Metrics for expm1 (example 3.7)

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	74.6%	25.4%	0%	0%	0%	0
100%	74.6%	0%	25.4%	0%	0%	0%	1

Compiler

Compiled 8 to 6 computations (25% saved)

sample1.1s (76.3%)

Results

575.0ms	2734×	body	1024	valid
221.0ms	2840×	body	256	infinite
165.0ms	1376×	body	512	valid
85.0ms	1046×	body	256	valid
63.0ms	260×	body	2048	valid

Bogosity

preprocess67.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

1258×	`fma-neg`
876×	`associate-r`
868×	`unswap-sqr`
826×	`*-commutative`
650×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	21	14
2	27	14
3	35	14
4	58	14
5	109	14
6	253	14
7	703	14
8	2646	14
9	6667	14

Stop Event

1×	node limit

Calls

Call 1

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

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

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify3.0ms (0.2%)

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)

prune2.0ms (0.1%)

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
▶	37.6%	(-.f64 (exp.f64 x) 1)
▶	100.0%	(expm1.f64 x)
▶	37.6%	(-.f64 (exp.f64 x) 1)
▶	100.0%	(expm1.f64 x)

Compiler

Compiled 16 to 12 computations (25% saved)

localize70.0ms (4.7%)

Local Accuracy

Found 2 expressions with local accuracy:

New	Accuracy	Program
✓	37.6%	(-.f64 (exp.f64 x) 1)
✓	100.0%	(expm1.f64 x)

Compiler

Compiled 13 to 7 computations (46.2% saved)

series1.0ms (0%)

Counts

2 → 16

Calls

6 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)
0.0ms	x	@	0	(-.f64 (exp.f64 x) 1)
0.0ms	x	@	-inf	(-.f64 (exp.f64 x) 1)

rewrite61.0ms (4.2%)

Algorithm

1×	batch-egg-rewrite

Rules

1272×	`pow1`
1174×	`add-exp-log`
1172×	`log1p-expm1-u`
1170×	`expm1-log1p-u`
1152×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	158	10
2	1660	10

Stop Event

1×	node limit

Counts

2 → 64

Calls

Call 1

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

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

simplify55.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

1968×	`fma-def`
844×	`div-sub`
668×	`associate-r`
590×	`associate-l`
538×	`log-prod`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	94	1424
1	206	1424
2	642	1028
3	3828	938

Stop Event

1×	node limit

Counts

80 → 51

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

eval9.0ms (0.6%)

Compiler: Compiled 514 to 282 computations (45.1% saved)

prune8.0ms (0.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	50	3	53

Accurracy

100.0%

Counts

53 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	37.6%	(-.f64 (exp.f64 x) 1)
✓	100.0%	(expm1.f64 x)
	68.3%	x
✓	37.6%	(-.f64 (exp.f64 x) 1)
✓	100.0%	(expm1.f64 x)
	68.3%	x

Compiler

Compiled 20 to 14 computations (30% saved)

localize0.0ms (0%)

eval0.0ms (0%)

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

prune2.0ms (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
✓	37.6%	(-.f64 (exp.f64 x) 1)
✓	100.0%	(expm1.f64 x)
	68.3%	x
✓	37.6%	(-.f64 (exp.f64 x) 1)
✓	100.0%	(expm1.f64 x)
	68.3%	x

Compiler

Compiled 20 to 14 computations (30% saved)

localize0.0ms (0%)

eval0.0ms (0%)

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

prune2.0ms (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
✓	37.6%	(-.f64 (exp.f64 x) 1)
✓	100.0%	(expm1.f64 x)
	68.3%	x
✓	37.6%	(-.f64 (exp.f64 x) 1)
✓	100.0%	(expm1.f64 x)
	68.3%	x

Compiler

Compiled 20 to 14 computations (30% saved)

localize0.0ms (0%)

eval0.0ms (0%)

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

prune2.0ms (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
✓	37.6%	(-.f64 (exp.f64 x) 1)
✓	100.0%	(expm1.f64 x)
	68.3%	x

Compiler

Compiled 18 to 12 computations (33.3% saved)

regimes9.0ms (0.6%)

Counts

3 → 1

Calls

Call 1

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

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 18 to 12 computations (33.3% saved)

regimes3.0ms (0.2%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
x

Outputs
x

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
68.3%	1	`x`

Compiler

Compiled 4 to 2 computations (50% 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)

soundness12.0ms (0.8%)

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)

end0.0ms (0%)

preprocess38.0ms (2.6%)

Compiler: Compiled 46 to 32 computations (30.4% saved)

analyze0.0ms (0%)

sample1.1s (76.3%)

preprocess67.0ms (4.6%)

simplify3.0ms (0.2%)

eval0.0ms (0%)

prune2.0ms (0.1%)

localize70.0ms (4.7%)

series1.0ms (0%)

rewrite61.0ms (4.2%)

simplify55.0ms (3.7%)

eval9.0ms (0.6%)

prune8.0ms (0.6%)

localize0.0ms (0%)

eval0.0ms (0%)

prune2.0ms (0.1%)

localize0.0ms (0%)

eval0.0ms (0%)

prune2.0ms (0.1%)

localize0.0ms (0%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes9.0ms (0.6%)

regimes3.0ms (0.2%)

simplify4.0ms (0.2%)

soundness12.0ms (0.8%)

end0.0ms (0%)

preprocess38.0ms (2.6%)

Profiling