Details

analyze164.0ms (4.5%)

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

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample1.5s (40.6%)

Results

765.0ms	2739×	body	1024	valid
336.0ms	3896×	body	256	valid
225.0ms	1349×	body	512	valid
136.0ms	272×	body	2048	valid
0.0ms	4×	body	256	invalid
0.0ms	1×	body	2048	invalid

preprocess20.0ms (0.5%)

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 9 to 6 computations (33.3% 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))

eval1.0ms (0%)

Compiler: Compiled 13 to 7 computations (46.2% 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 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

rewrite37.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

516×	`pow1_binary64`
493×	`add-sqr-sqrt_binary64`
477×	`add-log-exp_binary64`
477×	`log1p-expm1-u_binary64`
477×	`expm1-log1p-u_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 → 30

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 log1p.f64 (expm1.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))))) (#(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))))))))

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 log1p.f64 (expm1.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))))) (#(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))))))))

simplify138.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

1329×	`sqr-pow_binary64`
715×	`pow-sqr_binary64`
530×	`cube-prod_binary64`
472×	`fabs-mul_binary64`
438×	`associate-l_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
16	5448	104
17	5769	104
18	6053	104
19	6277	104
20	6455	104
21	6539	104
22	7479	104

Stop Event

1×	node limit

Counts

42 → 39

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))

eval7.0ms (0.2%)

Compiler: Compiled 379 to 159 computations (58% saved)

prune9.0ms (0.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	34	5	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	34	6	40

Error

Counts

40 → 6

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))
▶	22.9b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
▶	23.1b	(/.f64 1 x)
✓	0.0b	(/.f64 (exp.f64 x) (expm1.f64 x))
▶	23.1b	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
▶	23.1b	(+.f64 (/.f64 1 x) 1/2)

Compiler

Compiled 94 to 74 computations (21.3% saved)

localize5.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1 (expm1.f64 x))
	0.0b	(*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))
✓	0.0b	(*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))
✓	0.0b	(/.f64 1 (expm1.f64 x))

series4.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(/.f64 1 (expm1.f64 x))
1.0ms	x	@	-inf	(/.f64 1 (expm1.f64 x))
0.0ms	x	@	0	(/.f64 1 (expm1.f64 x))
0.0ms	x	@	0	(*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))
0.0ms	x	@	-inf	(*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))

rewrite42.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

589×	`pow1_binary64`
542×	`add-log-exp_binary64`
542×	`log1p-expm1-u_binary64`
542×	`expm1-log1p-u_binary64`
529×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	133	14
2	1545	14

Stop Event

1×	node limit

Counts

2 → 41

Calls

Call 1

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

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

Outputs

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

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

simplify86.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

533×	`times-frac_binary64`
512×	`fma-neg_binary64`
410×	`distribute-rgt-neg-in_binary64`
393×	`sub-neg_binary64`
321×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	192
1	59	192
2	123	192
3	306	192
4	519	192
5	1081	192
6	2162	192
7	3979	192
8	4905	192
9	5696	192
10	6108	192
11	7099	192

Stop Event

1×	node limit

Counts

65 → 57

Calls

Call 1

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

localize2.0ms (0%)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite42.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

621×	`pow1_binary64`
582×	`add-log-exp_binary64`
582×	`log1p-expm1-u_binary64`
582×	`expm1-log1p-u_binary64`
572×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	130	7
2	1577	7

Stop Event

1×	node limit

Counts

1 → 30

Calls

Call 1

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

Outputs

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

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	69
1	9	69

Stop Event

1×

saturated

Counts

42 → 34

Calls

Call 1

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

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

localize5.0ms (0.1%)

Local error

Found 6 expressions with local error:

New	Error	Program
	0.3b	(*.f64 1/12 x)
	0.0b	(+.f64 (*.f64 1/12 x) (/.f64 1 x))
	0.0b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
✓	0.0b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
✓	0.0b	(+.f64 (*.f64 1/12 x) (/.f64 1 x))
✓	0.3b	(*.f64 1/12 x)

series4.0ms (0.1%)

Counts

3 → 19

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
1.0ms	x	@	inf	(*.f64 1/12 x)
0.0ms	x	@	-inf	(*.f64 1/12 x)
0.0ms	x	@	0	(*.f64 1/12 x)
0.0ms	x	@	inf	(+.f64 (*.f64 1/12 x) (/.f64 1 x))

rewrite62.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

936×	`prod-diff_binary64`
626×	`unpow-prod-down_binary64`
409×	`log-prod_binary64`
332×	`fma-def_binary64`
252×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	204	23
2	2710	23

Stop Event

1×	node limit

Counts

3 → 154

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 1/12) x)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 1/12) x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 1/12) x))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 1/12) x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 1/12 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/12 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 1/12 x) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 1/12 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 1/12 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/1728 (pow.f64 x 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 1/12 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/12) x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 1/12 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 1/1728 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/12 x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/12 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 1/12 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 1/12 x)) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 1/12 x (/.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (*.f64 1/12 x) 2) (-.f64 (*.f64 1/12 x) (/.f64 1 x))) (/.f64 (pow.f64 x -2) (-.f64 (*.f64 1/12 x) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 1/12 x (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 1/12 x (/.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x))) (cbrt.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2)) (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 1/12 x (/.f64 1 x))) (sqrt.f64 (fma.f64 1/12 x (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) (/.f64 1 (-.f64 (fma.f64 1/144 (*.f64 x x) (pow.f64 x -2)) (/.f64 (*.f64 1/12 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) (pow.f64 (/.f64 1 (-.f64 (fma.f64 1/144 (*.f64 x x) (pow.f64 x -2)) (/.f64 (*.f64 1/12 x) x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (*.f64 1/12 x) 2) (pow.f64 x -2)) (/.f64 1 (-.f64 (*.f64 1/12 x) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (*.f64 1/12 x) 2) (pow.f64 x -2)) (pow.f64 (/.f64 1 (-.f64 (*.f64 1/12 x) (/.f64 1 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (fma.f64 1/12 x (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x)))) 2) 3) (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 3/2) 1/3) (pow.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 3/2) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2) (cbrt.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2))) 1/3) (cbrt.f64 (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2) (sqrt.f64 (fma.f64 1/12 x (/.f64 1 x)))) 1/3) (cbrt.f64 (sqrt.f64 (fma.f64 1/12 x (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (fma.f64 1/144 (*.f64 x x) (pow.f64 x -2)) (/.f64 (*.f64 1/12 x) x)) (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (*.f64 1/12 x) (/.f64 1 x)) (-.f64 (pow.f64 (*.f64 1/12 x) 2) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) (-.f64 (fma.f64 1/144 (*.f64 x x) (pow.f64 x -2)) (/.f64 (*.f64 1/12 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) (+.f64 (pow.f64 x -2) (-.f64 (pow.f64 (*.f64 1/12 x) 2) (/.f64 (*.f64 1/12 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 1/12 x) 2) (pow.f64 x -2)) (-.f64 (*.f64 1/12 x) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3))) (neg.f64 (-.f64 (fma.f64 1/144 (*.f64 x x) (pow.f64 x -2)) (/.f64 (*.f64 1/12 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 1/12 x) 2) (pow.f64 x -2))) (neg.f64 (-.f64 (*.f64 1/12 x) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x -2) (pow.f64 (*.f64 1/12 x) 2)) (-.f64 (/.f64 1 x) (*.f64 1/12 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 1/12 x (/.f64 1 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (fma.f64 1/144 (*.f64 x x) (pow.f64 x -2)) (/.f64 (*.f64 1/12 x) x)) (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (*.f64 1/12 x) (/.f64 1 x)) (-.f64 (pow.f64 (*.f64 1/12 x) 2) (pow.f64 x -2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 1/12 x (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 1/12 x (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 1/12 x))) (exp.f64 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (exp.f64 1/12) x) (+.f64 1 (expm1.f64 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 1/12 x))) (+.f64 1 (expm1.f64 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (/.f64 1 x))) (pow.f64 (exp.f64 1/12) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (/.f64 1 x)) (+.f64 1 (expm1.f64 (*.f64 1/12 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (/.f64 1 x))) (+.f64 1 (expm1.f64 (*.f64 1/12 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/12 x (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1/12 (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/12 x) 1 (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 1/12 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 1 x) (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) 1 (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (cbrt.f64 x)) (cbrt.f64 (pow.f64 x -2)) (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 1 (cbrt.f64 x)) (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) 1/12) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 1/12 x)) (cbrt.f64 (pow.f64 (*.f64 1/12 x) 2)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (*.f64 1/12 x) 2)) (cbrt.f64 (*.f64 1/12 x)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 1/12) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 1/12 x)) (sqrt.f64 (*.f64 1/12 x)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (/.f64 1 (neg.f64 x)) (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/12 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/12 (sqrt.f64 x)) (sqrt.f64 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/12 x (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 1/12 x (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 1/12 x (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 1/12 x (/.f64 1 x))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/4 (-.f64 1/2 (fma.f64 1/12 x (/.f64 1 x)))) (/.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2) (-.f64 1/2 (fma.f64 1/12 x (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2))) (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2))) 2) (cbrt.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2))) (sqrt.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1/8 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 3)) (/.f64 1 (fma.f64 (fma.f64 1/12 x (/.f64 1 x)) (-.f64 (fma.f64 1/12 x (/.f64 1 x)) 1/2) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1/8 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 3)) (pow.f64 (/.f64 1 (fma.f64 (fma.f64 1/12 x (/.f64 1 x)) (-.f64 (fma.f64 1/12 x (/.f64 1 x)) 1/2) 1/4)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/4 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2)) (/.f64 1 (-.f64 1/2 (fma.f64 1/12 x (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/4 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2)) (pow.f64 (/.f64 1 (-.f64 1/2 (fma.f64 1/12 x (/.f64 1 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (pow.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2)) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2)) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (pow.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2)) 2) (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2))) 2)) 1/3) (cbrt.f64 (cbrt.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (pow.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2)) 2) (sqrt.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2)))) 1/3) (cbrt.f64 (sqrt.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2)))) 2) 3) (cbrt.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (fma.f64 1/12 x (/.f64 1 x)) (-.f64 (fma.f64 1/12 x (/.f64 1 x)) 1/2) 1/4) (+.f64 1/8 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1/2 (fma.f64 1/12 x (/.f64 1 x))) (-.f64 1/4 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/8 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 3)) (fma.f64 (fma.f64 1/12 x (/.f64 1 x)) (-.f64 (fma.f64 1/12 x (/.f64 1 x)) 1/2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/8 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 3)) (+.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2) (-.f64 1/4 (*.f64 (fma.f64 1/12 x (/.f64 1 x)) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/4 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2)) (-.f64 1/2 (fma.f64 1/12 x (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1/8 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 3))) (neg.f64 (fma.f64 (fma.f64 1/12 x (/.f64 1 x)) (-.f64 (fma.f64 1/12 x (/.f64 1 x)) 1/2) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1/4 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2))) (neg.f64 (-.f64 1/2 (fma.f64 1/12 x (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 1/12 x 1/2) 3) (pow.f64 x -3)) (+.f64 (pow.f64 (fma.f64 1/12 x 1/2) 2) (-.f64 (pow.f64 x -2) (*.f64 (fma.f64 1/12 x 1/2) (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2) 1/4) (-.f64 (fma.f64 1/12 x (/.f64 1 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 1/12 x 1/2) 2) (pow.f64 x -2)) (-.f64 (fma.f64 1/12 x 1/2) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (fma.f64 1/12 x (/.f64 1 x)) (-.f64 (fma.f64 1/12 x (/.f64 1 x)) 1/2) 1/4) (+.f64 1/8 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 1/2 (fma.f64 1/12 x (/.f64 1 x))) (-.f64 1/4 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (/.f64 1 x)) (exp.f64 (fma.f64 1/12 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (/.f64 1 x))) (exp.f64 (fma.f64 1/12 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (fma.f64 1/12 x 1/2)) (+.f64 1 (expm1.f64 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/12 x (+.f64 (/.f64 1 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1/12 (+.f64 (/.f64 1 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/12 x) 1 (+.f64 (/.f64 1 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 1/12 x) (+.f64 (/.f64 1 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 1 x) (fma.f64 1/12 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 1/12 x (/.f64 1 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 1/12 x 1/2) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) 1 (fma.f64 1/12 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 1/12 x (/.f64 1 x)) 1 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (cbrt.f64 x)) (cbrt.f64 (pow.f64 x -2)) (fma.f64 1/12 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 1 (cbrt.f64 x)) (fma.f64 1/12 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) 1/12) (+.f64 (/.f64 1 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x))) (cbrt.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2)) (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 1/12 x)) (cbrt.f64 (pow.f64 (*.f64 1/12 x) 2)) (+.f64 (/.f64 1 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (*.f64 1/12 x) 2)) (cbrt.f64 (*.f64 1/12 x)) (+.f64 (/.f64 1 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) (fma.f64 1/12 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 1/12) (+.f64 (/.f64 1 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 1/12 x (/.f64 1 x))) (sqrt.f64 (fma.f64 1/12 x (/.f64 1 x))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 1/12 x)) (sqrt.f64 (*.f64 1/12 x)) (+.f64 (/.f64 1 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (/.f64 1 (neg.f64 x)) (fma.f64 1/12 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) (/.f64 1 (-.f64 (fma.f64 1/144 (*.f64 x x) (pow.f64 x -2)) (/.f64 (*.f64 1/12 x) x))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 (*.f64 1/12 x) 2) (pow.f64 x -2)) (/.f64 1 (-.f64 (*.f64 1/12 x) (/.f64 1 x))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 1/12 x 1/2) 1 (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 1/12 x 1/2)) 2) (cbrt.f64 (fma.f64 1/12 x 1/2)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 1/12 x 1/2)) (sqrt.f64 (fma.f64 1/12 x 1/2)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/12 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (+.f64 (/.f64 1 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/12 (sqrt.f64 x)) (sqrt.f64 x) (+.f64 (/.f64 1 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2))) 1))))))

simplify11.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	157
1	19	133
2	26	133
3	28	133

Stop Event

1×

saturated

Counts

173 → 164

Calls

Call 1

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

localize13.0ms (0.4%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.1b	(*.f64 -1/720 (pow.f64 x 3))
	0.0b	(+.f64 (*.f64 1/12 x) (/.f64 1 x))
	0.0b	(+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x)))
	0.0b	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
✓	0.0b	(+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x)))
	0.0b	(+.f64 (*.f64 1/12 x) (/.f64 1 x))
✓	0.1b	(*.f64 -1/720 (pow.f64 x 3))
	0.3b	(*.f64 1/12 x)

series3.0ms (0.1%)

Counts

2 → 12

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(*.f64 -1/720 (pow.f64 x 3))
1.0ms	x	@	inf	(*.f64 -1/720 (pow.f64 x 3))
1.0ms	x	@	-inf	(*.f64 -1/720 (pow.f64 x 3))
0.0ms	x	@	inf	(+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x)))
0.0ms	x	@	0	(+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x)))

rewrite63.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

552×	`fma-def_binary64`
549×	`log-prod_binary64`
320×	`pow2_binary64`
303×	`fma-neg_binary64`
220×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	273	22
2	3498	22

Stop Event

1×	node limit

Counts

2 → 106

Calls

Call 1

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

Outputs

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(pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x 1/12)) (sqrt.f64 (*.f64 x 1/12)) (+.f64 (/.f64 1 x) (*.f64 -1/720 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 -1/720) (pow.f64 x 3/2)) (*.f64 (sqrt.f64 -1/720) (pow.f64 x 3/2)) (fma.f64 x 1/12 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 1/12) (+.f64 (/.f64 1 x) (*.f64 -1/720 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) (fma.f64 -1/720 (pow.f64 x 3) (*.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (/.f64 1 (neg.f64 x)) (fma.f64 -1/720 (pow.f64 x 3) (*.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 (pow.f64 x 3) 1/1728 (pow.f64 x -3)) (/.f64 1 (-.f64 (fma.f64 (*.f64 x x) 1/144 (pow.f64 x -2)) (/.f64 (*.f64 x 1/12) x))) (*.f64 -1/720 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 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1 x) (*.f64 -1/720 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/12 (sqrt.f64 x)) (sqrt.f64 x) (+.f64 (/.f64 1 x) (*.f64 -1/720 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/720 x) (*.f64 x x) (fma.f64 x 1/12 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/720 (*.f64 x x)) x (fma.f64 x 1/12 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/720 (pow.f64 x 3/2)) (pow.f64 x 3/2) (fma.f64 x 1/12 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x)))) 1))))))

simplify135.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

1332×	`sqr-pow_binary64`
715×	`pow-sqr_binary64`
530×	`cube-prod_binary64`
473×	`fabs-mul_binary64`
439×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	138
1	39	138
2	64	138
3	128	138
4	201	138
5	426	138
6	1267	138
7	2010	138
8	2097	138
9	2230	138
10	2388	138
11	2618	138
12	2940	138
13	3361	138
14	3861	138
15	4456	138
16	5178	138
17	5503	138
18	5787	138
19	6009	138
20	6187	138
21	6269	138
22	7209	138

Stop Event

1×	node limit

Counts

118 → 114

Calls

Call 1

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

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

eval182.0ms (5%)

Compiler: Compiled 7520 to 5841 computations (22.3% saved)

prune57.0ms (1.6%)

Pruning

11 alts after pruning (5 fresh and 6 done)

	Pruned	Kept	Total
New	449	5	454
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	449	11	460

Error

Counts

460 → 11

Alt Table

Click to see full alt table

Status	Error	Program
	62.1b	1/2
✓	23.1b	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
✓	0.0b	(*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))
✓	22.9b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
✓	23.1b	(/.f64 1 x)
▶	0.9b	(.f64 (-.f64 (+.f64 (.f64 1/12 x) (/.f64 1 x)) 1/2) (exp.f64 x))
▶	1.2b	(*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x))
▶	1.7b	(*.f64 (/.f64 1 x) (exp.f64 x))
✓	0.0b	(/.f64 (exp.f64 x) (expm1.f64 x))
▶	23.1b	(-.f64 (+.f64 1 (+.f64 (/.f64 1 x) 1/2)) 1)
✓	23.1b	(+.f64 (/.f64 1 x) 1/2)

Compiler

Compiled 91 to 72 computations (20.9% saved)

localize5.0ms (0.1%)

Local error

Found 6 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (+.f64 1 (+.f64 (/.f64 1 x) 1/2)) 1)
	0.0b	(+.f64 (/.f64 1 x) 1/2)
	0.0b	(+.f64 1 (+.f64 (/.f64 1 x) 1/2))
✓	0.0b	(+.f64 1 (+.f64 (/.f64 1 x) 1/2))
	0.0b	(+.f64 (/.f64 1 x) 1/2)
✓	0.0b	(-.f64 (+.f64 1 (+.f64 (/.f64 1 x) 1/2)) 1)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite53.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

981×	`pow1_binary64`
925×	`add-log-exp_binary64`
924×	`log1p-expm1-u_binary64`
924×	`expm1-log1p-u_binary64`
99×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	192	14
2	2689	14

Stop Event

1×	node limit

Counts

2 → 91

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 (/.f64 1 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (+.f64 (/.f64 1 x) -1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (/.f64 1 x) 1/2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (/.f64 1 x) 3/2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (+.f64 (/.f64 1 x) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (/.f64 1 x) -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (/.f64 1 x)) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (/.f64 1 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (/.f64 1 x) 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 1/2)) (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 1/2)) 2) (cbrt.f64 (+.f64 (/.f64 1 x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (/.f64 1 x) 1/2)) (sqrt.f64 (+.f64 (/.f64 1 x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 3) -1) (/.f64 1 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) (+.f64 (+.f64 (/.f64 1 x) 1/2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1/8 (pow.f64 x -3)) (/.f64 1 (+.f64 (pow.f64 x -2) (-.f64 1/4 (/.f64 1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) -1) (/.f64 1 (+.f64 (+.f64 (/.f64 1 x) 1/2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x -2) -1/4) (/.f64 1 (+.f64 (/.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (+.f64 (/.f64 1 x) 3/2)) 1) (-.f64 (sqrt.f64 (+.f64 (/.f64 1 x) 3/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 x -2) (-.f64 1/4 (/.f64 1/2 x))) (+.f64 1/8 (pow.f64 x -3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (/.f64 1 x) -1/2) (+.f64 (pow.f64 x -2) -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) (+.f64 (+.f64 (/.f64 1 x) 1/2) 2)) (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (+.f64 (/.f64 1 x) 1/2) 2) (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 3) -1) (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) (+.f64 (+.f64 (/.f64 1 x) 1/2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 3) -1) (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) (-.f64 1 (*.f64 (+.f64 (/.f64 1 x) 3/2) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 (pow.f64 x -2) (-.f64 1/4 (/.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/8 (pow.f64 x -3)) (+.f64 1/4 (-.f64 (pow.f64 x -2) (/.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) -1) (+.f64 (+.f64 (/.f64 1 x) 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) -1) (-.f64 (+.f64 (/.f64 1 x) 3/2) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x -2) -1/4) (+.f64 (/.f64 1 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1/8 (pow.f64 x -3))) (neg.f64 (+.f64 (pow.f64 x -2) (-.f64 1/4 (/.f64 1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x -2) -1/4)) (neg.f64 (+.f64 (/.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 3) -1)) (neg.f64 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) (+.f64 (+.f64 (/.f64 1 x) 1/2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) 3/2) 2) -1)) (neg.f64 (+.f64 (+.f64 (/.f64 1 x) 1/2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 (/.f64 1 x) -1/2) 3)) (+.f64 1 (-.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (+.f64 (/.f64 1 x) -1/2)) (+.f64 (/.f64 1 x) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (+.f64 (/.f64 1 x) -1/2) (+.f64 (/.f64 1 x) -1/2))) (-.f64 1 (+.f64 (/.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/4 (pow.f64 x -2)) (-.f64 1/2 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (/.f64 1 x) 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (/.f64 1 x) 1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (/.f64 1 x) 1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (/.f64 1 x) 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (/.f64 1 x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (/.f64 1 x) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (/.f64 1 x) 1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 1 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (/.f64 1 x) 3/2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) 3/2)) 2) (cbrt.f64 (+.f64 (/.f64 1 x) 3/2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -2)) (cbrt.f64 (/.f64 1 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 (/.f64 1 x) 3/2)) (sqrt.f64 (+.f64 (/.f64 1 x) 3/2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (/.f64 1 x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (/.f64 1 x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (/.f64 1 x) 1/2)))))))

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

simplify11.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	138
1	12	138

Stop Event

1×

saturated

Counts

115 → 96

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (/.f64 1 x))
1/2
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (/.f64 1 x))
1/2
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (/.f64 1 x))
(/.f64 1 x)
(+.f64 3/2 (/.f64 1 x))
(+.f64 3/2 (/.f64 1 x))
(+.f64 3/2 (/.f64 1 x))
3/2
(+.f64 3/2 (/.f64 1 x))
(+.f64 3/2 (/.f64 1 x))
(+.f64 3/2 (/.f64 1 x))
3/2
(+.f64 3/2 (/.f64 1 x))
(+.f64 3/2 (/.f64 1 x))
(+.f64 3/2 (/.f64 1 x))

Outputs
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
1/2
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
1/2
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(/.f64 1 x)
(+.f64 3/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 3/2)
(+.f64 3/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 3/2)
(+.f64 3/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 3/2)
3/2
(+.f64 3/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 3/2)
(+.f64 3/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 3/2)
(+.f64 3/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 3/2)
3/2
(+.f64 3/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 3/2)
(+.f64 3/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 3/2)
(+.f64 3/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 3/2)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (/.f64 1 x) (exp.f64 x))
✓	0.0b	(*.f64 (/.f64 1 x) (exp.f64 x))

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(*.f64 (/.f64 1 x) (exp.f64 x))
0.0ms	x	@	0	(*.f64 (/.f64 1 x) (exp.f64 x))
0.0ms	x	@	inf	(*.f64 (/.f64 1 x) (exp.f64 x))

rewrite37.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

515×	`pow1_binary64`
493×	`add-sqr-sqrt_binary64`
475×	`add-log-exp_binary64`
475×	`log1p-expm1-u_binary64`
475×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
1	115	6
2	1350	6

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

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

Outputs

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

simplify48.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

830×	`times-frac_binary64`
812×	`fma-def_binary64`
529×	`associate-l_binary64`
452×	`unswap-sqr_binary64`
398×	`associate-/r*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	88
1	38	88
2	74	88
3	168	85
4	340	85
5	768	85
6	2380	85
7	6888	85
8	7373	85

Stop Event

1×	node limit

Counts

33 → 27

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 1 (/.f64 1 x))
(+.f64 1 (+.f64 (*.f64 1/2 x) (/.f64 1 x)))
(+.f64 1 (+.f64 (.f64 1/6 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (/.f64 1 x))))
(/.f64 (exp.f64 x) x)
(/.f64 (exp.f64 x) x)
(/.f64 (exp.f64 x) x)
(/.f64 (exp.f64 x) x)
(/.f64 (exp.f64 x) x)
(/.f64 (exp.f64 x) x)
(/.f64 (exp.f64 x) x)
(/.f64 (exp.f64 x) x)

Outputs
(/.f64 1 x)
(+.f64 1 (/.f64 1 x))
(+.f64 1 (+.f64 (*.f64 1/2 x) (/.f64 1 x)))
(+.f64 1 (fma.f64 1/2 x (/.f64 1 x)))
(+.f64 1 (fma.f64 x 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 x 1/2 1))
(+.f64 1 (+.f64 (.f64 1/6 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (/.f64 1 x))))
(+.f64 1 (fma.f64 1/6 (*.f64 x x) (fma.f64 1/2 x (/.f64 1 x))))
(+.f64 1 (fma.f64 1/6 (*.f64 x x) (fma.f64 x 1/2 (/.f64 1 x))))
(+.f64 (fma.f64 x 1/2 (/.f64 1 x)) (fma.f64 x (*.f64 x 1/6) 1))
(+.f64 (/.f64 1 x) (fma.f64 x (fma.f64 x 1/6 1/2) 1))
(+.f64 1 (fma.f64 x (fma.f64 x 1/6 1/2) (/.f64 1 x)))
(fma.f64 x (fma.f64 x 1/6 1/2) (+.f64 1 (/.f64 1 x)))
(/.f64 (exp.f64 x) x)
(/.f64 (exp.f64 x) x)
(/.f64 (exp.f64 x) x)
(/.f64 (exp.f64 x) x)
(/.f64 (exp.f64 x) x)
(/.f64 (exp.f64 x) x)
(/.f64 (exp.f64 x) x)
(/.f64 (exp.f64 x) x)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x))
✓	0.0b	(*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x))

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite41.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

800×	`pow1_binary64`
745×	`add-log-exp_binary64`
745×	`log1p-expm1-u_binary64`
745×	`expm1-log1p-u_binary64`
731×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	166	12
2	2031	12

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

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

Outputs

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

simplify63.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

806×	`fma-def_binary64`
536×	`unswap-sqr_binary64`
465×	`times-frac_binary64`
439×	`associate-l_binary64`
374×	`associate-/l/_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	22	142
1	49	130
2	101	130
3	252	130
4	591	127
5	1895	127
6	4326	127
7	6630	127
8	7062	127
9	7678	127

Stop Event

1×	node limit

Counts

33 → 31

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (+.f64 (*.f64 -1/12 (pow.f64 x 2)) (/.f64 1 x)))
(+.f64 (.f64 -1/24 (pow.f64 x 3)) (+.f64 1/2 (+.f64 (.f64 -1/12 (pow.f64 x 2)) (/.f64 1 x))))
(*.f64 -1/2 (exp.f64 x))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(*.f64 -1/2 (exp.f64 x))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))

Outputs
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/12 (pow.f64 x 2)) (/.f64 1 x)))
(+.f64 1/2 (fma.f64 -1/12 (*.f64 x x) (/.f64 1 x)))
(+.f64 1/2 (fma.f64 x (*.f64 x -1/12) (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 x (*.f64 x -1/12) 1/2))
(+.f64 (.f64 -1/24 (pow.f64 x 3)) (+.f64 1/2 (+.f64 (.f64 -1/12 (pow.f64 x 2)) (/.f64 1 x))))
(fma.f64 -1/24 (pow.f64 x 3) (+.f64 1/2 (fma.f64 -1/12 (*.f64 x x) (/.f64 1 x))))
(+.f64 (fma.f64 -1/12 (*.f64 x x) (/.f64 1 x)) (fma.f64 -1/24 (pow.f64 x 3) 1/2))
(+.f64 1/2 (fma.f64 -1/24 (pow.f64 x 3) (fma.f64 x (*.f64 x -1/12) (/.f64 1 x))))
(+.f64 (fma.f64 x (*.f64 x -1/12) 1/2) (fma.f64 -1/24 (pow.f64 x 3) (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 x (*.f64 x (fma.f64 x -1/24 -1/12)) 1/2))
(+.f64 (/.f64 1 x) (fma.f64 (*.f64 x x) (fma.f64 x -1/24 -1/12) 1/2))
(*.f64 -1/2 (exp.f64 x))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(+.f64 (*.f64 -1/2 (exp.f64 x)) (/.f64 (exp.f64 x) x))
(fma.f64 -1/2 (exp.f64 x) (/.f64 (exp.f64 x) x))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(+.f64 (*.f64 -1/2 (exp.f64 x)) (/.f64 (exp.f64 x) x))
(fma.f64 -1/2 (exp.f64 x) (/.f64 (exp.f64 x) x))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(+.f64 (*.f64 -1/2 (exp.f64 x)) (/.f64 (exp.f64 x) x))
(fma.f64 -1/2 (exp.f64 x) (/.f64 (exp.f64 x) x))
(*.f64 -1/2 (exp.f64 x))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(+.f64 (*.f64 -1/2 (exp.f64 x)) (/.f64 (exp.f64 x) x))
(fma.f64 -1/2 (exp.f64 x) (/.f64 (exp.f64 x) x))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(+.f64 (*.f64 -1/2 (exp.f64 x)) (/.f64 (exp.f64 x) x))
(fma.f64 -1/2 (exp.f64 x) (/.f64 (exp.f64 x) x))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(+.f64 (*.f64 -1/2 (exp.f64 x)) (/.f64 (exp.f64 x) x))
(fma.f64 -1/2 (exp.f64 x) (/.f64 (exp.f64 x) x))

localize7.0ms (0.2%)

Local error

Found 6 expressions with local error:

New	Error	Program
	0.3b	(*.f64 1/12 x)
	0.0b	(+.f64 (*.f64 1/12 x) (/.f64 1 x))
	0.0b	(.f64 (-.f64 (+.f64 (.f64 1/12 x) (/.f64 1 x)) 1/2) (exp.f64 x))
✓	0.0b	(.f64 (-.f64 (+.f64 (.f64 1/12 x) (/.f64 1 x)) 1/2) (exp.f64 x))
	0.0b	(+.f64 (*.f64 1/12 x) (/.f64 1 x))
	0.3b	(*.f64 1/12 x)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

(*.f64 (-.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x)) 1/2) (exp.f64 x))

0.0ms

inf

(*.f64 (-.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x)) 1/2) (exp.f64 x))

0.0ms

-inf

(*.f64 (-.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x)) 1/2) (exp.f64 x))

rewrite48.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

904×	`prod-diff_binary64`
512×	`log-prod_binary64`
413×	`fma-def_binary64`
299×	`pow2_binary64`
242×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	242	16
2	3170	16

Stop Event

1×	node limit

Counts

1 → 32

Calls

Call 1

Inputs
(.f64 (-.f64 (+.f64 (.f64 1/12 x) (/.f64 1 x)) 1/2) (exp.f64 x))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x -1/2)) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 1/12 x) (exp.f64 x)) (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (fma.f64 1/12 x (/.f64 1 x)) (exp.f64 x)) (*.f64 -1/2 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (exp.f64 x) (*.f64 1/12 x)) (*.f64 (exp.f64 x) (+.f64 (/.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (exp.f64 x) (fma.f64 1/12 x (/.f64 1 x))) (*.f64 (exp.f64 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (exp.f64 x)) (+.f64 (/.f64 1 x) (fma.f64 1/12 x -1/2)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (exp.f64 x)) (+.f64 (/.f64 1 x) (fma.f64 1/12 x -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (exp.f64 x)) (+.f64 (/.f64 1 x) (fma.f64 1/12 x -1/2))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (exp.f64 x)) (+.f64 (/.f64 1 x) (fma.f64 1/12 x -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x -1/2)) (exp.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 3) -1/8) (exp.f64 x)) (+.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2) (fma.f64 (fma.f64 1/12 x (/.f64 1 x)) 1/2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2) -1/4) (exp.f64 x)) (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (exp.f64 x) (+.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 3) -1/8)) (+.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2) (fma.f64 (fma.f64 1/12 x (/.f64 1 x)) 1/2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (exp.f64 x) (+.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2) -1/4)) (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x -1/2)) (exp.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x -1/2)) (exp.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x -1/2)) (exp.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x -1/2)) (exp.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x -1/2)) 3) (pow.f64 (exp.f64 x) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x -1/2)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x -1/2)) (exp.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (exp.f64 x)) (+.f64 (/.f64 1 x) (fma.f64 1/12 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x -1/2)) (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x -1/2)) (exp.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x -1/2)) 3) (pow.f64 (exp.f64 x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x -1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/12 x) (exp.f64 x) (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 1/12 x (/.f64 1 x)) (exp.f64 x) (*.f64 -1/2 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (exp.f64 x) (*.f64 1/12 x) (*.f64 (exp.f64 x) (+.f64 (/.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (exp.f64 x) (fma.f64 1/12 x (/.f64 1 x)) (*.f64 (exp.f64 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x -1/2)) (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x -1/2)) (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 x (log.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (+.f64 x (log.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x -1/2)))) 1))))))

simplify75.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

822×	`fma-def_binary64`
696×	`sqr-pow_binary64`
516×	`associate-l_binary64`
425×	`times-frac_binary64`
394×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	25	182
1	55	180
2	106	162
3	203	142
4	333	142
5	693	142
6	1915	142
7	3442	142
8	5558	142
9	6056	142
10	6558	142
11	7322	142

Stop Event

1×	node limit

Counts

44 → 45

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 1/12 x) (+.f64 (/.f64 1 x) (.f64 1/720 (pow.f64 x 4)))))
(.f64 1/12 (.f64 (exp.f64 x) x))
(+.f64 (.f64 -1/2 (exp.f64 x)) (.f64 1/12 (*.f64 (exp.f64 x) x)))
(+.f64 (/.f64 (exp.f64 x) x) (+.f64 (.f64 -1/2 (exp.f64 x)) (.f64 1/12 (*.f64 (exp.f64 x) x))))
(+.f64 (/.f64 (exp.f64 x) x) (+.f64 (.f64 -1/2 (exp.f64 x)) (.f64 1/12 (*.f64 (exp.f64 x) x))))
(.f64 1/12 (.f64 (exp.f64 x) x))
(+.f64 (.f64 -1/2 (exp.f64 x)) (.f64 1/12 (*.f64 (exp.f64 x) x)))
(+.f64 (/.f64 (exp.f64 x) x) (+.f64 (.f64 -1/2 (exp.f64 x)) (.f64 1/12 (*.f64 (exp.f64 x) x))))
(+.f64 (/.f64 (exp.f64 x) x) (+.f64 (.f64 -1/2 (exp.f64 x)) (.f64 1/12 (*.f64 (exp.f64 x) x))))

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 1/12 x) (+.f64 (/.f64 1 x) (.f64 1/720 (pow.f64 x 4)))))
(+.f64 1/2 (+.f64 (fma.f64 1/12 x (/.f64 1 x)) (*.f64 1/720 (pow.f64 x 4))))
(+.f64 1/2 (fma.f64 x 1/12 (fma.f64 1/720 (pow.f64 x 4) (/.f64 1 x))))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 1/720 (pow.f64 x 4) 1/2)))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) (fma.f64 1/720 (pow.f64 x 4) 1/2))
(fma.f64 x (fma.f64 1/720 (pow.f64 x 3) 1/12) (+.f64 (/.f64 1 x) 1/2))
(.f64 1/12 (.f64 (exp.f64 x) x))
(.f64 1/12 (.f64 x (exp.f64 x)))
(.f64 x (.f64 1/12 (exp.f64 x)))
(+.f64 (.f64 -1/2 (exp.f64 x)) (.f64 1/12 (*.f64 (exp.f64 x) x)))
(fma.f64 -1/2 (exp.f64 x) (.f64 1/12 (.f64 x (exp.f64 x))))
(fma.f64 1/12 (.f64 x (exp.f64 x)) (.f64 (exp.f64 x) -1/2))
(.f64 (exp.f64 x) (+.f64 (.f64 x 1/12) -1/2))
(*.f64 (exp.f64 x) (fma.f64 x 1/12 -1/2))
(+.f64 (/.f64 (exp.f64 x) x) (+.f64 (.f64 -1/2 (exp.f64 x)) (.f64 1/12 (*.f64 (exp.f64 x) x))))
(+.f64 (fma.f64 -1/2 (exp.f64 x) (.f64 1/12 (.f64 x (exp.f64 x)))) (/.f64 (exp.f64 x) x))
(+.f64 (fma.f64 1/12 (.f64 x (exp.f64 x)) (.f64 (exp.f64 x) -1/2)) (/.f64 (exp.f64 x) x))
(+.f64 (.f64 (exp.f64 x) (+.f64 (.f64 x 1/12) -1/2)) (/.f64 (exp.f64 x) x))
(fma.f64 (exp.f64 x) (fma.f64 x 1/12 -1/2) (/.f64 (exp.f64 x) x))
(+.f64 (/.f64 (exp.f64 x) x) (+.f64 (.f64 -1/2 (exp.f64 x)) (.f64 1/12 (*.f64 (exp.f64 x) x))))
(+.f64 (fma.f64 -1/2 (exp.f64 x) (.f64 1/12 (.f64 x (exp.f64 x)))) (/.f64 (exp.f64 x) x))
(+.f64 (fma.f64 1/12 (.f64 x (exp.f64 x)) (.f64 (exp.f64 x) -1/2)) (/.f64 (exp.f64 x) x))
(+.f64 (.f64 (exp.f64 x) (+.f64 (.f64 x 1/12) -1/2)) (/.f64 (exp.f64 x) x))
(fma.f64 (exp.f64 x) (fma.f64 x 1/12 -1/2) (/.f64 (exp.f64 x) x))
(.f64 1/12 (.f64 (exp.f64 x) x))
(.f64 1/12 (.f64 x (exp.f64 x)))
(.f64 x (.f64 1/12 (exp.f64 x)))
(+.f64 (.f64 -1/2 (exp.f64 x)) (.f64 1/12 (*.f64 (exp.f64 x) x)))
(fma.f64 -1/2 (exp.f64 x) (.f64 1/12 (.f64 x (exp.f64 x))))
(fma.f64 1/12 (.f64 x (exp.f64 x)) (.f64 (exp.f64 x) -1/2))
(.f64 (exp.f64 x) (+.f64 (.f64 x 1/12) -1/2))
(*.f64 (exp.f64 x) (fma.f64 x 1/12 -1/2))
(+.f64 (/.f64 (exp.f64 x) x) (+.f64 (.f64 -1/2 (exp.f64 x)) (.f64 1/12 (*.f64 (exp.f64 x) x))))
(+.f64 (fma.f64 -1/2 (exp.f64 x) (.f64 1/12 (.f64 x (exp.f64 x)))) (/.f64 (exp.f64 x) x))
(+.f64 (fma.f64 1/12 (.f64 x (exp.f64 x)) (.f64 (exp.f64 x) -1/2)) (/.f64 (exp.f64 x) x))
(+.f64 (.f64 (exp.f64 x) (+.f64 (.f64 x 1/12) -1/2)) (/.f64 (exp.f64 x) x))
(fma.f64 (exp.f64 x) (fma.f64 x 1/12 -1/2) (/.f64 (exp.f64 x) x))
(+.f64 (/.f64 (exp.f64 x) x) (+.f64 (.f64 -1/2 (exp.f64 x)) (.f64 1/12 (*.f64 (exp.f64 x) x))))
(+.f64 (fma.f64 -1/2 (exp.f64 x) (.f64 1/12 (.f64 x (exp.f64 x)))) (/.f64 (exp.f64 x) x))
(+.f64 (fma.f64 1/12 (.f64 x (exp.f64 x)) (.f64 (exp.f64 x) -1/2)) (/.f64 (exp.f64 x) x))
(+.f64 (.f64 (exp.f64 x) (+.f64 (.f64 x 1/12) -1/2)) (/.f64 (exp.f64 x) x))
(fma.f64 (exp.f64 x) (fma.f64 x 1/12 -1/2) (/.f64 (exp.f64 x) x))

eval104.0ms (2.9%)

Compiler: Compiled 4539 to 3464 computations (23.7% saved)

prune47.0ms (1.3%)

Pruning

13 alts after pruning (5 fresh and 8 done)

	Pruned	Kept	Total
New	313	5	318
Fresh	1	0	1
Picked	0	1	1
Done	2	7	9
Total	316	13	329

Error

Counts

329 → 13

Alt Table

Click to see full alt table

Status	Error	Program
▶	1.2b	(-.f64 (+.f64 1 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x))) 1)
✓	23.1b	(/.f64 1 x)
	62.1b	1/2
▶	23.6b	(+.f64 1 (/.f64 1 x))
✓	0.0b	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	0.0b	(*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))
✓	22.9b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
✓	0.9b	(.f64 (-.f64 (+.f64 (.f64 1/12 x) (/.f64 1 x)) 1/2) (exp.f64 x))
✓	1.2b	(*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x))
▶	39.8b	(*.f64 -1/2 (exp.f64 x))
▶	3.2b	(-.f64 (+.f64 1 (/.f64 1 x)) 1)
✓	23.1b	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
✓	23.1b	(+.f64 (/.f64 1 x) 1/2)

Compiler

Compiled 106 to 85 computations (19.8% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	3.2b	(-.f64 (+.f64 1 (/.f64 1 x)) 1)
✓	3.2b	(-.f64 (+.f64 1 (/.f64 1 x)) 1)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite44.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

665×	`pow1_binary64`
626×	`add-log-exp_binary64`
626×	`log1p-expm1-u_binary64`
626×	`expm1-log1p-u_binary64`
615×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	139	4
2	1920	4

Stop Event

1×	node limit

Counts

1 → 46

Calls

Call 1

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

Outputs

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

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	48
1	6	48

Stop Event

1×

saturated

Counts

58 → 46

Calls

Call 1

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

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

localize2.0ms (0.1%)

localize3.0ms (0.1%)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(-.f64 (+.f64 1 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x))) 1)
	0.0b	(*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x))
	0.0b	(*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x))
✓	0.2b	(-.f64 (+.f64 1 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x))) 1)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite54.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

544×	`prod-diff_binary64`
474×	`fma-def_binary64`
437×	`log-prod_binary64`
287×	`pow-prod-down_binary64`
260×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	226	12
2	3069	12

Stop Event

1×	node limit

Counts

1 → 96

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 1 x) (exp.f64 x)) (*.f64 -1/2 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 -1/2 (exp.f64 x)) (*.f64 (/.f64 1 x) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (exp.f64 x) (/.f64 1 x)) (*.f64 (exp.f64 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (exp.f64 x) -1/2) (*.f64 (exp.f64 x) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (exp.f64 x)) (+.f64 (/.f64 1 x) -1/2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (exp.f64 x)) (+.f64 (/.f64 1 x) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (exp.f64 x)) (+.f64 (/.f64 1 x) -1/2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (exp.f64 x)) (+.f64 (/.f64 1 x) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (exp.f64 x) (+.f64 (/.f64 1 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x))) (cbrt.f64 (pow.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x)) 2)) (cbrt.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 (/.f64 1 x) -1/2) 2)) (*.f64 (cbrt.f64 (+.f64 (/.f64 1 x) -1/2)) (exp.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 (/.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x))) (sqrt.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (/.f64 1 x) -1/2)) (*.f64 (sqrt.f64 (+.f64 (/.f64 1 x) -1/2)) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (exp.f64 x)) (*.f64 (sqrt.f64 (exp.f64 x)) (+.f64 (/.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1) 3) -1) (/.f64 1 (+.f64 (pow.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1) 2) (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1) 2) -1) (/.f64 1 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1)) 1) (-.f64 (sqrt.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (pow.f64 (cbrt.f64 (exp.f64 x)) 2)) (cbrt.f64 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (sqrt.f64 (exp.f64 x))) (sqrt.f64 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (+.f64 (/.f64 1 x) -1/2) 2))) (cbrt.f64 (+.f64 (/.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (exp.f64 x) (sqrt.f64 (+.f64 (/.f64 1 x) -1/2))) (sqrt.f64 (+.f64 (/.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1) 2) (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 2)) (+.f64 (pow.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 2) (+.f64 (pow.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1) 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1) 3) -1) (+.f64 (pow.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1) 2) (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1) 3) -1) (+.f64 (pow.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1) 2) (-.f64 1 (*.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1) 2) -1) (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1) 3) -1)) (neg.f64 (+.f64 (pow.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1) 2) (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1) 2) -1)) (neg.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) -1) 3)) (+.f64 1 (-.f64 (pow.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) -1) 2) (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) -1) 2)) (-.f64 1 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 -1/8 (pow.f64 x -3)) (exp.f64 x)) (-.f64 (+.f64 (pow.f64 x -2) 1/4) (/.f64 -1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 x -2) -1/4) (exp.f64 x)) (+.f64 (/.f64 1 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (exp.f64 x) (+.f64 -1/8 (pow.f64 x -3))) (-.f64 (+.f64 (pow.f64 x -2) 1/4) (/.f64 -1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (exp.f64 x) (+.f64 (pow.f64 x -2) -1/4)) (+.f64 (/.f64 1 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 (pow.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1) 2) (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 2)) (+.f64 (pow.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1) 3) -1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 2) (+.f64 (pow.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1) 2) -1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (exp.f64 x)) (+.f64 (/.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) (exp.f64 x) (*.f64 -1/2 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1/2 (exp.f64 x) (*.f64 (/.f64 1 x) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (exp.f64 x) (/.f64 1 x) (*.f64 (exp.f64 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (exp.f64 x) -1/2 (*.f64 (exp.f64 x) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (exp.f64 x) (+.f64 (/.f64 1 x) -1/2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x)) 1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1) 1 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x))) (cbrt.f64 (pow.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x)) 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x)) 2)) (cbrt.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1)) (cbrt.f64 (pow.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1) 2)) (cbrt.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1) 2)) (*.f64 (cbrt.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (+.f64 (/.f64 1 x) -1/2) 2)) (*.f64 (cbrt.f64 (+.f64 (/.f64 1 x) -1/2)) (exp.f64 x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (*.f64 (cbrt.f64 (exp.f64 x)) (+.f64 (/.f64 1 x) -1/2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x))) (sqrt.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1)) (sqrt.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1)) (*.f64 (sqrt.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 (/.f64 1 x) -1/2)) (*.f64 (sqrt.f64 (+.f64 (/.f64 1 x) -1/2)) (exp.f64 x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (exp.f64 x)) (*.f64 (sqrt.f64 (exp.f64 x)) (+.f64 (/.f64 1 x) -1/2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1) 3) -1) (/.f64 1 (+.f64 (pow.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1) 2) (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (pow.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x)) 3)) (/.f64 1 (fma.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x)) (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) -1) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1) 2) -1) (/.f64 1 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 (pow.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x)) 2)) (/.f64 1 (-.f64 1 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) -1)) 2) (cbrt.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) -1)) (sqrt.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (sqrt.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1)) 1) (-.f64 (sqrt.f64 (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) 1)) 1) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (sqrt.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x))) 1) (-.f64 (sqrt.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x))) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (pow.f64 (cbrt.f64 (exp.f64 x)) 2)) (cbrt.f64 (exp.f64 x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (sqrt.f64 (exp.f64 x))) (sqrt.f64 (exp.f64 x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (+.f64 (/.f64 1 x) -1/2) 2))) (cbrt.f64 (+.f64 (/.f64 1 x) -1/2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (exp.f64 x) (sqrt.f64 (+.f64 (/.f64 1 x) -1/2))) (sqrt.f64 (+.f64 (/.f64 1 x) -1/2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (sqrt.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x))) (sqrt.f64 (*.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x)) (fma.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (*.f64 (log1p.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 x (log.f64 (+.f64 (/.f64 1 x) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (+.f64 x (log.f64 (+.f64 (/.f64 1 x) -1/2))) 1))))))

simplify67.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

806×	`fma-def_binary64`
536×	`unswap-sqr_binary64`
465×	`times-frac_binary64`
439×	`associate-l_binary64`
374×	`associate-/l/_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	22	142
1	49	130
2	101	130
3	252	130
4	591	127
5	1895	127
6	4326	127
7	6630	127
8	7062	127
9	7678	127

Stop Event

1×	node limit

Counts

108 → 106

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (+.f64 (*.f64 -1/12 (pow.f64 x 2)) (/.f64 1 x)))
(+.f64 (.f64 -1/24 (pow.f64 x 3)) (+.f64 1/2 (+.f64 (.f64 -1/12 (pow.f64 x 2)) (/.f64 1 x))))
(*.f64 -1/2 (exp.f64 x))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(*.f64 -1/2 (exp.f64 x))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))

Outputs
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/12 (pow.f64 x 2)) (/.f64 1 x)))
(+.f64 1/2 (fma.f64 -1/12 (*.f64 x x) (/.f64 1 x)))
(+.f64 1/2 (fma.f64 x (*.f64 x -1/12) (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 x (*.f64 x -1/12) 1/2))
(+.f64 (.f64 -1/24 (pow.f64 x 3)) (+.f64 1/2 (+.f64 (.f64 -1/12 (pow.f64 x 2)) (/.f64 1 x))))
(fma.f64 -1/24 (pow.f64 x 3) (+.f64 1/2 (fma.f64 -1/12 (*.f64 x x) (/.f64 1 x))))
(+.f64 (fma.f64 -1/12 (*.f64 x x) (/.f64 1 x)) (fma.f64 -1/24 (pow.f64 x 3) 1/2))
(+.f64 1/2 (fma.f64 -1/24 (pow.f64 x 3) (fma.f64 x (*.f64 x -1/12) (/.f64 1 x))))
(+.f64 (fma.f64 x (*.f64 x -1/12) 1/2) (fma.f64 -1/24 (pow.f64 x 3) (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 x (*.f64 x (fma.f64 x -1/24 -1/12)) 1/2))
(+.f64 (/.f64 1 x) (fma.f64 (*.f64 x x) (fma.f64 x -1/24 -1/12) 1/2))
(*.f64 -1/2 (exp.f64 x))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(+.f64 (*.f64 -1/2 (exp.f64 x)) (/.f64 (exp.f64 x) x))
(fma.f64 -1/2 (exp.f64 x) (/.f64 (exp.f64 x) x))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(+.f64 (*.f64 -1/2 (exp.f64 x)) (/.f64 (exp.f64 x) x))
(fma.f64 -1/2 (exp.f64 x) (/.f64 (exp.f64 x) x))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(+.f64 (*.f64 -1/2 (exp.f64 x)) (/.f64 (exp.f64 x) x))
(fma.f64 -1/2 (exp.f64 x) (/.f64 (exp.f64 x) x))
(*.f64 -1/2 (exp.f64 x))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(+.f64 (*.f64 -1/2 (exp.f64 x)) (/.f64 (exp.f64 x) x))
(fma.f64 -1/2 (exp.f64 x) (/.f64 (exp.f64 x) x))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(+.f64 (*.f64 -1/2 (exp.f64 x)) (/.f64 (exp.f64 x) x))
(fma.f64 -1/2 (exp.f64 x) (/.f64 (exp.f64 x) x))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(+.f64 (*.f64 -1/2 (exp.f64 x)) (/.f64 (exp.f64 x) x))
(fma.f64 -1/2 (exp.f64 x) (/.f64 (exp.f64 x) x))

eval67.0ms (1.9%)

Compiler: Compiled 2756 to 2044 computations (25.8% saved)

prune27.0ms (0.8%)

Pruning

14 alts after pruning (3 fresh and 11 done)

	Pruned	Kept	Total
New	181	2	183
Fresh	0	1	1
Picked	0	1	1
Done	1	10	11
Total	182	14	196

Error

Counts

196 → 14

Alt Table

Click to see full alt table

Status	Error	Program
✓	1.2b	(-.f64 (+.f64 1 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x))) 1)
✓	23.1b	(/.f64 1 x)
	62.1b	1/2
✓	23.6b	(+.f64 1 (/.f64 1 x))
✓	0.0b	(/.f64 (exp.f64 x) (expm1.f64 x))
	20.0b	(/.f64 (-.f64 1 (*.f64 (+.f64 (/.f64 1 x) -1) (+.f64 (/.f64 1 x) -1))) (-.f64 1 (+.f64 (/.f64 1 x) -1)))
✓	23.1b	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
✓	0.0b	(*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))
✓	22.9b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
	3.0b	(+.f64 (+.f64 (/.f64 1 x) -1) 1)
✓	0.9b	(.f64 (-.f64 (+.f64 (.f64 1/12 x) (/.f64 1 x)) 1/2) (exp.f64 x))
✓	1.2b	(*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x))
✓	39.8b	(*.f64 -1/2 (exp.f64 x))
✓	23.1b	(+.f64 (/.f64 1 x) 1/2)

Compiler

Compiled 128 to 104 computations (18.8% saved)

regimes30.0ms (0.8%)

Counts

19 → 1

Calls

Call 1

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

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

Calls

5 calls:

10.0ms	x
5.0ms	(exp.f64 x)
3.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
3.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
3.0ms	(exp.f64 x)

Results

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

Compiler

Compiled 169 to 121 computations (28.4% saved)

regimes22.0ms (0.6%)

Counts

16 → 1

Calls

Call 1

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

Outputs
(.f64 (-.f64 (+.f64 (.f64 1/12 x) (/.f64 1 x)) 1/2) (exp.f64 x))

Calls

3 calls:

13.0ms	x
3.0ms	(exp.f64 x)
3.0ms	(exp.f64 x)

Results

Error	Segments	Branch
0.9b	1	`x`
0.9b	1	`(exp.f64 x)`
0.9b	1	`(exp.f64 x)`

Compiler

Compiled 134 to 103 computations (23.1% saved)

regimes16.0ms (0.5%)

Counts

14 → 1

Calls

Call 1

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

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

Calls

3 calls:

7.0ms	x
3.0ms	(exp.f64 x)
3.0ms	(exp.f64 x)

Results

Error	Segments	Branch
1.2b	1	`x`
1.2b	1	`(exp.f64 x)`
1.2b	1	`(exp.f64 x)`

Compiler

Compiled 107 to 83 computations (22.4% saved)

regimes19.0ms (0.5%)

Counts

12 → 1

Calls

Call 1

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

Outputs
(*.f64 (/.f64 1 x) (exp.f64 x))

Calls

3 calls:

7.0ms	x
7.0ms	(exp.f64 x)
2.0ms	(exp.f64 x)

Results

Error	Segments	Branch
1.7b	1	`x`
1.7b	1	`(exp.f64 x)`
1.7b	1	`(exp.f64 x)`

Compiler

Compiled 87 to 69 computations (20.7% saved)

regimes27.0ms (0.8%)

Counts

11 → 2

Calls

Call 1

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

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

Calls

3 calls:

16.0ms	x
4.0ms	(exp.f64 x)
4.0ms	(exp.f64 x)

Results

Error	Segments	Branch
0.9b	2	`x`
0.9b	2	`(exp.f64 x)`
0.9b	2	`(exp.f64 x)`

Compiler

Compiled 81 to 66 computations (18.5% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.6814647106432018e-14	0.12022817518650757

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes9.0ms (0.2%)

Counts

10 → 1

Calls

Call 1

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

Outputs
(+.f64 (+.f64 (/.f64 1 x) -1) 1)

Calls

1 calls:

6.0ms

Results

Error	Segments	Branch
3.0b	1	`x`

Compiler

Compiled 71 to 59 computations (16.9% saved)

regimes11.0ms (0.3%)

Counts

5 → 1

Calls

Call 1

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

Outputs
(/.f64 1 x)

Calls

1 calls:

9.0ms

Results

Error	Segments	Branch
23.1b	1	`x`

Compiler

Compiled 18 to 14 computations (22.2% saved)

regimes4.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

2 → 1

Calls

Call 1

Inputs
1/2
1/2

Outputs
1/2

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
62.1b	1	`x`

Compiler

Compiled 5 to 4 computations (20% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
5×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	89
1	40	89
2	41	89

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (exp.f64 x) (expm1.f64 x))
(.f64 (-.f64 (+.f64 (.f64 1/12 x) (/.f64 1 x)) 1/2) (exp.f64 x))
(*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x))
(*.f64 (/.f64 1 x) (exp.f64 x))
(if (<=.f64 (exp.f64 x) 6338253001141147/316912650057057350374175801344) (.f64 -1/2 (exp.f64 x)) (+.f64 1/2 (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(+.f64 (+.f64 (/.f64 1 x) -1) 1)
(/.f64 1 x)
1/2

Outputs
(/.f64 (exp.f64 x) (expm1.f64 x))
(.f64 (-.f64 (+.f64 (.f64 1/12 x) (/.f64 1 x)) 1/2) (exp.f64 x))
(.f64 (exp.f64 x) (+.f64 (+.f64 (.f64 x 1/12) (/.f64 1 x)) -1/2))
(*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x))
(*.f64 (exp.f64 x) (+.f64 (/.f64 1 x) -1/2))
(*.f64 (/.f64 1 x) (exp.f64 x))
(*.f64 (exp.f64 x) (/.f64 1 x))
(if (<=.f64 (exp.f64 x) 6338253001141147/316912650057057350374175801344) (.f64 -1/2 (exp.f64 x)) (+.f64 1/2 (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(if (<=.f64 (exp.f64 x) 6338253001141147/316912650057057350374175801344) (.f64 (exp.f64 x) -1/2) (+.f64 (+.f64 (.f64 x 1/12) (/.f64 1 x)) 1/2))
(+.f64 (+.f64 (/.f64 1 x) -1) 1)
(+.f64 1 (+.f64 (/.f64 1 x) -1))
(/.f64 1 x)
1/2

end62.0ms (1.7%)

Stop Event

1×

fuel

Compiler

Compiled 129 to 93 computations (27.9% saved)

Details

analyze164.0ms (4.5%)

sample1.5s (40.6%)

preprocess20.0ms (0.5%)

simplify6.0ms (0.2%)

eval1.0ms (0%)

prune1.0ms (0%)

localize3.0ms (0.1%)

series2.0ms (0.1%)

rewrite37.0ms (1%)

simplify138.0ms (3.8%)

eval7.0ms (0.2%)

prune9.0ms (0.2%)

localize5.0ms (0.1%)

series4.0ms (0.1%)

rewrite42.0ms (1.1%)

simplify86.0ms (2.4%)

localize2.0ms (0%)

localize3.0ms (0.1%)

series1.0ms (0%)

rewrite42.0ms (1.2%)

simplify7.0ms (0.2%)

localize5.0ms (0.1%)

series4.0ms (0.1%)

rewrite62.0ms (1.7%)

simplify11.0ms (0.3%)

localize13.0ms (0.4%)

series3.0ms (0.1%)

rewrite63.0ms (1.7%)

simplify135.0ms (3.7%)

eval182.0ms (5%)

prune57.0ms (1.6%)

localize5.0ms (0.1%)

series2.0ms (0%)

rewrite53.0ms (1.5%)

simplify11.0ms (0.3%)

localize3.0ms (0.1%)

series2.0ms (0%)

rewrite37.0ms (1%)

simplify48.0ms (1.3%)

localize5.0ms (0.1%)

series1.0ms (0%)

rewrite41.0ms (1.1%)

simplify63.0ms (1.7%)

localize7.0ms (0.2%)

series1.0ms (0%)

rewrite48.0ms (1.3%)

simplify75.0ms (2.1%)

eval104.0ms (2.9%)

prune47.0ms (1.3%)

localize4.0ms (0.1%)

series1.0ms (0%)

rewrite44.0ms (1.2%)

simplify7.0ms (0.2%)

localize2.0ms (0.1%)

localize3.0ms (0.1%)

localize6.0ms (0.2%)

series1.0ms (0%)

rewrite54.0ms (1.5%)

simplify67.0ms (1.9%)

eval67.0ms (1.9%)

prune27.0ms (0.8%)

regimes30.0ms (0.8%)

regimes22.0ms (0.6%)

regimes16.0ms (0.5%)

regimes19.0ms (0.5%)

regimes27.0ms (0.8%)

bsearch0.0ms (0%)

regimes9.0ms (0.2%)

regimes11.0ms (0.3%)

regimes4.0ms (0.1%)

simplify3.0ms (0.1%)

end62.0ms (1.7%)

Profiling