Details

analyze3.0ms (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	4096×	body	1024	valid
304.0ms	2054×	body	512	valid
182.0ms	1657×	body	256	valid
160.0ms	449×	body	2048	valid
0.0ms	2×	body	256	infinite

Bogosity

preprocess29.0ms (1.2%)

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

1 alts after pruning (1 fresh and 0 done)

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

Accurracy

100.0%

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(expm1.f64 x)

Compiler

Compiled 3 to 2 computations (33.3% 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)

series40.0ms (1.7%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
40.0ms	x	@	0	(expm1.f64 x)
0.0ms	x	@	inf	(expm1.f64 x)
0.0ms	x	@	-inf	(expm1.f64 x)

rewrite48.0ms (2.1%)

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)

simplify65.0ms (2.8%)

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)

eval16.0ms (0.7%)

Compiler: Compiled 761 to 425 computations (44.2% saved)

prune8.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	72	3	75

Accurracy

100.0%

Counts

75 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(expm1.f64 x)
▶	45.5%	(exp.f64 (.f64 (.f64 3 (log.f64 (expm1.f64 x))) 1/3))
	97.7%	x

Compiler

Compiled 14 to 11 computations (21.4% saved)

localize12.0ms (0.5%)

Local Accuracy

Found 4 expressions with local accuracy:

New	Accuracy	Program
	100.0%	(expm1.f64 x)
✓	99.7%	(*.f64 3 (log.f64 (expm1.f64 x)))
✓	99.7%	(.f64 (.f64 3 (log.f64 (expm1.f64 x))) 1/3)
✓	95.4%	(exp.f64 (.f64 (.f64 3 (log.f64 (expm1.f64 x))) 1/3))

Compiler

Compiled 29 to 16 computations (44.8% saved)

series76.0ms (3.3%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
52.0ms	x	@	inf	(.f64 (.f64 3 (log.f64 (expm1.f64 x))) 1/3)
22.0ms	x	@	-inf	(.f64 (.f64 3 (log.f64 (expm1.f64 x))) 1/3)
0.0ms	x	@	0	(.f64 (.f64 3 (log.f64 (expm1.f64 x))) 1/3)
0.0ms	x	@	inf	(*.f64 3 (log.f64 (expm1.f64 x)))
0.0ms	x	@	-inf	(*.f64 3 (log.f64 (expm1.f64 x)))

rewrite65.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1524×	`pow1`
1408×	`add-exp-log`
1406×	`log1p-expm1-u`
1404×	`expm1-log1p-u`
1376×	`add-log-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	61
1	212	29
2	2389	29

Stop Event

1×	node limit

Counts

3 → 49

Calls

Call 1

Inputs
(exp.f64 (.f64 (.f64 3 (log.f64 (expm1.f64 x))) 1/3))
(.f64 (.f64 3 (log.f64 (expm1.f64 x))) 1/3)
(*.f64 3 (log.f64 (expm1.f64 x)))

Outputs
(+.f64 1 (-.f64 (expm1.f64 x) 1))
(+.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 (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 (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 (exp.f64 1/3) (*.f64 3 (log.f64 (expm1.f64 x))))
(pow.f64 (exp.f64 3) (*.f64 (log.f64 (expm1.f64 x)) 1/3))
(pow.f64 (cbrt.f64 (expm1.f64 x)) 3)
(pow.f64 (sqrt.f64 (expm1.f64 x)) 2)
(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))))
(pow.f64 (exp.f64 1) (log.f64 (expm1.f64 x)))
(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)
(log1p.f64 (expm1.f64 (expm1.f64 x)))
(+.f64 (log.f64 (sqrt.f64 (expm1.f64 x))) (log.f64 (sqrt.f64 (expm1.f64 x))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (log.f64 (cbrt.f64 (expm1.f64 x))))
(+.f64 0 (log.f64 (expm1.f64 x)))
(-.f64 (+.f64 1 (log.f64 (expm1.f64 x))) 1)
(pow.f64 (log.f64 (expm1.f64 x)) 1)
(pow.f64 (cbrt.f64 (log.f64 (expm1.f64 x))) 3)
(pow.f64 (pow.f64 (log.f64 (expm1.f64 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (log.f64 (expm1.f64 x))) 2)
(sqrt.f64 (pow.f64 (log.f64 (expm1.f64 x)) 2))
(log.f64 (expm1.f64 x))
(cbrt.f64 (pow.f64 (log.f64 (expm1.f64 x)) 3))
(expm1.f64 (log1p.f64 (log.f64 (expm1.f64 x))))
(exp.f64 (log.f64 (log.f64 (expm1.f64 x))))
(log1p.f64 (-.f64 (expm1.f64 x) 1))
(-.f64 (+.f64 1 (*.f64 3 (log.f64 (expm1.f64 x)))) 1)
(pow.f64 (*.f64 3 (log.f64 (expm1.f64 x))) 1)
(pow.f64 (cbrt.f64 (*.f64 3 (log.f64 (expm1.f64 x)))) 3)
(pow.f64 (pow.f64 (*.f64 3 (log.f64 (expm1.f64 x))) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 3 (log.f64 (expm1.f64 x)))) 2)
(sqrt.f64 (*.f64 (pow.f64 (log.f64 (expm1.f64 x)) 2) 9))
(log.f64 (pow.f64 (expm1.f64 x) 3))
(cbrt.f64 (pow.f64 (*.f64 3 (log.f64 (expm1.f64 x))) 3))
(expm1.f64 (log1p.f64 (*.f64 3 (log.f64 (expm1.f64 x)))))
(exp.f64 (log.f64 (*.f64 3 (log.f64 (expm1.f64 x)))))
(log1p.f64 (-.f64 (pow.f64 (expm1.f64 x) 3) 1))

simplify67.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

1062×	`fma-def`
922×	`log-prod`
808×	`unswap-sqr`
668×	`distribute-lft-in`
654×	`distribute-rgt-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	141	1095
1	333	1095
2	1200	1085
3	5708	1085

Stop Event

1×	node limit

Counts

85 → 92

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)
(log.f64 x)
(+.f64 (*.f64 1/2 x) (log.f64 x))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/24 (pow.f64 x 2)) (log.f64 x)))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/2880 (pow.f64 x 4)) (log.f64 x))))
(log.f64 (-.f64 (exp.f64 x) 1))
(log.f64 (-.f64 (exp.f64 x) 1))
(log.f64 (-.f64 (exp.f64 x) 1))
(log.f64 (-.f64 (exp.f64 x) 1))
(log.f64 (-.f64 (exp.f64 x) 1))
(log.f64 (-.f64 (exp.f64 x) 1))
(log.f64 (-.f64 (exp.f64 x) 1))
(log.f64 (-.f64 (exp.f64 x) 1))
(*.f64 3 (log.f64 x))
(+.f64 (.f64 3 (log.f64 x)) (.f64 3/2 x))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 3 (log.f64 x)) (*.f64 3/2 x)))
(+.f64 (.f64 -1/960 (pow.f64 x 4)) (+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 3 (log.f64 x)) (.f64 3/2 x))))
(*.f64 3 (log.f64 (-.f64 (exp.f64 x) 1)))
(*.f64 3 (log.f64 (-.f64 (exp.f64 x) 1)))
(*.f64 3 (log.f64 (-.f64 (exp.f64 x) 1)))
(*.f64 3 (log.f64 (-.f64 (exp.f64 x) 1)))
(*.f64 3 (log.f64 (-.f64 (exp.f64 x) 1)))
(*.f64 3 (log.f64 (-.f64 (exp.f64 x) 1)))
(*.f64 3 (log.f64 (-.f64 (exp.f64 x) 1)))
(*.f64 3 (log.f64 (-.f64 (exp.f64 x) 1)))
(+.f64 1 (-.f64 (expm1.f64 x) 1))
(+.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 (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 (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 (exp.f64 1/3) (*.f64 3 (log.f64 (expm1.f64 x))))
(pow.f64 (exp.f64 3) (*.f64 (log.f64 (expm1.f64 x)) 1/3))
(pow.f64 (cbrt.f64 (expm1.f64 x)) 3)
(pow.f64 (sqrt.f64 (expm1.f64 x)) 2)
(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))))
(pow.f64 (exp.f64 1) (log.f64 (expm1.f64 x)))
(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)
(log1p.f64 (expm1.f64 (expm1.f64 x)))
(+.f64 (log.f64 (sqrt.f64 (expm1.f64 x))) (log.f64 (sqrt.f64 (expm1.f64 x))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (log.f64 (cbrt.f64 (expm1.f64 x))))
(+.f64 0 (log.f64 (expm1.f64 x)))
(-.f64 (+.f64 1 (log.f64 (expm1.f64 x))) 1)
(pow.f64 (log.f64 (expm1.f64 x)) 1)
(pow.f64 (cbrt.f64 (log.f64 (expm1.f64 x))) 3)
(pow.f64 (pow.f64 (log.f64 (expm1.f64 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (log.f64 (expm1.f64 x))) 2)
(sqrt.f64 (pow.f64 (log.f64 (expm1.f64 x)) 2))
(log.f64 (expm1.f64 x))
(cbrt.f64 (pow.f64 (log.f64 (expm1.f64 x)) 3))
(expm1.f64 (log1p.f64 (log.f64 (expm1.f64 x))))
(exp.f64 (log.f64 (log.f64 (expm1.f64 x))))
(log1p.f64 (-.f64 (expm1.f64 x) 1))
(-.f64 (+.f64 1 (*.f64 3 (log.f64 (expm1.f64 x)))) 1)
(pow.f64 (*.f64 3 (log.f64 (expm1.f64 x))) 1)
(pow.f64 (cbrt.f64 (*.f64 3 (log.f64 (expm1.f64 x)))) 3)
(pow.f64 (pow.f64 (*.f64 3 (log.f64 (expm1.f64 x))) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 3 (log.f64 (expm1.f64 x)))) 2)
(sqrt.f64 (*.f64 (pow.f64 (log.f64 (expm1.f64 x)) 2) 9))
(log.f64 (pow.f64 (expm1.f64 x) 3))
(cbrt.f64 (pow.f64 (*.f64 3 (log.f64 (expm1.f64 x))) 3))
(expm1.f64 (log1p.f64 (*.f64 3 (log.f64 (expm1.f64 x)))))
(exp.f64 (log.f64 (*.f64 3 (log.f64 (expm1.f64 x)))))
(log1p.f64 (-.f64 (pow.f64 (expm1.f64 x) 3) 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 1/6 (pow.f64 x 3) (fma.f64 x (*.f64 x 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)))
(-.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)
(log.f64 x)
(+.f64 (*.f64 1/2 x) (log.f64 x))
(fma.f64 1/2 x (log.f64 x))
(fma.f64 x 1/2 (log.f64 x))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/24 (pow.f64 x 2)) (log.f64 x)))
(fma.f64 1/2 x (fma.f64 1/24 (*.f64 x x) (log.f64 x)))
(fma.f64 x 1/2 (fma.f64 (*.f64 x x) 1/24 (log.f64 x)))
(fma.f64 x 1/2 (fma.f64 x (*.f64 x 1/24) (log.f64 x)))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/24 (pow.f64 x 2)) (+.f64 (*.f64 -1/2880 (pow.f64 x 4)) (log.f64 x))))
(fma.f64 1/2 x (fma.f64 1/24 (*.f64 x x) (fma.f64 -1/2880 (pow.f64 x 4) (log.f64 x))))
(fma.f64 x 1/2 (fma.f64 (*.f64 x x) 1/24 (fma.f64 (pow.f64 x 4) -1/2880 (log.f64 x))))
(fma.f64 x (*.f64 x 1/24) (fma.f64 x 1/2 (fma.f64 (pow.f64 x 4) -1/2880 (log.f64 x))))
(log.f64 (-.f64 (exp.f64 x) 1))
(log.f64 (expm1.f64 x))
(log.f64 (-.f64 (exp.f64 x) 1))
(log.f64 (expm1.f64 x))
(log.f64 (-.f64 (exp.f64 x) 1))
(log.f64 (expm1.f64 x))
(log.f64 (-.f64 (exp.f64 x) 1))
(log.f64 (expm1.f64 x))
(log.f64 (-.f64 (exp.f64 x) 1))
(log.f64 (expm1.f64 x))
(log.f64 (-.f64 (exp.f64 x) 1))
(log.f64 (expm1.f64 x))
(log.f64 (-.f64 (exp.f64 x) 1))
(log.f64 (expm1.f64 x))
(log.f64 (-.f64 (exp.f64 x) 1))
(log.f64 (expm1.f64 x))
(*.f64 3 (log.f64 x))
(+.f64 (.f64 3 (log.f64 x)) (.f64 3/2 x))
(fma.f64 3 (log.f64 x) (*.f64 x 3/2))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 3 (log.f64 x)) (*.f64 3/2 x)))
(fma.f64 1/8 (.f64 x x) (fma.f64 3 (log.f64 x) (.f64 x 3/2)))
(fma.f64 (.f64 x x) 1/8 (fma.f64 3 (log.f64 x) (.f64 x 3/2)))
(fma.f64 3 (log.f64 x) (.f64 x (+.f64 3/2 (.f64 x 1/8))))
(+.f64 (.f64 -1/960 (pow.f64 x 4)) (+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 3 (log.f64 x)) (.f64 3/2 x))))
(fma.f64 -1/960 (pow.f64 x 4) (fma.f64 1/8 (.f64 x x) (fma.f64 3 (log.f64 x) (.f64 x 3/2))))
(fma.f64 (pow.f64 x 4) -1/960 (fma.f64 (.f64 x x) 1/8 (fma.f64 3 (log.f64 x) (.f64 x 3/2))))
(fma.f64 (pow.f64 x 4) -1/960 (fma.f64 3 (log.f64 x) (.f64 x (+.f64 3/2 (.f64 x 1/8)))))
(*.f64 3 (log.f64 (-.f64 (exp.f64 x) 1)))
(*.f64 3 (log.f64 (expm1.f64 x)))
(*.f64 3 (log.f64 (-.f64 (exp.f64 x) 1)))
(*.f64 3 (log.f64 (expm1.f64 x)))
(*.f64 3 (log.f64 (-.f64 (exp.f64 x) 1)))
(*.f64 3 (log.f64 (expm1.f64 x)))
(*.f64 3 (log.f64 (-.f64 (exp.f64 x) 1)))
(*.f64 3 (log.f64 (expm1.f64 x)))
(*.f64 3 (log.f64 (-.f64 (exp.f64 x) 1)))
(*.f64 3 (log.f64 (expm1.f64 x)))
(*.f64 3 (log.f64 (-.f64 (exp.f64 x) 1)))
(*.f64 3 (log.f64 (expm1.f64 x)))
(*.f64 3 (log.f64 (-.f64 (exp.f64 x) 1)))
(*.f64 3 (log.f64 (expm1.f64 x)))
(*.f64 3 (log.f64 (-.f64 (exp.f64 x) 1)))
(*.f64 3 (log.f64 (expm1.f64 x)))
(+.f64 1 (-.f64 (expm1.f64 x) 1))
(expm1.f64 x)
(+.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 (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 (-.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) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (exp.f64 x) 1)))
(/.f64 (+.f64 -1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (exp.f64 x) 1)))
(/.f64 (expm1.f64 (*.f64 3 x)) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (exp.f64 x) 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 (exp.f64 1/3) (*.f64 3 (log.f64 (expm1.f64 x))))
(pow.f64 (exp.f64 3) (*.f64 (log.f64 (expm1.f64 x)) 1/3))
(pow.f64 (exp.f64 3) (*.f64 1/3 (log.f64 (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)
(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))))
(pow.f64 (exp.f64 1) (log.f64 (expm1.f64 x)))
(pow.f64 (E.f64) (log.f64 (expm1.f64 x)))
(sqrt.f64 (pow.f64 (expm1.f64 x) 2))
(expm1.f64 x)
(log.f64 (exp.f64 (expm1.f64 x)))
(expm1.f64 x)
(cbrt.f64 (pow.f64 (expm1.f64 x) 3))
(expm1.f64 x)
(expm1.f64 x)
(log1p.f64 (expm1.f64 (expm1.f64 x)))
(expm1.f64 x)
(+.f64 (log.f64 (sqrt.f64 (expm1.f64 x))) (log.f64 (sqrt.f64 (expm1.f64 x))))
(log.f64 (expm1.f64 x))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (log.f64 (cbrt.f64 (expm1.f64 x))))
(log.f64 (expm1.f64 x))
(+.f64 0 (log.f64 (expm1.f64 x)))
(log.f64 (expm1.f64 x))
(-.f64 (+.f64 1 (log.f64 (expm1.f64 x))) 1)
(log.f64 (expm1.f64 x))
(pow.f64 (log.f64 (expm1.f64 x)) 1)
(log.f64 (expm1.f64 x))
(pow.f64 (cbrt.f64 (log.f64 (expm1.f64 x))) 3)
(log.f64 (expm1.f64 x))
(pow.f64 (pow.f64 (log.f64 (expm1.f64 x)) 3) 1/3)
(log.f64 (expm1.f64 x))
(pow.f64 (sqrt.f64 (log.f64 (expm1.f64 x))) 2)
(log.f64 (expm1.f64 x))
(sqrt.f64 (pow.f64 (log.f64 (expm1.f64 x)) 2))
(log.f64 (expm1.f64 x))
(log.f64 (expm1.f64 x))
(cbrt.f64 (pow.f64 (log.f64 (expm1.f64 x)) 3))
(log.f64 (expm1.f64 x))
(expm1.f64 (log1p.f64 (log.f64 (expm1.f64 x))))
(log.f64 (expm1.f64 x))
(exp.f64 (log.f64 (log.f64 (expm1.f64 x))))
(log.f64 (expm1.f64 x))
(log1p.f64 (-.f64 (expm1.f64 x) 1))
(log.f64 (expm1.f64 x))
(-.f64 (+.f64 1 (*.f64 3 (log.f64 (expm1.f64 x)))) 1)
(*.f64 3 (log.f64 (expm1.f64 x)))
(pow.f64 (*.f64 3 (log.f64 (expm1.f64 x))) 1)
(*.f64 3 (log.f64 (expm1.f64 x)))
(pow.f64 (cbrt.f64 (*.f64 3 (log.f64 (expm1.f64 x)))) 3)
(*.f64 3 (log.f64 (expm1.f64 x)))
(pow.f64 (pow.f64 (*.f64 3 (log.f64 (expm1.f64 x))) 3) 1/3)
(*.f64 3 (log.f64 (expm1.f64 x)))
(pow.f64 (sqrt.f64 (*.f64 3 (log.f64 (expm1.f64 x)))) 2)
(*.f64 3 (log.f64 (expm1.f64 x)))
(sqrt.f64 (*.f64 (pow.f64 (log.f64 (expm1.f64 x)) 2) 9))
(*.f64 3 (log.f64 (expm1.f64 x)))
(log.f64 (pow.f64 (expm1.f64 x) 3))
(*.f64 3 (log.f64 (expm1.f64 x)))
(cbrt.f64 (pow.f64 (*.f64 3 (log.f64 (expm1.f64 x))) 3))
(*.f64 3 (log.f64 (expm1.f64 x)))
(expm1.f64 (log1p.f64 (*.f64 3 (log.f64 (expm1.f64 x)))))
(*.f64 3 (log.f64 (expm1.f64 x)))
(exp.f64 (log.f64 (*.f64 3 (log.f64 (expm1.f64 x)))))
(*.f64 3 (log.f64 (expm1.f64 x)))
(log1p.f64 (-.f64 (pow.f64 (expm1.f64 x) 3) 1))
(log1p.f64 (+.f64 (pow.f64 (expm1.f64 x) 3) -1))
(log1p.f64 (+.f64 -1 (pow.f64 (expm1.f64 x) 3)))

eval39.0ms (1.7%)

Compiler: Compiled 2098 to 1394 computations (33.6% saved)

prune51.0ms (2.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	166	3	169

Accurracy

100.0%

Counts

169 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(expm1.f64 x)
✓	45.5%	(exp.f64 (.f64 (.f64 3 (log.f64 (expm1.f64 x))) 1/3))
	97.7%	x

Compiler

Compiled 14 to 11 computations (21.4% saved)

eval0.0ms (0%)

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

prune1.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Accurracy

100.0%

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(expm1.f64 x)
✓	45.5%	(exp.f64 (.f64 (.f64 3 (log.f64 (expm1.f64 x))) 1/3))
	97.7%	x

Compiler

Compiled 14 to 11 computations (21.4% saved)

eval0.0ms (0%)

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

prune1.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Accurracy

100.0%

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(expm1.f64 x)
✓	45.5%	(exp.f64 (.f64 (.f64 3 (log.f64 (expm1.f64 x))) 1/3))
	97.7%	x

Compiler

Compiled 14 to 11 computations (21.4% saved)

regimes8.0ms (0.4%)

Accuracy

Total -61.7b remaining (-1578705%)

Threshold costs -61.7b (-1578705%)

Counts

4 → 1

Calls

Call 1

Inputs
x
(expm1.f64 x)
(-.f64 (exp.f64 x) 1)
(exp.f64 (.f64 (.f64 3 (log.f64 (expm1.f64 x))) 1/3))

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 26 to 18 computations (30.8% 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)

soundness13.0ms (0.6%)

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)

end43.0ms (1.8%)

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

Details

analyze3.0ms (0.1%)

sample1.7s (74.1%)

preprocess29.0ms (1.2%)

simplify11.0ms (0.5%)

eval0.0ms (0%)

prune1.0ms (0%)

localize2.0ms (0.1%)

series40.0ms (1.7%)

rewrite48.0ms (2.1%)

simplify65.0ms (2.8%)

eval16.0ms (0.7%)

prune8.0ms (0.3%)

localize12.0ms (0.5%)

series76.0ms (3.3%)

rewrite65.0ms (2.8%)

simplify67.0ms (2.9%)

eval39.0ms (1.7%)

prune51.0ms (2.2%)

eval0.0ms (0%)

prune1.0ms (0.1%)

eval0.0ms (0%)

prune1.0ms (0.1%)

regimes8.0ms (0.4%)

simplify4.0ms (0.2%)

soundness13.0ms (0.6%)

end43.0ms (1.8%)

Profiling