Details

analyze10.0ms (0.4%)

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
0%	0%	100%	0%	0%	0%	0%	2
25%	25%	75%	0%	0%	0%	0%	3
62.5%	62.5%	37.5%	0%	0%	0%	0%	4
78.6%	68.7%	18.7%	0%	12.5%	0%	0%	5
88.5%	71.8%	9.4%	0%	18.7%	0%	0%	6
94%	73.4%	4.7%	0%	21.9%	0%	0%	7
96.9%	74.2%	2.3%	0%	23.4%	0%	0%	8
98.5%	74.6%	1.2%	0%	24.2%	0%	0%	9
99.2%	75%	0.6%	0%	24.4%	0%	0%	10
99.6%	75.1%	0.3%	0%	24.6%	0%	0%	11
99.8%	75.1%	0.1%	0%	24.7%	0%	0%	12

Compiler

Compiled 8 to 6 computations (25% saved)

sample2.3s (87%)

Results

1.2s	2694×	body	1024	valid
495.0ms	3859×	body	256	valid
485.0ms	1426×	body	512	valid
87.0ms	277×	body	2048	valid
1.0ms	13×	body	256	infinite

Bogosity

preprocess44.0ms (1.7%)

Algorithm

2×	egg-herbie

Rules

186×	`fma-def`
78×	`associate-r`
78×	`associate--r+`
70×	`*-commutative`
66×	`associate-+l-`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	17	11
2	20	11
3	24	11
4	33	11
5	43	11
6	62	11
7	118	11
8	179	11
9	263	11
10	400	11
11	589	11
12	667	11
13	709	11
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 8 to 6 computations (25% saved)

simplify26.0ms (1%)

Algorithm

1×	egg-herbie

Rules

186×	`fma-def`
78×	`associate-r`
78×	`associate--r+`
70×	`*-commutative`
66×	`associate-+l-`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	17	11
2	20	11
3	24	11
4	33	11
5	43	11
6	62	11
7	118	11
8	179	11
9	263	11
10	400	11
11	589	11
12	667	11
13	709	11

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

eval0.0ms (0%)

Compiler: Compiled 11 to 7 computations (36.4% 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

Error

0.0b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(/.f64 (expm1.f64 x) x)

Compiler

Compiled 5 to 3 computations (40% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 x)
✓	0.0b	(/.f64 (expm1.f64 x) x)

Compiler

Compiled 8 to 3 computations (62.5% saved)

series2.0ms (0.1%)

Counts

2 → 24

Calls

6 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)
0.0ms	x	@	0	(expm1.f64 x)
0.0ms	x	@	inf	(expm1.f64 x)

rewrite56.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1258×	`add-sqr-sqrt`
1246×	`*-un-lft-identity`
1158×	`add-cube-cbrt`
1142×	`add-cbrt-cube`
1130×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	120	16
2	1538	16

Stop Event

1×	node limit

Counts

2 → 49

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (expm1.f64 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (expm1.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (expm1.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (expm1.f64 x)) (.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) (cbrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (.f64 (cbrt.f64 (expm1.f64 x)) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 x) (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (expm1.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (expm1.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (expm1.f64 x) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (expm1.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (exp.f64 x) (exp.f64 x)) 1) (+.f64 (exp.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((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))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (expm1.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (expm1.f64 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (expm1.f64 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (expm1.f64 x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (expm1.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (expm1.f64 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (expm1.f64 x)))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (expm1.f64 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (expm1.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (expm1.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (expm1.f64 x)) (*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) (cbrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (*.f64 (cbrt.f64 (expm1.f64 x)) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (expm1.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (expm1.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (expm1.f64 x) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (expm1.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (exp.f64 x) (exp.f64 x)) 1) (+.f64 (exp.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((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))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (expm1.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (expm1.f64 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (expm1.f64 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (expm1.f64 x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (expm1.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (expm1.f64 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (expm1.f64 x)))))))

simplify46.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1460×	`associate-*r/`
1406×	`associate-/l*`
1058×	`times-frac`
864×	`unswap-sqr`
806×	`associate-*l/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	137	917
1	337	877
2	1840	877

Stop Event

1×	node limit

Counts

73 → 79

Calls

Call 1

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

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

eval48.0ms (1.8%)

Compiler: Compiled 744 to 364 computations (51.1% saved)

prune17.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	77	2	79
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	77	3	80

Error

Counts

80 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(/.f64 (expm1.f64 x) x)
▶	21.9b	(+.f64 (*.f64 1/2 x) 1)
	21.5b	1

Compiler

Compiled 13 to 10 computations (23.1% saved)

localize5.0ms (0.2%)

Compiler: Compiled 12 to 9 computations (25% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(/.f64 (expm1.f64 x) x)
✓	21.9b	(+.f64 (*.f64 1/2 x) 1)
	21.5b	1

Compiler

Compiled 13 to 10 computations (23.1% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

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

Error

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(/.f64 (expm1.f64 x) x)
✓	21.9b	(+.f64 (*.f64 1/2 x) 1)
	21.5b	1

Compiler

Compiled 13 to 10 computations (23.1% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

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

Error

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(/.f64 (expm1.f64 x) x)
✓	21.9b	(+.f64 (*.f64 1/2 x) 1)
	21.5b	1

Compiler

Compiled 13 to 10 computations (23.1% saved)

regimes9.0ms (0.3%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`(/.f64 (-.f64 (exp.f64 x) 1) x)`

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes4.0ms (0.1%)

Accuracy

Total -0.8b remaining (-3.7%)

Threshold costs -0.8b (-3.7%)

Counts

2 → 1

Calls

Call 1

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

Outputs
1

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
21.5b	1	`x`

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2× 1-exp

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	9	12

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

Outputs
(/.f64 (expm1.f64 x) x)
1

Compiler

Compiled 7 to 5 computations (28.6% saved)

soundness47.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

186×	`fma-def`
78×	`associate-r`
78×	`associate--r+`
70×	`*-commutative`
66×	`associate-+l-`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	17	11
2	20	11
3	24	11
4	33	11
5	43	11
6	62	11
7	118	11
8	179	11
9	263	11
10	400	11
11	589	11
12	667	11
13	709	11

Stop Event

1×

saturated

Compiler

Compiled 11 to 7 computations (36.4% saved)

end15.0ms (0.6%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

Iter	Nodes	Cost
0	8	11
1	17	11
2	20	11
3	24	11
4	33	11
5	43	11
6	62	11
7	118	11
8	179	11
9	263	11
10	400	11
11	589	11
12	667	11
13	709	11
0	1	1

Iter	Nodes	Cost
0	8	11
1	17	11
2	20	11
3	24	11
4	33	11
5	43	11
6	62	11
7	118	11
8	179	11
9	263	11
10	400	11
11	589	11
12	667	11
13	709	11

Iter	Nodes	Cost
0	8	11
1	17	11
2	20	11
3	24	11
4	33	11
5	43	11
6	62	11
7	118	11
8	179	11
9	263	11
10	400	11
11	589	11
12	667	11
13	709	11

Iter	Nodes	Cost
0	8	11
1	17	11
2	20	11
3	24	11
4	33	11
5	43	11
6	62	11
7	118	11
8	179	11
9	263	11
10	400	11
11	589	11
12	667	11
13	709	11
0	1	1

Iter	Nodes	Cost
0	8	11
1	17	11
2	20	11
3	24	11
4	33	11
5	43	11
6	62	11
7	118	11
8	179	11
9	263	11
10	400	11
11	589	11
12	667	11
13	709	11

Iter	Nodes	Cost
0	8	11
1	17	11
2	20	11
3	24	11
4	33	11
5	43	11
6	62	11
7	118	11
8	179	11
9	263	11
10	400	11
11	589	11
12	667	11
13	709	11

Details

analyze10.0ms (0.4%)

sample2.3s (87%)

preprocess44.0ms (1.7%)

simplify26.0ms (1%)

eval0.0ms (0%)

prune1.0ms (0%)

localize4.0ms (0.1%)

series2.0ms (0.1%)

rewrite56.0ms (2.1%)

simplify46.0ms (1.7%)

eval48.0ms (1.8%)

prune17.0ms (0.7%)

localize5.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

eval0.0ms (0%)

prune1.0ms (0%)

eval0.0ms (0%)

prune1.0ms (0%)

regimes9.0ms (0.3%)

regimes4.0ms (0.1%)

simplify4.0ms (0.1%)

soundness47.0ms (1.8%)

end15.0ms (0.6%)

Profiling

Iter	Nodes	Cost
0	8	11
1	17	11
2	20	11
3	24	11
4	33	11
5	43	11
6	62	11
7	118	11
8	179	11
9	263	11
10	400	11
11	589	11
12	667	11
13	709	11
0	1	1

Iter	Nodes	Cost
0	8	11
1	17	11
2	20	11
3	24	11
4	33	11
5	43	11
6	62	11
7	118	11
8	179	11
9	263	11
10	400	11
11	589	11
12	667	11
13	709	11

Iter	Nodes	Cost
0	8	11
1	17	11
2	20	11
3	24	11
4	33	11
5	43	11
6	62	11
7	118	11
8	179	11
9	263	11
10	400	11
11	589	11
12	667	11
13	709	11