64 1/6 (pow.f64 x 3) x))
(fma.f64 x (*.f64 x (fma.f64 x 1/6 1/2)) x)
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/24 (pow.f64 x 4)) x)))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 4) x)))
(fma.f64 x (*.f64 x 1/2) (fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/24 (pow.f64 x 4) x)))
(fma.f64 x (*.f64 x (fma.f64 x 1/6 1/2)) (fma.f64 1/24 (pow.f64 x 4) x))
(+.f64 (exp.f64 x) -1)
(expm1.f64 x)
(+.f64 -1 (exp.f64 x))
(+.f64 (exp.f64 x) -1)
(expm1.f64 x)
(*.f64 1 (expm1.f64 x))
(+.f64 (exp.f64 x) -1)
(expm1.f64 x)
(*.f64 (expm1.f64 x) 1)
(+.f64 (exp.f64 x) -1)
(expm1.f64 x)
(*.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))
(+.f64 (exp.f64 x) -1)
(expm1.f64 x)
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (expm1.f64 x)))
(+.f64 (exp.f64 x) -1)
(expm1.f64 x)
(*.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 x)))
(+.f64 (exp.f64 x) -1)
(expm1.f64 x)
(.f64 (+.f64 (exp.f64 (.f64 x 3)) -1) (/.f64 1 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (exp.f64 x) 1))))
(*.f64 (+.f64 -1 (pow.f64 (exp.f64 x) 3)) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1))))
(/.f64 (+.f64 -1 (pow.f64 (exp.f64 x) 3)) (+.f64 (+.f64 (exp.f64 x) 1) (pow.f64 (exp.f64 x) 2)))
(/.f64 (+.f64 -1 (pow.f64 (exp.f64 x) 3)) (+.f64 (exp.f64 x) (+.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 (expm1.f64 (*.f64 x 3)) (fma.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1) 1))
(*.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (/.f64 1 (+.f64 (exp.f64 x) 1)))
(+.f64 (exp.f64 x) -1)
(expm1.f64 x)
(*.f64 (+.f64 (sqrt.f64 (exp.f64 x)) 1) (-.f64 (sqrt.f64 (exp.f64 x)) 1))
(+.f64 (exp.f64 x) -1)
(expm1.f64 x)
(/.f64 1 (/.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (exp.f64 x) 1)) (+.f64 (exp.f64 (*.f64 x 3)) -1)))
(*.f64 (+.f64 -1 (pow.f64 (exp.f64 x) 3)) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1))))
(/.f64 (+.f64 -1 (pow.f64 (exp.f64 x) 3)) (+.f64 (+.f64 (exp.f64 x) 1) (pow.f64 (exp.f64 x) 2)))
(/.f64 (+.f64 -1 (pow.f64 (exp.f64 x) 3)) (+.f64 (exp.f64 x) (+.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 (expm1.f64 (*.f64 x 3)) (fma.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1) 1))
(/.f64 1 (/.f64 (+.f64 (exp.f64 x) 1) (+.f64 (pow.f64 (exp.f64 x) 2) -1)))
(+.f64 (exp.f64 x) -1)
(expm1.f64 x)
(/.f64 (+.f64 (exp.f64 (*.f64 x 3)) -1) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (exp.f64 x) 1)))
(*.f64 (+.f64 -1 (pow.f64 (exp.f64 x) 3)) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1))))
(/.f64 (+.f64 -1 (pow.f64 (exp.f64 x) 3)) (+.f64 (+.f64 (exp.f64 x) 1) (pow.f64 (exp.f64 x) 2)))
(/.f64 (+.f64 -1 (pow.f64 (exp.f64 x) 3)) (+.f64 (exp.f64 x) (+.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 (expm1.f64 (*.f64 x 3)) (fma.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1) 1))
(/.f64 (+.f64 (exp.f64 (.f64 x 3)) -1) (+.f64 (pow.f64 (exp.f64 x) 2) (-.f64 1 (.f64 (exp.f64 x) -1))))
(*.f64 (+.f64 -1 (pow.f64 (exp.f64 x) 3)) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1))))
(/.f64 (+.f64 -1 (pow.f64 (exp.f64 x) 3)) (+.f64 (+.f64 (exp.f64 x) 1) (pow.f64 (exp.f64 x) 2)))
(/.f64 (+.f64 -1 (pow.f64 (exp.f64 x) 3)) (+.f64 (exp.f64 x) (+.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 (expm1.f64 (*.f64 x 3)) (fma.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1) 1))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1))
(+.f64 (exp.f64 x) -1)
(expm1.f64 x)
(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (-.f64 (exp.f64 x) -1))
(+.f64 (exp.f64 x) -1)
(expm1.f64 x)
(/.f64 (neg.f64 (+.f64 (exp.f64 (*.f64 x 3)) -1)) (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (exp.f64 x) 1))))
(*.f64 (+.f64 -1 (pow.f64 (exp.f64 x) 3)) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1))))
(/.f64 (+.f64 -1 (pow.f64 (exp.f64 x) 3)) (+.f64 (+.f64 (exp.f64 x) 1) (pow.f64 (exp.f64 x) 2)))
(/.f64 (+.f64 -1 (pow.f64 (exp.f64 x) 3)) (+.f64 (exp.f64 x) (+.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 (expm1.f64 (*.f64 x 3)) (fma.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1) 1))
(/.f64 (neg.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1)) (neg.f64 (+.f64 (exp.f64 x) 1)))
(+.f64 (exp.f64 x) -1)
(expm1.f64 x)
(pow.f64 (expm1.f64 x) 1)
(+.f64 (exp.f64 x) -1)
(expm1.f64 x)
(pow.f64 (cbrt.f64 (expm1.f64 x)) 3)
(+.f64 (exp.f64 x) -1)
(expm1.f64 x)
(pow.f64 (pow.f64 (expm1.f64 x) 3) 1/3)
(+.f64 (exp.f64 x) -1)
(expm1.f64 x)
(pow.f64 (sqrt.f64 (expm1.f64 x)) 2)
(+.f64 (exp.f64 x) -1)
(expm1.f64 x)
(sqrt.f64 (pow.f64 (expm1.f64 x) 2))
(+.f64 (exp.f64 x) -1)
(expm1.f64 x)
(log.f64 (exp.f64 (expm1.f64 x)))
(+.f64 (exp.f64 x) -1)
(expm1.f64 x)
(cbrt.f64 (pow.f64 (expm1.f64 x) 3))
(+.f64 (exp.f64 x) -1)
(expm1.f64 x)
(expm1.f64 x)
(+.f64 (exp.f64 x) -1)
(exp.f64 (log.f64 (expm1.f64 x)))
(+.f64 (exp.f64 x) -1)
(expm1.f64 x)
(log1p.f64 (expm1.f64 (expm1.f64 x)))
(+.f64 (exp.f64 x) -1)
(expm1.f64 x)
(fma.f64 1 (exp.f64 x) -1)
(+.f64 (exp.f64 x) -1)
(expm1.f64 x)
(fma.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (cbrt.f64 (exp.f64 x)) -1)
(+.f64 (exp.f64 x) -1)
(expm1.f64 x)
(fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) -1)
(+.f64 (exp.f64 x) -1)
(expm1.f64 x)

eval23.0ms (1%)

Compiler: Compiled 1227 to 692 computations (43.6% saved)

prune28.0ms (1.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	120	4	124

Accurracy

100.0%

Counts

124 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	9.9%	(-.f64 (exp.f64 x) 1)
✓	100.0%	(expm1.f64 x)
▶	37.7%	(cbrt.f64 (pow.f64 (expm1.f64 x) 3))
	96.8%	x

Compiler

Compiled 16 to 12 computations (25% saved)

localize6.0ms (0.3%)

Local Accuracy

Found 3 expressions with local accuracy:

New	Accuracy	Program
	100.0%	(expm1.f64 x)
✓	99.9%	(pow.f64 (expm1.f64 x) 3)
✓	37.7%	(cbrt.f64 (pow.f64 (expm1.f64 x) 3))

Compiler

Compiled 14 to 8 computations (42.9% saved)

series2.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(pow.f64 (expm1.f64 x) 3)
1.0ms	x	@	inf	(pow.f64 (expm1.f64 x) 3)
0.0ms	x	@	0	(pow.f64 (expm1.f64 x) 3)
0.0ms	x	@	0	(cbrt.f64 (pow.f64 (expm1.f64 x) 3))
0.0ms	x	@	inf	(cbrt.f64 (pow.f64 (expm1.f64 x) 3))

rewrite55.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1192×	`pow1`
1114×	`add-exp-log`
1114×	`log1p-expm1-u`
1112×	`expm1-log1p-u`
1090×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	161	16
2	1588	16

Stop Event

1×	node limit

Counts

2 → 41

Calls

Call 1

Inputs
(cbrt.f64 (pow.f64 (expm1.f64 x) 3))
(pow.f64 (expm1.f64 x) 3)

Outputs
(+.f64 (exp.f64 x) -1)
(-.f64 (exp.f64 x) 1)
(*.f64 (expm1.f64 x) 1)
(*.f64 1 (expm1.f64 x))
(*.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))
(*.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 (pow.f64 (expm1.f64 x) 2) 1/3))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (expm1.f64 x)))
(*.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 x)))
(*.f64 (pow.f64 (pow.f64 (expm1.f64 x) 2) 1/3) (cbrt.f64 (expm1.f64 x)))
(*.f64 (pow.f64 1 1/3) (expm1.f64 x))
(*.f64 (pow.f64 (pow.f64 (expm1.f64 x) 3/2) 1/3) (pow.f64 (pow.f64 (expm1.f64 x) 3/2) 1/3))
(/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 (.f64 (exp.f64 x) (exp.f64 x)) (+.f64 1 (.f64 (exp.f64 x) 1))))
(/.f64 (-.f64 (*.f64 (exp.f64 x) (exp.f64 x)) 1) (+.f64 (exp.f64 x) 1))
(pow.f64 (expm1.f64 x) 1)
(pow.f64 (pow.f64 (expm1.f64 x) 3) 1/3)
(pow.f64 (cbrt.f64 (expm1.f64 x)) 3)
(pow.f64 (sqrt.f64 (expm1.f64 x)) 2)
(sqrt.f64 (pow.f64 (expm1.f64 x) 2))
(log.f64 (exp.f64 (expm1.f64 x)))
(expm1.f64 x)
(exp.f64 (log.f64 (expm1.f64 x)))
(log1p.f64 (expm1.f64 (expm1.f64 x)))
(-.f64 (+.f64 1 (pow.f64 (expm1.f64 x) 3)) 1)
(*.f64 (expm1.f64 x) (pow.f64 (expm1.f64 x) 2))
(*.f64 (pow.f64 (expm1.f64 x) 3) 1)
(*.f64 1 (pow.f64 (expm1.f64 x) 3))
(.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 (expm1.f64 x) 2)))
(*.f64 (pow.f64 (expm1.f64 x) 2) (expm1.f64 x))
(.f64 (sqrt.f64 (expm1.f64 x)) (.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (expm1.f64 x) 2)))
(*.f64 (pow.f64 (expm1.f64 x) 3/2) (pow.f64 (expm1.f64 x) 3/2))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 3) (expm1.f64 x))
(*.f64 (pow.f64 (sqrt.f64 (expm1.f64 x)) 3) (pow.f64 (sqrt.f64 (expm1.f64 x)) 3))
(.f64 (.f64 (pow.f64 (expm1.f64 x) 2) 1) (expm1.f64 x))
(.f64 (.f64 (pow.f64 (expm1.f64 x) 2) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (expm1.f64 x)))
(.f64 (.f64 (pow.f64 (expm1.f64 x) 2) (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (expm1.f64 x)))
(sqrt.f64 (pow.f64 (expm1.f64 x) 6))
(log.f64 (exp.f64 (pow.f64 (expm1.f64 x) 3)))
(cbrt.f64 (pow.f64 (pow.f64 (expm1.f64 x) 3) 3))
(expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 x) 3)))
(exp.f64 (*.f64 3 (log.f64 (expm1.f64 x))))
(log1p.f64 (expm1.f64 (pow.f64 (expm1.f64 x) 3)))

simplify62.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

2028×	`fma-def`
802×	`unswap-sqr`
574×	`times-frac`
568×	`exp-prod`
528×	`associate-+l+`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	114	691
1	259	691
2	845	685
3	3917	669

Stop Event

1×	node limit

Counts

65 → 73

Calls

Call 1

Inputs
x
(+.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 2)) x))
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/24 (pow.f64 x 4)) x)))
(-.f64 (exp.f64 x) 1)
(-.f64 (exp.f64 x) 1)
(-.f64 (exp.f64 x) 1)
(-.f64 (exp.f64 x) 1)
(-.f64 (exp.f64 x) 1)
(-.f64 (exp.f64 x) 1)
(-.f64 (exp.f64 x) 1)
(-.f64 (exp.f64 x) 1)
(pow.f64 x 3)
(+.f64 (*.f64 3/2 (pow.f64 x 4)) (pow.f64 x 3))
(+.f64 (.f64 5/4 (pow.f64 x 5)) (+.f64 (.f64 3/2 (pow.f64 x 4)) (pow.f64 x 3)))
(+.f64 (.f64 3/4 (pow.f64 x 6)) (+.f64 (.f64 5/4 (pow.f64 x 5)) (+.f64 (*.f64 3/2 (pow.f64 x 4)) (pow.f64 x 3))))
(pow.f64 (-.f64 (exp.f64 x) 1) 3)
(pow.f64 (-.f64 (exp.f64 x) 1) 3)
(pow.f64 (-.f64 (exp.f64 x) 1) 3)
(pow.f64 (-.f64 (exp.f64 x) 1) 3)
(pow.f64 (-.f64 (exp.f64 x) 1) 3)
(pow.f64 (-.f64 (exp.f64 x) 1) 3)
(pow.f64 (-.f64 (exp.f64 x) 1) 3)
(pow.f64 (-.f64 (exp.f64 x) 1) 3)
(+.f64 (exp.f64 x) -1)
(-.f64 (exp.f64 x) 1)
(*.f64 (expm1.f64 x) 1)
(*.f64 1 (expm1.f64 x))
(*.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))
(*.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 (pow.f64 (expm1.f64 x) 2) 1/3))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (expm1.f64 x)))
(*.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 x)))
(*.f64 (pow.f64 (pow.f64 (expm1.f64 x) 2) 1/3) (cbrt.f64 (expm1.f64 x)))
(*.f64 (pow.f64 1 1/3) (expm1.f64 x))
(*.f64 (pow.f64 (pow.f64 (expm1.f64 x) 3/2) 1/3) (pow.f64 (pow.f64 (expm1.f64 x) 3/2) 1/3))
(/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 (.f64 (exp.f64 x) (exp.f64 x)) (+.f64 1 (.f64 (exp.f64 x) 1))))
(/.f64 (-.f64 (*.f64 (exp.f64 x) (exp.f64 x)) 1) (+.f64 (exp.f64 x) 1))
(pow.f64 (expm1.f64 x) 1)
(pow.f64 (pow.f64 (expm1.f64 x) 3) 1/3)
(pow.f64 (cbrt.f64 (expm1.f64 x)) 3)
(pow.f64 (sqrt.f64 (expm1.f64 x)) 2)
(sqrt.f64 (pow.f64 (expm1.f64 x) 2))
(log.f64 (exp.f64 (expm1.f64 x)))
(expm1.f64 x)
(exp.f64 (log.f64 (expm1.f64 x)))
(log1p.f64 (expm1.f64 (expm1.f64 x)))
(-.f64 (+.f64 1 (pow.f64 (expm1.f64 x) 3)) 1)
(*.f64 (expm1.f64 x) (pow.f64 (expm1.f64 x) 2))
(*.f64 (pow.f64 (expm1.f64 x) 3) 1)
(*.f64 1 (pow.f64 (expm1.f64 x) 3))
(.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 (expm1.f64 x) 2)))
(*.f64 (pow.f64 (expm1.f64 x) 2) (expm1.f64 x))
(.f64 (sqrt.f64 (expm1.f64 x)) (.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (expm1.f64 x) 2)))
(*.f64 (pow.f64 (expm1.f64 x) 3/2) (pow.f64 (expm1.f64 x) 3/2))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 3) (expm1.f64 x))
(*.f64 (pow.f64 (sqrt.f64 (expm1.f64 x)) 3) (pow.f64 (sqrt.f64 (expm1.f64 x)) 3))
(.f64 (.f64 (pow.f64 (expm1.f64 x) 2) 1) (expm1.f64 x))
(.f64 (.f64 (pow.f64 (expm1.f64 x) 2) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (expm1.f64 x)))
(.f64 (.f64 (pow.f64 (expm1.f64 x) 2) (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (expm1.f64 x)))
(sqrt.f64 (pow.f64 (expm1.f64 x) 6))
(log.f64 (exp.f64 (pow.f64 (expm1.f64 x) 3)))
(cbrt.f64 (pow.f64 (pow.f64 (expm1.f64 x) 3) 3))
(expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 x) 3)))
(exp.f64 (*.f64 3 (log.f64 (expm1.f64 x))))
(log1p.f64 (expm1.f64 (pow.f64 (expm1.f64 x) 3)))

Outputs
x
(+.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(fma.f64 1/2 (*.f64 x x) x)
(fma.f64 x (*.f64 x 1/2) x)
(*.f64 (fma.f64 x 1/2 1) x)
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 2)) x))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) x))
(fma.f64 x (*.f64 x 1/2) (fma.f64 1/6 (pow.f64 x 3) x))
(fma.f64 (*.f64 x x) (fma.f64 x 1/6 1/2) x)
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/24 (pow.f64 x 4)) x)))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 4) x)))
(fma.f64 x (*.f64 x 1/2) (fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/24 (pow.f64 x 4) x)))
(fma.f64 (*.f64 x x) (fma.f64 x 1/6 1/2) (fma.f64 1/24 (pow.f64 x 4) x))
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(pow.f64 x 3)
(+.f64 (*.f64 3/2 (pow.f64 x 4)) (pow.f64 x 3))
(fma.f64 3/2 (pow.f64 x 4) (pow.f64 x 3))
(fma.f64 (pow.f64 x 4) 3/2 (pow.f64 x 3))
(+.f64 (.f64 5/4 (pow.f64 x 5)) (+.f64 (.f64 3/2 (pow.f64 x 4)) (pow.f64 x 3)))
(fma.f64 5/4 (pow.f64 x 5) (fma.f64 3/2 (pow.f64 x 4) (pow.f64 x 3)))
(fma.f64 5/4 (pow.f64 x 5) (fma.f64 (pow.f64 x 4) 3/2 (pow.f64 x 3)))
(fma.f64 (pow.f64 x 4) 3/2 (fma.f64 5/4 (pow.f64 x 5) (pow.f64 x 3)))
(+.f64 (.f64 3/4 (pow.f64 x 6)) (+.f64 (.f64 5/4 (pow.f64 x 5)) (+.f64 (*.f64 3/2 (pow.f64 x 4)) (pow.f64 x 3))))
(fma.f64 3/4 (pow.f64 x 6) (fma.f64 5/4 (pow.f64 x 5) (fma.f64 3/2 (pow.f64 x 4) (pow.f64 x 3))))
(fma.f64 3/4 (pow.f64 x 6) (fma.f64 5/4 (pow.f64 x 5) (fma.f64 (pow.f64 x 4) 3/2 (pow.f64 x 3))))
(fma.f64 5/4 (pow.f64 x 5) (fma.f64 3/4 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) 3/2 (pow.f64 x 3))))
(fma.f64 5/4 (pow.f64 x 5) (fma.f64 (pow.f64 x 4) 3/2 (fma.f64 3/4 (pow.f64 x 6) (pow.f64 x 3))))
(pow.f64 (-.f64 (exp.f64 x) 1) 3)
(pow.f64 (expm1.f64 x) 3)
(pow.f64 (-.f64 (exp.f64 x) 1) 3)
(pow.f64 (expm1.f64 x) 3)
(pow.f64 (-.f64 (exp.f64 x) 1) 3)
(pow.f64 (expm1.f64 x) 3)
(pow.f64 (-.f64 (exp.f64 x) 1) 3)
(pow.f64 (expm1.f64 x) 3)
(pow.f64 (-.f64 (exp.f64 x) 1) 3)
(pow.f64 (expm1.f64 x) 3)
(pow.f64 (-.f64 (exp.f64 x) 1) 3)
(pow.f64 (expm1.f64 x) 3)
(pow.f64 (-.f64 (exp.f64 x) 1) 3)
(pow.f64 (expm1.f64 x) 3)
(pow.f64 (-.f64 (exp.f64 x) 1) 3)
(pow.f64 (expm1.f64 x) 3)
(+.f64 (exp.f64 x) -1)
(expm1.f64 x)
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(*.f64 (expm1.f64 x) 1)
(expm1.f64 x)
(*.f64 1 (expm1.f64 x))
(expm1.f64 x)
(*.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))
(expm1.f64 x)
(*.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 (pow.f64 (expm1.f64 x) 2) 1/3))
(expm1.f64 x)
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (expm1.f64 x)))
(expm1.f64 x)
(*.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 x)))
(expm1.f64 x)
(*.f64 (pow.f64 (pow.f64 (expm1.f64 x) 2) 1/3) (cbrt.f64 (expm1.f64 x)))
(expm1.f64 x)
(*.f64 (pow.f64 1 1/3) (expm1.f64 x))
(expm1.f64 x)
(*.f64 (pow.f64 (pow.f64 (expm1.f64 x) 3/2) 1/3) (pow.f64 (pow.f64 (expm1.f64 x) 3/2) 1/3))
(expm1.f64 x)
(/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 (.f64 (exp.f64 x) (exp.f64 x)) (+.f64 1 (.f64 (exp.f64 x) 1))))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) 3) -1) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) 1)))
(/.f64 (+.f64 -1 (pow.f64 (exp.f64 x) 3)) (+.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (exp.f64 x) 1)))
(/.f64 (expm1.f64 (*.f64 3 x)) (+.f64 (exp.f64 x) (+.f64 1 (pow.f64 (exp.f64 2) x))))
(/.f64 (expm1.f64 (*.f64 3 x)) (fma.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1) 1))
(/.f64 (-.f64 (*.f64 (exp.f64 x) (exp.f64 x)) 1) (+.f64 (exp.f64 x) 1))
(expm1.f64 x)
(pow.f64 (expm1.f64 x) 1)
(expm1.f64 x)
(pow.f64 (pow.f64 (expm1.f64 x) 3) 1/3)
(expm1.f64 x)
(pow.f64 (cbrt.f64 (expm1.f64 x)) 3)
(expm1.f64 x)
(pow.f64 (sqrt.f64 (expm1.f64 x)) 2)
(expm1.f64 x)
(sqrt.f64 (pow.f64 (expm1.f64 x) 2))
(expm1.f64 x)
(log.f64 (exp.f64 (expm1.f64 x)))
(expm1.f64 x)
(expm1.f64 x)
(exp.f64 (log.f64 (expm1.f64 x)))
(expm1.f64 x)
(log1p.f64 (expm1.f64 (expm1.f64 x)))
(expm1.f64 x)
(-.f64 (+.f64 1 (pow.f64 (expm1.f64 x) 3)) 1)
(pow.f64 (expm1.f64 x) 3)
(*.f64 (expm1.f64 x) (pow.f64 (expm1.f64 x) 2))
(pow.f64 (expm1.f64 x) 3)
(*.f64 (pow.f64 (expm1.f64 x) 3) 1)
(pow.f64 (expm1.f64 x) 3)
(*.f64 1 (pow.f64 (expm1.f64 x) 3))
(pow.f64 (expm1.f64 x) 3)
(.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 (expm1.f64 x) 2)))
(pow.f64 (expm1.f64 x) 3)
(*.f64 (pow.f64 (expm1.f64 x) 2) (expm1.f64 x))
(pow.f64 (expm1.f64 x) 3)
(.f64 (sqrt.f64 (expm1.f64 x)) (.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (expm1.f64 x) 2)))
(pow.f64 (expm1.f64 x) 3)
(*.f64 (pow.f64 (expm1.f64 x) 3/2) (pow.f64 (expm1.f64 x) 3/2))
(pow.f64 (expm1.f64 x) 3)
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 3) (expm1.f64 x))
(pow.f64 (expm1.f64 x) 3)
(*.f64 (pow.f64 (sqrt.f64 (expm1.f64 x)) 3) (pow.f64 (sqrt.f64 (expm1.f64 x)) 3))
(pow.f64 (expm1.f64 x) 3)
(.f64 (.f64 (pow.f64 (expm1.f64 x) 2) 1) (expm1.f64 x))
(pow.f64 (expm1.f64 x) 3)
(.f64 (.f64 (pow.f64 (expm1.f64 x) 2) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (expm1.f64 x)))
(pow.f64 (expm1.f64 x) 3)
(.f64 (.f64 (pow.f64 (expm1.f64 x) 2) (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (expm1.f64 x)))
(pow.f64 (expm1.f64 x) 3)
(sqrt.f64 (pow.f64 (expm1.f64 x) 6))
(pow.f64 (expm1.f64 x) 3)
(log.f64 (exp.f64 (pow.f64 (expm1.f64 x) 3)))
(pow.f64 (expm1.f64 x) 3)
(cbrt.f64 (pow.f64 (pow.f64 (expm1.f64 x) 3) 3))
(pow.f64 (expm1.f64 x) 3)
(expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 x) 3)))
(pow.f64 (expm1.f64 x) 3)
(exp.f64 (*.f64 3 (log.f64 (expm1.f64 x))))
(pow.f64 (expm1.f64 x) 3)
(log1p.f64 (expm1.f64 (pow.f64 (expm1.f64 x) 3)))
(pow.f64 (expm1.f64 x) 3)

eval47.0ms (2%)

Compiler: Compiled 1707 to 1093 computations (36% saved)

prune17.0ms (0.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	147	4	151

Accurracy

100.0%

Counts

151 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	9.9%	(-.f64 (exp.f64 x) 1)
✓	100.0%	(expm1.f64 x)
✓	37.7%	(cbrt.f64 (pow.f64 (expm1.f64 x) 3))
	96.8%	x

Compiler

Compiled 16 to 12 computations (25% saved)

eval0.0ms (0%)

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

prune1.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

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

Accurracy

100.0%

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	9.9%	(-.f64 (exp.f64 x) 1)
✓	100.0%	(expm1.f64 x)
✓	37.7%	(cbrt.f64 (pow.f64 (expm1.f64 x) 3))
	96.8%	x

Compiler

Compiled 16 to 12 computations (25% saved)

eval0.0ms (0%)

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

prune1.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

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

Accurracy

100.0%

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	9.9%	(-.f64 (exp.f64 x) 1)
✓	100.0%	(expm1.f64 x)
✓	37.7%	(cbrt.f64 (pow.f64 (expm1.f64 x) 3))
	96.8%	x

Compiler

Compiled 16 to 12 computations (25% saved)

regimes8.0ms (0.4%)

Accuracy

Total -58.8b remaining (-752255.6%)

Threshold costs -58.8b (-752255.6%)

Counts

4 → 1

Calls

Call 1

Inputs
x
(expm1.f64 x)
(-.f64 (exp.f64 x) 1)
(cbrt.f64 (pow.f64 (expm1.f64 x) 3))

Outputs
(expm1.f64 x)

Calls

3 calls:

4.0ms	x
2.0ms	(-.f64 (exp.f64 x) 1)
2.0ms	(exp.f64 x)

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(-.f64 (exp.f64 x) 1)`
100.0%	1	`(exp.f64 x)`

Compiler

Compiled 23 to 15 computations (34.8% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(expm1.f64 x)
x

Outputs
(expm1.f64 x)
x

Compiler

Compiled 5 to 3 computations (40% saved)

soundness45.0ms (1.9%)

Rules

2×	`1-exp`
2×	`expm1-def`
2×	`sub-neg`
2×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	5
1	13	5
2	14	5

Stop Event

1×

saturated

Compiler

Compiled 7 to 5 computations (28.6% saved)

end12.0ms (0.5%)

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

Details

analyze2.0ms (0.1%)

sample1.7s (74.1%)

preprocess52.0ms (2.3%)

simplify11.0ms (0.5%)

eval0.0ms (0%)

prune1.0ms (0%)

localize2.0ms (0.1%)

series0.0ms (0%)

rewrite47.0ms (2%)

simplify60.0ms (2.6%)

localize4.0ms (0.2%)

series0.0ms (0%)

rewrite49.0ms (2.1%)

simplify55.0ms (2.4%)

eval23.0ms (1%)

prune28.0ms (1.2%)

localize6.0ms (0.3%)

series2.0ms (0.1%)

rewrite55.0ms (2.4%)

simplify62.0ms (2.7%)

eval47.0ms (2%)

prune17.0ms (0.8%)

eval0.0ms (0%)

prune1.0ms (0.1%)

eval0.0ms (0%)

prune1.0ms (0.1%)

regimes8.0ms (0.4%)

simplify4.0ms (0.2%)

soundness45.0ms (1.9%)

end12.0ms (0.5%)

Profiling