Metrics for Kahan's exp quotient

analyze1.0ms (0.1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
50%	50%	50%	0%	0%	0%	0%	2
75%	75%	25%	0%	0%	0%	0%	3
87.5%	87.5%	12.5%	0%	0%	0%	0%	4
93.8%	93.7%	6.2%	0%	0%	0%	0%	5
96.9%	96.8%	3.1%	0%	0%	0%	0%	6
98.4%	98.4%	1.6%	0%	0%	0%	0%	7
99.2%	99.2%	0.8%	0%	0%	0%	0%	8
99.6%	99.6%	0.4%	0%	0%	0%	0%	9
99.8%	99.8%	0.2%	0%	0%	0%	0%	10
99.9%	99.9%	0.1%	0%	0%	0%	0%	11
100%	99.9%	0%	0%	0%	0%	0%	12

Compiler

Compiled 8 to 6 computations (25% saved)

sample1.1s (58.2%)

Results

448.0ms	2108×	body	1024	valid
259.0ms	2870×	body	256	valid
168.0ms	2045×	body	256	infinite
134.0ms	1026×	body	512	valid
60.0ms	207×	body	2048	valid

Bogosity

preprocess112.0ms (6%)

Algorithm

1×	egg-herbie

Rules

1784×	`div-sub`
1494×	`fma-neg`
1012×	`times-frac`
642×	`distribute-lft-neg-in`
556×	`distribute-rgt-neg-in`

Problems

138×	`(-.f64 (exp.f64 x) 1)`
118×	No Errors

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	88
1	36	88
2	65	86
3	144	80
4	380	80
5	1034	80
6	4094	80
7	7626	80

Stop Event

1×	node limit

Calls

Call 1

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

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

Compiler

Compiled 23 to 14 computations (39.1% saved)

eval0.0ms (0%)

Compiler: Compiled 5 to 3 computations (40% saved)

prune1.0ms (0.1%)

Alt Table

Click to see full alt table

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

Compiler

Compiled 10 to 6 computations (40% saved)

localize40.0ms (2.1%)

Localize:

Found 1 expressions with local error:

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

Compiler

Compiled 9 to 4 computations (55.6% saved)

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite97.0ms (5.2%)

Algorithm

1×	batch-egg-rewrite

Rules

508×	`unpow-prod-down`
354×	`cbrt-prod`
352×	`log-prod`
332×	`log1p-expm1-u`
331×	`expm1-log1p-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	68	17
2	882	17

Stop Event

1×	node limit

Counts

1 → 64

Calls

Call 1

Inputs
(/.f64 (expm1.f64 x) x)

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

simplify74.0ms (4%)

Algorithm

1×	egg-herbie

Rules

960×	`fma-def`
714×	`associate-*r/`
690×	`unswap-sqr`
682×	`distribute-lft-in`
626×	`distribute-rgt-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	215	2185
1	500	2106
2	1594	2042
3	7882	2042

Stop Event

1×	node limit

Counts

76 → 99

Calls

Call 1

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

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

eval66.0ms (3.5%)

Compiler: Compiled 1124 to 513 computations (54.4% saved)

prune14.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	96	3	99
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	96	4	100

Accuracy

100.0%

Counts

100 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (expm1.f64 x) x)
▶	55.3%	(+.f64 1 (*.f64 1/2 x))
▶	99.9%	(*.f64 (/.f64 1 x) (expm1.f64 x))
	54.8%	1
✓	100.0%	(/.f64 (expm1.f64 x) x)
▶	55.3%	(+.f64 1 (*.f64 1/2 x))
▶	99.9%	(*.f64 (/.f64 1 x) (expm1.f64 x))
	54.8%	1

Compiler

Compiled 40 to 30 computations (25% saved)

localize46.0ms (2.5%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	99.9%	(*.f64 (/.f64 1 x) (expm1.f64 x))

Compiler

Compiled 26 to 17 computations (34.6% saved)

series0.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite49.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

634×	`unpow-prod-down`
422×	`log-prod`
404×	`cbrt-prod`
370×	`log1p-expm1-u`
369×	`expm1-log1p-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	91	17
2	1067	17

Stop Event

1×	node limit

Counts

1 → 34

Calls

Call 1

Inputs
(*.f64 (/.f64 1 x) (expm1.f64 x))

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

simplify45.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

820×	`log-prod`
628×	`associate-r`
622×	`div-sub`
568×	`associate-l`
414×	`fma-neg`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	110	1010
1	236	972
2	714	957
3	4400	957

Stop Event

1×	node limit

Counts

46 → 51

Calls

Call 1

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

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

eval9.0ms (0.5%)

Compiler: Compiled 464 to 226 computations (51.3% saved)

prune8.0ms (0.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	1	1
Picked	0	2	2
Done	0	1	1
Total	51	4	55

Accuracy

100.0%

Counts

55 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (expm1.f64 x) x)
✓	55.3%	(+.f64 1 (*.f64 1/2 x))
✓	99.9%	(*.f64 (/.f64 1 x) (expm1.f64 x))
	54.8%	1
✓	100.0%	(/.f64 (expm1.f64 x) x)
✓	55.3%	(+.f64 1 (*.f64 1/2 x))
✓	99.9%	(*.f64 (/.f64 1 x) (expm1.f64 x))
	54.8%	1

Compiler

Compiled 40 to 30 computations (25% saved)

localize0.0ms (0%)

eval0.0ms (0%)

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

prune3.0ms (0.2%)

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

Accuracy

100.0%

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (expm1.f64 x) x)
✓	55.3%	(+.f64 1 (*.f64 1/2 x))
✓	99.9%	(*.f64 (/.f64 1 x) (expm1.f64 x))
	54.8%	1
✓	100.0%	(/.f64 (expm1.f64 x) x)
✓	55.3%	(+.f64 1 (*.f64 1/2 x))
✓	99.9%	(*.f64 (/.f64 1 x) (expm1.f64 x))
	54.8%	1

Compiler

Compiled 40 to 30 computations (25% saved)

localize0.0ms (0%)

eval0.0ms (0%)

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

prune2.0ms (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

Accuracy

100.0%

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (expm1.f64 x) x)
✓	55.3%	(+.f64 1 (*.f64 1/2 x))
✓	99.9%	(*.f64 (/.f64 1 x) (expm1.f64 x))
	54.8%	1

Compiler

Compiled 43 to 30 computations (30.2% saved)

regimes16.0ms (0.9%)

Counts

5 → 1

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 1/2 x))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 1 x) (expm1.f64 x))
(/.f64 (-.f64 (exp.f64 x) 1) x)

Outputs
(/.f64 (expm1.f64 x) x)

Calls

2 calls:

10.0ms	(/.f64 (-.f64 (exp.f64 x) 1) x)
4.0ms	x

Results

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

Compiler

Compiled 32 to 21 computations (34.4% saved)

regimes4.0ms (0.2%)

Counts

2 → 1

Calls

Call 1

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

Outputs
(+.f64 1 (*.f64 1/2 x))

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
55.3%	1	`x`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes5.0ms (0.3%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
1

Outputs
1

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
54.8%	1	`x`

Compiler

Compiled 4 to 3 computations (25% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`1-exp`
2×	`+-commutative`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	34
1	16	34

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 (expm1.f64 x) x)
(+.f64 1 (*.f64 1/2 x))
1

Outputs
(/.f64 (expm1.f64 x) x)
(+.f64 1 (*.f64 1/2 x))
(+.f64 1 (*.f64 x 1/2))
1

Compiler

Compiled 13 to 10 computations (23.1% saved)

soundness135.0ms (7.3%)

Rules

1784×	`div-sub`
1494×	`fma-neg`
1012×	`times-frac`
642×	`distribute-lft-neg-in`
556×	`distribute-rgt-neg-in`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	88
1	36	88
2	65	86
3	144	80
4	380	80
5	1034	80
6	4094	80
7	7626	80

Stop Event

1×	node limit

Compiler

Compiled 11 to 7 computations (36.4% saved)

end0.0ms (0%)

preprocess47.0ms (2.5%)

Compiler: Compiled 82 to 56 computations (31.7% saved)

analyze1.0ms (0.1%)

sample1.1s (58.2%)

preprocess112.0ms (6%)

eval0.0ms (0%)

prune1.0ms (0.1%)

localize40.0ms (2.1%)

series2.0ms (0.1%)

rewrite97.0ms (5.2%)

simplify74.0ms (4%)

eval66.0ms (3.5%)

prune14.0ms (0.7%)

localize46.0ms (2.5%)

series0.0ms (0%)

rewrite49.0ms (2.6%)

simplify45.0ms (2.4%)

eval9.0ms (0.5%)

prune8.0ms (0.5%)

localize0.0ms (0%)

eval0.0ms (0%)

prune3.0ms (0.2%)

localize0.0ms (0%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes16.0ms (0.9%)

regimes4.0ms (0.2%)

regimes5.0ms (0.3%)

simplify2.0ms (0.1%)

soundness135.0ms (7.3%)

end0.0ms (0%)

preprocess47.0ms (2.5%)

Profiling