Details

analyze495.0ms (18.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample1.7s (62.1%)

Results

903.0ms	2780×	body	1024	valid
293.0ms	1320×	body	512	valid
255.0ms	3216×	body	128	valid
106.0ms	280×	body	2048	valid
101.0ms	660×	body	256	valid
1.0ms	3×	body	2048	invalid

preprocess20.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`
1×	`expm1-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	12	8
2	13	8
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 8 to 5 computations (37.5% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`
1×	`expm1-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	12	8
2	13	8

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

prune3.0ms (0.1%)

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

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

Compiler

Compiled 25 to 15 computations (40% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite33.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

516×	`pow1_binary64`
477×	`add-log-exp_binary64`
477×	`log1p-expm1-u_binary64`
477×	`expm1-log1p-u_binary64`
465×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	99	8
2	1287	8

Stop Event

1×	node limit

Counts

1 → 31

Calls

Call 1

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

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

Outputs

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

simplify65.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

567×	`sqr-pow_binary64`
438×	`associate-l_binary64`
362×	`unswap-sqr_binary64`
313×	`pow-sqr_binary64`
311×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	104
1	48	104
2	94	104
3	215	104
4	331	104
5	568	104
6	1456	104
7	2283	104
8	2369	104
9	2502	104
10	2660	104
11	2890	104
12	3212	104
13	3633	104
14	4133	104
15	4728	104

Stop Event

1×	node limit

Counts

43 → 40

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))

Outputs
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (fma.f64 1/12 x (/.f64 1 x)))
(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 1/12 x (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x))))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) (fma.f64 -1/720 (pow.f64 x 3) 1/2))
(+.f64 (/.f64 1 x) (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 1/2)))
(+.f64 (/.f64 1 x) (fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) 1/2))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))

prune26.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	38	2	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	38	3	41

Error

Counts

41 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (exp.f64 x) (expm1.f64 x))
▶	1.0b	(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (exp.f64 x) (cbrt.f64 (expm1.f64 x))))
	23.2b	(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))

Compiler

Compiled 443 to 203 computations (54.2% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))
✓	0.2b	(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (exp.f64 x) (cbrt.f64 (expm1.f64 x))))
✓	0.4b	(pow.f64 (cbrt.f64 (expm1.f64 x)) 2)
✓	0.4b	(cbrt.f64 (expm1.f64 x))

series13.0ms (0.5%)

Counts

4 → 36

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))
2.0ms	x	@	-inf	(/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))
2.0ms	x	@	inf	(cbrt.f64 (expm1.f64 x))
1.0ms	x	@	-inf	(cbrt.f64 (expm1.f64 x))
1.0ms	x	@	0	(/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))

rewrite61.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

496×	`log-prod_binary64`
173×	`expm1-udef_binary64`
173×	`log1p-udef_binary64`
159×	`pow3_binary64`
158×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	29
1	228	29
2	2803	29

Stop Event

1×	node limit

Counts

4 → 145

Calls

Call 1

Inputs
(cbrt.f64 (expm1.f64 x))
(pow.f64 (cbrt.f64 (expm1.f64 x)) 2)
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (exp.f64 x) (cbrt.f64 (expm1.f64 x))))
(/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))

Outputs
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#<rule egg-rr> (2) ((x pow.f64 (/.f64 (cbrt.f64 (expm1.f64 x)) (.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) -2) (exp.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (exp.f64 x) (expm1.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (exp.f64 (.f64 3 x)) (pow.f64 (expm1.f64 x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (/.f64 (exp.f64 x) (cbrt.f64 (expm1.f64 x))) 3) (pow.f64 (expm1.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) -2) 3) (pow.f64 (/.f64 (exp.f64 x) (cbrt.f64 (expm1.f64 x))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (/.f64 (exp.f64 x) (cbrt.f64 (expm1.f64 x))) 3) (pow.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) -2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 x (log.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (-.f64 x (log.f64 (expm1.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (cbrt.f64 (expm1.f64 x)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) -2))) (cbrt.f64 (exp.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) -2))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) -2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) -2)) (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) -4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) -4)) (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (/.f64 1 (neg.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 (expm1.f64 x))) (/.f64 1 (cbrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (expm1.f64 x))) 2) -2) (pow.f64 (cbrt.f64 (cbrt.f64 (expm1.f64 x))) -2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (expm1.f64 x) 1/6) -2) (pow.f64 (pow.f64 (expm1.f64 x) 1/6) -2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 4))) (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (expm1.f64 x) -2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (expm1.f64 x)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) -2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) -2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (expm1.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (neg.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) -4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) -2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 -2/3 (log.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (expm1.f64 x))) -2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 2/3 (log.f64 (expm1.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 -2/3 (log.f64 (expm1.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) -2)))))))

simplify46.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

649×	`associate-/l/_binary64`
614×	`fma-def_binary64`
383×	`associate-/r*_binary64`
336×	`unswap-sqr_binary64`
313×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	296
1	69	296
2	135	296
3	320	296
4	610	296
5	1423	296
6	2818	296
7	4731	296

Stop Event

1×	node limit

Counts

181 → 158

Calls

Call 1

Inputs
(pow.f64 (-.f64 (exp.f64 x) 1) 1/3)
(pow.f64 (-.f64 (exp.f64 x) 1) 1/3)
(pow.f64 (-.f64 (exp.f64 x) 1) 1/3)
(pow.f64 (-.f64 (exp.f64 x) 1) 1/3)
(pow.f64 (-.f64 (exp.f64 x) 1) 1/3)
(pow.f64 (-.f64 (exp.f64 x) 1) 1/3)
(pow.f64 (-.f64 (exp.f64 x) 1) 1/3)
(pow.f64 (-.f64 (exp.f64 x) 1) 1/3)
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) 1/3)
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) 1/3)
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) 1/3)
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) 1/3)
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) 1/3)
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) 1/3)
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) 1/3)
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) 1/3)
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(pow.f64 (/.f64 1 (pow.f64 (-.f64 (exp.f64 x) 1) 2)) 1/3)
(pow.f64 (/.f64 1 (pow.f64 (-.f64 (exp.f64 x) 1) 2)) 1/3)
(pow.f64 (/.f64 1 (pow.f64 (-.f64 (exp.f64 x) 1) 2)) 1/3)
(pow.f64 (/.f64 1 (pow.f64 (-.f64 (exp.f64 x) 1) 2)) 1/3)
(pow.f64 (/.f64 1 (pow.f64 (-.f64 (exp.f64 x) 1) 2)) 1/3)
(pow.f64 (/.f64 1 (pow.f64 (-.f64 (exp.f64 x) 1) 2)) 1/3)
(pow.f64 (/.f64 1 (pow.f64 (-.f64 (exp.f64 x) 1) 2)) 1/3)
(pow.f64 (/.f64 1 (pow.f64 (-.f64 (exp.f64 x) 1) 2)) 1/3)

Outputs
(pow.f64 (-.f64 (exp.f64 x) 1) 1/3)
(cbrt.f64 (expm1.f64 x))
(pow.f64 (-.f64 (exp.f64 x) 1) 1/3)
(cbrt.f64 (expm1.f64 x))
(pow.f64 (-.f64 (exp.f64 x) 1) 1/3)
(cbrt.f64 (expm1.f64 x))
(pow.f64 (-.f64 (exp.f64 x) 1) 1/3)
(cbrt.f64 (expm1.f64 x))
(pow.f64 (-.f64 (exp.f64 x) 1) 1/3)
(cbrt.f64 (expm1.f64 x))
(pow.f64 (-.f64 (exp.f64 x) 1) 1/3)
(cbrt.f64 (expm1.f64 x))
(pow.f64 (-.f64 (exp.f64 x) 1) 1/3)
(cbrt.f64 (expm1.f64 x))
(pow.f64 (-.f64 (exp.f64 x) 1) 1/3)
(cbrt.f64 (expm1.f64 x))
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) 1/3)
(cbrt.f64 (pow.f64 (expm1.f64 x) 2))
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) 1/3)
(cbrt.f64 (pow.f64 (expm1.f64 x) 2))
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) 1/3)
(cbrt.f64 (pow.f64 (expm1.f64 x) 2))
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) 1/3)
(cbrt.f64 (pow.f64 (expm1.f64 x) 2))
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) 1/3)
(cbrt.f64 (pow.f64 (expm1.f64 x) 2))
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) 1/3)
(cbrt.f64 (pow.f64 (expm1.f64 x) 2))
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) 1/3)
(cbrt.f64 (pow.f64 (expm1.f64 x) 2))
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 2) 1/3)
(cbrt.f64 (pow.f64 (expm1.f64 x) 2))
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (fma.f64 1/12 x (/.f64 1 x)))
(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 1/12 x (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x))))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) (fma.f64 -1/720 (pow.f64 x 3) 1/2))
(+.f64 (fma.f64 x 1/12 1/2) (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)))
(+.f64 (/.f64 1 x) (fma.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12) 1/2))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(pow.f64 (/.f64 1 (pow.f64 (-.f64 (exp.f64 x) 1) 2)) 1/3)
(cbrt.f64 (/.f64 1 (pow.f64 (expm1.f64 x) 2)))
(pow.f64 (/.f64 1 (pow.f64 (-.f64 (exp.f64 x) 1) 2)) 1/3)
(cbrt.f64 (/.f64 1 (pow.f64 (expm1.f64 x) 2)))
(pow.f64 (/.f64 1 (pow.f64 (-.f64 (exp.f64 x) 1) 2)) 1/3)
(cbrt.f64 (/.f64 1 (pow.f64 (expm1.f64 x) 2)))
(pow.f64 (/.f64 1 (pow.f64 (-.f64 (exp.f64 x) 1) 2)) 1/3)
(cbrt.f64 (/.f64 1 (pow.f64 (expm1.f64 x) 2)))
(pow.f64 (/.f64 1 (pow.f64 (-.f64 (exp.f64 x) 1) 2)) 1/3)
(cbrt.f64 (/.f64 1 (pow.f64 (expm1.f64 x) 2)))
(pow.f64 (/.f64 1 (pow.f64 (-.f64 (exp.f64 x) 1) 2)) 1/3)
(cbrt.f64 (/.f64 1 (pow.f64 (expm1.f64 x) 2)))
(pow.f64 (/.f64 1 (pow.f64 (-.f64 (exp.f64 x) 1) 2)) 1/3)
(cbrt.f64 (/.f64 1 (pow.f64 (expm1.f64 x) 2)))
(pow.f64 (/.f64 1 (pow.f64 (-.f64 (exp.f64 x) 1) 2)) 1/3)
(cbrt.f64 (/.f64 1 (pow.f64 (expm1.f64 x) 2)))

prune87.0ms (3.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	186	3	189

Error

Counts

189 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	1.0b	(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (exp.f64 x) (cbrt.f64 (expm1.f64 x))))
▶	23.2b	(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))

Compiler

Compiled 2964 to 1256 computations (57.6% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
✓	0.2b	(fma.f64 x 1/12 1/2)

series2.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(fma.f64 x 1/12 1/2)
0.0ms	x	@	-inf	(fma.f64 x 1/12 1/2)
0.0ms	x	@	inf	(fma.f64 x 1/12 1/2)
0.0ms	x	@	-inf	(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
0.0ms	x	@	0	(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))

rewrite42.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

842×	`pow1_binary64`
790×	`log1p-expm1-u_binary64`
790×	`expm1-log1p-u_binary64`
85×	`add-sqr-sqrt_binary64`
80×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	172	16
2	2127	16

Stop Event

1×	node limit

Counts

2 → 58

Calls

Call 1

Inputs
(fma.f64 x 1/12 1/2)
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (*.f64 x 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x 1/12) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x 1/12) 1) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x 1/12 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x 1/12 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x 1/12 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x 1/12 1/2)) (pow.f64 (cbrt.f64 (fma.f64 x 1/12 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x 1/12 1/2)) 2) (cbrt.f64 (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x 1/12 1/2)) (sqrt.f64 (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x 1/12) 3) 1/8) (+.f64 (*.f64 (*.f64 x 1/12) (*.f64 x 1/12)) (-.f64 1/4 (*.f64 (*.f64 x 1/12) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x 1/12) (*.f64 x 1/12)) 1/4) (-.f64 (*.f64 x 1/12) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x 1/12 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x 1/12 1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x 1/12 1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x 1/12 1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x 1/12 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x 1/12 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x 1/12 1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 x 1/12 1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x 1/12 1/2)))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 x -2) (-.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))) (/.f64 (pow.f64 (fma.f64 x 1/12 1/2) 2) (-.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x))) (pow.f64 (cbrt.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x))) 2) (cbrt.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x))) (sqrt.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x -3) (pow.f64 (fma.f64 x 1/12 1/2) 3)) (/.f64 1 (+.f64 (pow.f64 x -2) (-.f64 (pow.f64 (fma.f64 x 1/12 1/2) 2) (/.f64 (fma.f64 x 1/12 1/2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x -2) (pow.f64 (fma.f64 x 1/12 1/2) 2)) (/.f64 1 (-.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 x -2) (-.f64 (pow.f64 (fma.f64 x 1/12 1/2) 2) (/.f64 (fma.f64 x 1/12 1/2) x))) (+.f64 (pow.f64 x -3) (pow.f64 (fma.f64 x 1/12 1/2) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2)) (-.f64 (pow.f64 x -2) (pow.f64 (fma.f64 x 1/12 1/2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x -3) (pow.f64 (fma.f64 x 1/12 1/2) 3)) (+.f64 (pow.f64 x -2) (-.f64 (pow.f64 (fma.f64 x 1/12 1/2) 2) (/.f64 (fma.f64 x 1/12 1/2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x -3) (pow.f64 (fma.f64 x 1/12 1/2) 3)) (+.f64 (pow.f64 (fma.f64 x 1/12 1/2) 2) (-.f64 (pow.f64 x -2) (/.f64 (fma.f64 x 1/12 1/2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x -2) (pow.f64 (fma.f64 x 1/12 1/2) 2)) (-.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x -3) (pow.f64 (fma.f64 x 1/12 1/2) 3))) (neg.f64 (+.f64 (pow.f64 x -2) (-.f64 (pow.f64 (fma.f64 x 1/12 1/2) 2) (/.f64 (fma.f64 x 1/12 1/2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x -2) (pow.f64 (fma.f64 x 1/12 1/2) 2))) (neg.f64 (-.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 x 1/12 1/2) 2) (pow.f64 x -2)) (-.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 x 1/12 1/2) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 1 x) (fma.f64 x 1/12 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 x 1/12 1/2)) 2) (cbrt.f64 (fma.f64 x 1/12 1/2)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -2)) (cbrt.f64 (/.f64 1 x)) (fma.f64 x 1/12 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 x 1/12 1/2)) (sqrt.f64 (fma.f64 x 1/12 1/2)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) (fma.f64 x 1/12 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x))))))))

simplify9.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
5×	`+-commutative_binary64`
2×	`associate-+r+_binary64`
2×	`associate-+l+_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	171
1	23	149
2	28	149
3	30	149

Stop Event

1×

saturated

Counts

82 → 67

Calls

Call 1

Inputs
1/2
(+.f64 1/2 (*.f64 1/12 x))
(+.f64 1/2 (*.f64 1/12 x))
(+.f64 1/2 (*.f64 1/12 x))
(*.f64 1/12 x)
(+.f64 1/2 (*.f64 1/12 x))
(+.f64 1/2 (*.f64 1/12 x))
(+.f64 1/2 (*.f64 1/12 x))
(*.f64 1/12 x)
(+.f64 1/2 (*.f64 1/12 x))
(+.f64 1/2 (*.f64 1/12 x))
(+.f64 1/2 (*.f64 1/12 x))
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(*.f64 1/12 x)
(+.f64 1/2 (*.f64 1/12 x))
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 1/12 x)))
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 1/12 x)))
(*.f64 1/12 x)
(+.f64 1/2 (*.f64 1/12 x))
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 1/12 x)))
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 1/12 x)))

Outputs
1/2
(+.f64 1/2 (*.f64 1/12 x))
(fma.f64 1/12 x 1/2)
(+.f64 1/2 (*.f64 1/12 x))
(fma.f64 1/12 x 1/2)
(+.f64 1/2 (*.f64 1/12 x))
(fma.f64 1/12 x 1/2)
(*.f64 1/12 x)
(+.f64 1/2 (*.f64 1/12 x))
(fma.f64 1/12 x 1/2)
(+.f64 1/2 (*.f64 1/12 x))
(fma.f64 1/12 x 1/2)
(+.f64 1/2 (*.f64 1/12 x))
(fma.f64 1/12 x 1/2)
(*.f64 1/12 x)
(+.f64 1/2 (*.f64 1/12 x))
(fma.f64 1/12 x 1/2)
(+.f64 1/2 (*.f64 1/12 x))
(fma.f64 1/12 x 1/2)
(+.f64 1/2 (*.f64 1/12 x))
(fma.f64 1/12 x 1/2)
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (fma.f64 1/12 x (/.f64 1 x)))
(+.f64 (fma.f64 1/12 x 1/2) (/.f64 1 x))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (fma.f64 1/12 x (/.f64 1 x)))
(+.f64 (fma.f64 1/12 x 1/2) (/.f64 1 x))
(*.f64 1/12 x)
(+.f64 1/2 (*.f64 1/12 x))
(fma.f64 1/12 x 1/2)
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 1/12 x)))
(+.f64 1/2 (fma.f64 1/12 x (/.f64 1 x)))
(+.f64 (fma.f64 1/12 x 1/2) (/.f64 1 x))
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 1/12 x)))
(+.f64 1/2 (fma.f64 1/12 x (/.f64 1 x)))
(+.f64 (fma.f64 1/12 x 1/2) (/.f64 1 x))
(*.f64 1/12 x)
(+.f64 1/2 (*.f64 1/12 x))
(fma.f64 1/12 x 1/2)
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 1/12 x)))
(+.f64 1/2 (fma.f64 1/12 x (/.f64 1 x)))
(+.f64 (fma.f64 1/12 x 1/2) (/.f64 1 x))
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 1/12 x)))
(+.f64 1/2 (fma.f64 1/12 x (/.f64 1 x)))
(+.f64 (fma.f64 1/12 x 1/2) (/.f64 1 x))

prune36.0ms (1.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	67	3	70

Error

Counts

70 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	1.0b	(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (exp.f64 x) (cbrt.f64 (expm1.f64 x))))
✓	23.2b	(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))

Compiler

Compiled 950 to 758 computations (20.2% saved)

regimes17.0ms (0.6%)

Accuracy

Total -22.0b remaining (-6137.5%)

Threshold costs -22.0b (-6137.5%)

Counts

10 → 1

Compiler

Compiled 89 to 52 computations (41.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8

Stop Event

1×

saturated

Calls

Call 1

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

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

end35.0ms (1.3%)

Stop Event

1×

done

Compiler

Compiled 39 to 21 computations (46.2% saved)

Details

analyze495.0ms (18.4%)

sample1.7s (62.1%)

preprocess20.0ms (0.7%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series2.0ms (0.1%)

rewrite33.0ms (1.2%)

simplify65.0ms (2.4%)

prune26.0ms (1%)

localize11.0ms (0.4%)

series13.0ms (0.5%)

rewrite61.0ms (2.3%)

simplify46.0ms (1.7%)

prune87.0ms (3.2%)

localize5.0ms (0.2%)

series2.0ms (0.1%)

rewrite42.0ms (1.6%)

simplify9.0ms (0.3%)

prune36.0ms (1.3%)

regimes17.0ms (0.6%)

simplify2.0ms (0.1%)

end35.0ms (1.3%)

Profiling