Details

analyze272.0ms (5.9%)

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)

sample1.6s (34.5%)

Results

858.0ms	2671×	body	1024	valid
326.0ms	3958×	body	256	valid
302.0ms	1358×	body	512	valid
91.0ms	269×	body	2048	valid
0.0ms	5×	body	256	invalid
0.0ms	1×	body	2048	invalid

preprocess19.0ms (0.4%)

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 (0.1%)

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

0.8b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.8b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.7b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 11 to 4 computations (63.6% saved)

series2.0ms (0%)

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))

rewrite52.0ms (1.1%)

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

simplify177.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

1274×	`sqr-pow_binary64`
666×	`pow-sqr_binary64`
529×	`cube-prod_binary64`
470×	`fabs-mul_binary64`
446×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	104
1	48	104
2	94	104
3	213	104
4	327	104
5	572	104
6	1504	104
7	2330	104
8	2416	104
9	2549	104
10	2707	104
11	2961	104
12	3283	104
13	3707	104
14	4207	104
15	4809	104
16	5533	104
17	5856	104
18	6138	104
19	6358	104
20	6534	104
21	6616	104
22	7556	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 1/2 (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x))))
(+.f64 1/2 (fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) 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)))
(/.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 160 computations (57.8% saved)

prune10.0ms (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

0.6b

Counts

40 → 6

Alt Table

Click to see full alt table

Status	Error	Program
▶	20.9b	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
▶	20.6b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
▶	0.8b	(*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))
▶	20.6b	(+.f64 (/.f64 1 x) 1/2)
▶	20.5b	(/.f64 1 x)
✓	0.8b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 94 to 74 computations (21.3% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (expm1.f64 x))
✓	0.7b	(*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))

Compiler

Compiled 18 to 9 computations (50% saved)

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite51.0ms (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 (/.f64 1 (expm1.f64 x)) (exp.f64 x))
(/.f64 1 (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 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 expm1.f64 (log1p.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))))) (#(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 exp.f64 (-.f64 x (log.f64 (expm1.f64 x))))))))
((#(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 expm1.f64 (log1p.f64 (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (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 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 expm1.f64 (log1p.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))))) (#(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 exp.f64 (-.f64 x (log.f64 (expm1.f64 x))))))))

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

simplify122.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

533×	`times-frac_binary64`
512×	`fma-neg_binary64`
410×	`distribute-rgt-neg-in_binary64`
385×	`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	307	192
4	519	192
5	1085	192
6	2168	192
7	3978	192
8	4906	192
9	5707	192
10	6110	192
11	7106	192

Stop Event

1×	node limit

Counts

65 → 57

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))
(/.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))

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

localize3.0ms (0.1%)

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

localize5.0ms (0.1%)

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

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	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)

Compiler

Compiled 27 to 20 computations (25.9% saved)

series4.0ms (0.1%)

Counts

3 → 19

Calls

9 calls:

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

rewrite80.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

936×	`prod-diff_binary64`
625×	`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	2715	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 (*.f64 1/144 (*.f64 x x)) 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 (pow.f64 (*.f64 1/12 x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/144 (*.f64 x x)))))) (#(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 (pow.f64 (*.f64 1/12 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/12 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.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))))))

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

simplify11.0ms (0.2%)

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))

localize24.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 56 to 43 computations (23.2% saved)

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)))

rewrite82.0ms (1.8%)

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	3506	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

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 -1/720 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/720) (pow.f64 x 3))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/720) (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/720) (pow.f64 x 3)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/720) (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 -1/720 (pow.f64 x 3)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 -1/720 (pow.f64 x 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 6) 1/518400) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (cbrt.f64 -1/720)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 -1/720) (pow.f64 x 3/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 9) -1/373248000) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 6) 1/518400))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 -1/720) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 -1/720 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 9) -1/373248000))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 -1/720 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 -1/720 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 3 (log.f64 x) (log.f64 -1/720)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 3 (log.f64 x) (log.f64 -1/720)) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (pow.f64 x 6) 1/518400) (-.f64 (*.f64 -1/720 (pow.f64 x 3)) (fma.f64 x 1/12 (/.f64 1 x)))) (/.f64 (pow.f64 (fma.f64 x 1/12 (/.f64 1 x)) 2) (-.f64 (*.f64 -1/720 (pow.f64 x 3)) (fma.f64 x 1/12 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x)))) (pow.f64 (cbrt.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x)))) 2) (cbrt.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x)))) (sqrt.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (pow.f64 x 9) -1/373248000 (pow.f64 (fma.f64 x 1/12 (/.f64 1 x)) 3)) (/.f64 1 (fma.f64 (fma.f64 x 1/12 (/.f64 1 x)) (-.f64 (fma.f64 x 1/12 (/.f64 1 x)) (*.f64 -1/720 (pow.f64 x 3))) (*.f64 (pow.f64 x 6) 1/518400))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (pow.f64 x 6) 1/518400) (pow.f64 (fma.f64 x 1/12 (/.f64 1 x)) 2)) (/.f64 1 (-.f64 (*.f64 -1/720 (pow.f64 x 3)) (fma.f64 x 1/12 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (fma.f64 x 1/12 (/.f64 1 x)) (-.f64 (fma.f64 x 1/12 (/.f64 1 x)) (*.f64 -1/720 (pow.f64 x 3))) (*.f64 (pow.f64 x 6) 1/518400)) (fma.f64 (pow.f64 x 9) -1/373248000 (pow.f64 (fma.f64 x 1/12 (/.f64 1 x)) 3))))))) (#(struct:change 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simplify183.0ms (4%)

Algorithm

1×	egg-herbie

Rules

1274×	`sqr-pow_binary64`
666×	`pow-sqr_binary64`
529×	`cube-prod_binary64`
472×	`fabs-mul_binary64`
445×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	138
1	39	138
2	64	138
3	126	138
4	199	138
5	424	138
6	1345	138
7	2090	138
8	2177	138
9	2310	138
10	2468	138
11	2713	138
12	3035	138
13	3458	138
14	3959	138
15	4558	138
16	5278	138
17	5599	138
18	5885	138
19	6109	138
20	6289	138
21	6371	138
22	7311	138

Stop Event

1×	node limit

Counts

118 → 115

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

eval326.0ms (7.1%)

Compiler: Compiled 7191 to 5519 computations (23.3% saved)

prune102.0ms (2.2%)

Pruning

9 alts after pruning (3 fresh and 6 done)

	Pruned	Kept	Total
New	418	3	421
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	418	9	427

Error

0.6b

Counts

427 → 9

Alt Table

Click to see full alt table

Status	Error	Program
✓	20.9b	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
▶	1.4b	(*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x))
✓	20.6b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
✓	0.8b	(*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))
✓	20.6b	(+.f64 (/.f64 1 x) 1/2)
✓	20.5b	(/.f64 1 x)
✓	0.8b	(/.f64 (exp.f64 x) (expm1.f64 x))
▶	43.2b	(+.f64 1/2 (/.f64 (-.f64 (pow.f64 x -2) (.f64 1/144 (.f64 x x))) (-.f64 (/.f64 1 x) (*.f64 1/12 x))))
▶	1.1b	(.f64 (-.f64 (+.f64 (.f64 1/12 x) (/.f64 1 x)) 1/2) (exp.f64 x))

Compiler

Compiled 92 to 71 computations (22.8% saved)

localize34.0ms (0.7%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 41 to 29 computations (29.3% saved)

series5.0ms (0.1%)

Counts

2 → 22

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(.f64 (-.f64 (+.f64 (.f64 1/12 x) (/.f64 1 x)) 1/2) (exp.f64 x))
1.0ms	x	@	inf	(.f64 (-.f64 (+.f64 (.f64 1/12 x) (/.f64 1 x)) 1/2) (exp.f64 x))
1.0ms	x	@	0	(.f64 (-.f64 (+.f64 (.f64 1/12 x) (/.f64 1 x)) 1/2) (exp.f64 x))
1.0ms	x	@	inf	(-.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x)) 1/2)
0.0ms	x	@	0	(-.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x)) 1/2)

rewrite112.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	242	27
2	3175	27

Stop Event

1×	node limit

Counts

2 → 113

Calls

Call 1

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

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 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 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 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))))) (#(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 +.f64 (*.f64 1/12 x) (+.f64 (/.f64 1 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/12 x) (*.f64 (+.f64 (/.f64 1 x) -1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1 x) (fma.f64 1/12 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1/12 x (/.f64 1 x)) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (+.f64 (/.f64 1 x) (fma.f64 1/12 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1/2 (fma.f64 1/12 x (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (/.f64 1 x) -1/2) (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x -1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x -1/2))))) (log.f64 (sqrt.f64 (exp.f64 (+.f64 (/.f64 1 x) 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(#(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 (+.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)) (+.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 3) -1/8)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 x 1/2)) (+.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2) -1/4)) -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 (+.f64 1 (expm1.f64 (*.f64 1/12 x))) (exp.f64 (+.f64 (/.f64 1 x) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (+.f64 (/.f64 1 x) -1/2)) (pow.f64 (exp.f64 x) 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (+.f64 (/.f64 1 x) -1/2)) (+.f64 1 (expm1.f64 (*.f64 1/12 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 expm1.f64 (log1p.f64 (+.f64 (/.f64 1 x) (fma.f64 1/12 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 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))))) (#(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 1/12 x (*.f64 (+.f64 (/.f64 1 x) -1/2) 1))))) (#(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 x 1/12 (*.f64 (+.f64 (/.f64 1 x) -1/2) 1))))) (#(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 (*.f64 1/12 x) 1 (*.f64 (+.f64 (/.f64 1 x) -1/2) 1))))) (#(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 1/12 x) (*.f64 (+.f64 (/.f64 1 x) -1/2) 1))))) (#(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 (+.f64 (/.f64 1 x) -1/2) (*.f64 1/12 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 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) 1/12) (*.f64 (+.f64 (/.f64 1 x) -1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x))) (pow.f64 (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x))) 2) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.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)) (pow.f64 (cbrt.f64 (*.f64 1/12 x)) 2) (+.f64 (/.f64 1 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 1/12 x)) (pow.f64 (cbrt.f64 (*.f64 1/12 x)) 2) (*.f64 (+.f64 (/.f64 1 x) -1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.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 (cbrt.f64 (*.f64 1/12 x)) 2) (cbrt.f64 (*.f64 1/12 x)) (*.f64 (+.f64 (/.f64 1 x) -1/2) 1))))) (#(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 x) (*.f64 (sqrt.f64 x) 1/12) (*.f64 (+.f64 (/.f64 1 x) -1/2) 1))))) (#(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 (sqrt.f64 (*.f64 1/12 x)) (sqrt.f64 (*.f64 1/12 x)) (*.f64 (+.f64 (/.f64 1 x) -1/2) 1))))) (#(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 (*.f64 1/144 (*.f64 x x)) (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 (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) -1/2)) 2) (cbrt.f64 (+.f64 (/.f64 1 x) -1/2)) (*.f64 1/12 x))))) (#(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)) (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 1 (cbrt.f64 x)) (fma.f64 1/12 x -1/2))))) (#(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 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (*.f64 (+.f64 (/.f64 1 x) -1/2) 1))))) (#(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 fma.f64 (*.f64 1/12 (sqrt.f64 x)) (sqrt.f64 x) (*.f64 (+.f64 (/.f64 1 x) -1/2) 1))))))

simplify89.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

886×	`fma-def_binary64`
669×	`fma-neg_binary64`
515×	`associate-l_binary64`
515×	`times-frac_binary64`
394×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	255
1	66	253
2	123	223
3	223	215
4	358	215
5	768	215
6	2156	215
7	4150	215
8	7852	215

Stop Event

1×	node limit

Counts

135 → 134

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

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

localize19.0ms (0.4%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 22 to 15 computations (31.8% saved)

series4.0ms (0.1%)

Counts

2 → 15

Calls

6 calls:

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

rewrite59.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

806×	`pow1_binary64`
751×	`add-log-exp_binary64`
751×	`log1p-expm1-u_binary64`
751×	`expm1-log1p-u_binary64`
737×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	168	19
2	2044	19

Stop Event

1×	node limit

Counts

2 → 49

Calls

Call 1

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

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 (exp.f64 x) (/.f64 1 x)) (*.f64 (exp.f64 x) -1/2))))) (#(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 (pow.f64 x -3) -1/8) (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 (pow.f64 x -3) -1/8)) (+.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 expm1.f64 (log1p.f64 (*.f64 (+.f64 (/.f64 1 x) -1/2) (exp.f64 x))))))) (#(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 exp.f64 (+.f64 x (log.f64 (+.f64 (/.f64 1 x) -1/2))))))))

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

simplify84.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	22	148
1	49	136
2	101	136
3	253	136
4	613	133
5	1996	133
6	4431	133
7	6739	133
8	7171	133
9	7787	133

Stop Event

1×	node limit

Counts

64 → 60

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

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 (*.f64 x x) (fma.f64 x -1/24 -1/12) 1/2))
(fma.f64 (*.f64 x x) (fma.f64 x -1/24 -1/12) (+.f64 (/.f64 1 x) 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))
(/.f64 1 x)
-1/2
-1/2

localize30.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 x) (*.f64 1/12 x))
✓	0.2b	(.f64 1/144 (.f64 x x))
	0.3b	(*.f64 1/12 x)
✓	29.1b	(/.f64 (-.f64 (pow.f64 x -2) (.f64 1/144 (.f64 x x))) (-.f64 (/.f64 1 x) (*.f64 1/12 x)))

Compiler

Compiled 76 to 49 computations (35.5% saved)

series6.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(/.f64 (-.f64 (pow.f64 x -2) (.f64 1/144 (.f64 x x))) (-.f64 (/.f64 1 x) (*.f64 1/12 x)))
1.0ms	x	@	0	(/.f64 (-.f64 (pow.f64 x -2) (.f64 1/144 (.f64 x x))) (-.f64 (/.f64 1 x) (*.f64 1/12 x)))
1.0ms	x	@	inf	(/.f64 (-.f64 (pow.f64 x -2) (.f64 1/144 (.f64 x x))) (-.f64 (/.f64 1 x) (*.f64 1/12 x)))
0.0ms	x	@	inf	(.f64 1/144 (.f64 x x))
0.0ms	x	@	0	(.f64 1/144 (.f64 x x))

rewrite94.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

727×	`log-prod_binary64`
533×	`fma-def_binary64`
259×	`fma-neg_binary64`
253×	`expm1-udef_binary64`
253×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	42
1	326	27
2	4576	23

Stop Event

1×	node limit

Counts

3 → 205

Calls

Call 1

Inputs
(/.f64 (-.f64 (pow.f64 x -2) (.f64 1/144 (.f64 x x))) (-.f64 (/.f64 1 x) (*.f64 1/12 x)))
(.f64 1/144 (.f64 x x))
(-.f64 (/.f64 1 x) (*.f64 1/12 x))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1 x) (*.f64 x 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x 1/12) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (fma.f64 x 1/12 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 x -2) (fma.f64 x -1/12 (/.f64 1 x))) (neg.f64 (/.f64 1/144 (/.f64 (fma.f64 x -1/12 (/.f64 1 x)) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (fma.f64 x 1/12 (/.f64 1 x)))) (cbrt.f64 (exp.f64 (fma.f64 x 1/12 (/.f64 1 x)))))) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 x 1/12 (/.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 x 1/12 (/.f64 1 x))))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 x 1/12 (/.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 x -2) (fma.f64 x -1/12 (/.f64 1 x))) (/.f64 1/144 (/.f64 (fma.f64 x -1/12 (/.f64 1 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x 1/12 (/.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2)) (/.f64 1 (fma.f64 x -1/12 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x 1/12 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x 1/12 (/.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x 1/12 (/.f64 1 x))) (pow.f64 (cbrt.f64 (fma.f64 x 1/12 (/.f64 1 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x 1/12 (/.f64 1 x))) 2) (cbrt.f64 (fma.f64 x 1/12 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2))) 2) (*.f64 (cbrt.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2))) (/.f64 1 (fma.f64 x -1/12 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x 1/12 (/.f64 1 x))) (sqrt.f64 (fma.f64 x 1/12 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2))) (*.f64 (sqrt.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2))) (/.f64 1 (fma.f64 x -1/12 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2))) (/.f64 1 (neg.f64 (fma.f64 x -1/12 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 x -1/12 (/.f64 1 x))) (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2))) 2) 1) (/.f64 (cbrt.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2))) (fma.f64 x -1/12 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2))) 1) (/.f64 (sqrt.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2))) (fma.f64 x -1/12 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 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egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x -1/12 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x -1/12 (/.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 x 1/12)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (+.f64 1 (expm1.f64 (/.f64 1 x))) (+.f64 1 (expm1.f64 (*.f64 x 1/12)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (/.f64 1 x))) (exp.f64 (*.f64 x -1/12))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (/.f64 1 x)) (/.f64 1 (pow.f64 (exp.f64 1/12) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (/.f64 1 x))) (/.f64 1 (pow.f64 (exp.f64 1/12) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (*.f64 x -1/12)) (exp.f64 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (/.f64 1 (pow.f64 (exp.f64 1/12) x)) (exp.f64 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (*.f64 x -1/12)) (+.f64 1 (expm1.f64 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (/.f64 1 (pow.f64 (exp.f64 1/12) x)) (+.f64 1 (expm1.f64 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x -1/12 (/.f64 1 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x -1/12 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x -1/12 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x -1/12 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 x -1/12 (/.f64 1 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x -1/12 (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 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x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 x -1/12 (/.f64 1 x)) (fma.f64 -1/12 x (*.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x -1/12) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) 1 (*.f64 x -1/12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) 1 (*.f64 (*.f64 x -1/12) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/12 (neg.f64 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 x -1/12 (/.f64 1 x)) 1 (fma.f64 (*.f64 x -1/12) 1 (*.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 x -1/12 (/.f64 1 x)) 1 (fma.f64 (neg.f64 (cbrt.f64 (*.f64 x 1/12))) (cbrt.f64 (*.f64 x (*.f64 x 1/144))) (*.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 x -1/12 (/.f64 1 x)) 1 (fma.f64 -1/12 x (*.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 x -1/12 (/.f64 1 x))) (pow.f64 (cbrt.f64 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x))) (fma.f64 (*.f64 x -1/12) 1 (*.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 x -1/12 (/.f64 1 x))) (sqrt.f64 (fma.f64 x -1/12 (/.f64 1 x))) (fma.f64 (neg.f64 (cbrt.f64 (*.f64 x 1/12))) (cbrt.f64 (*.f64 x (*.f64 x 1/144))) (*.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 x -1/12 (/.f64 1 x))) (sqrt.f64 (fma.f64 x -1/12 (/.f64 1 x))) (fma.f64 -1/12 x (*.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) (*.f64 x -1/12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) (*.f64 (*.f64 x -1/12) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (*.f64 x 1/12) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (/.f64 1 (neg.f64 x)) (*.f64 x -1/12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (/.f64 1 (neg.f64 x)) (*.f64 (*.f64 x -1/12) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 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(2) ((x fma.f64 (sqrt.f64 (*.f64 x -1/12)) (sqrt.f64 (*.f64 x -1/12)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (cbrt.f64 (pow.f64 x -4))) (sqrt.f64 (cbrt.f64 (pow.f64 x -2))) (*.f64 x -1/12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (cbrt.f64 (pow.f64 x -4))) (sqrt.f64 (cbrt.f64 (pow.f64 x -2))) (*.f64 (*.f64 x -1/12) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (cbrt.f64 (*.f64 x (*.f64 x 1/144)))) (cbrt.f64 (*.f64 x 1/12)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (sqrt.f64 (*.f64 x 1/12))) (sqrt.f64 (*.f64 x 1/12)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 2) -1) (pow.f64 (cbrt.f64 x) -1) (*.f64 x -1/12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 2) -1) (pow.f64 (cbrt.f64 x) -1) (*.f64 (*.f64 x -1/12) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (sqrt.f64 x) -1) (pow.f64 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(sqrt.f64 x) (/.f64 1 x))))))

simplify140.0ms (3%)

Algorithm

1×	egg-herbie

Rules

778×	`sqr-pow_binary64`
574×	`associate-l_binary64`
542×	`associate-/l/_binary64`
439×	`cube-prod_binary64`
434×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	252
1	27	252
2	38	252
3	69	252
4	161	252
5	477	252
6	1695	252
7	2808	252
8	3727	252
9	3941	252
10	4166	252
11	4472	252
12	4897	252
13	5476	252
14	6042	252
15	6724	252
16	7565	252
17	7959	252

Stop Event

1×	node limit

Counts

241 → 215

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 (*.f64 1/12 x) (/.f64 1 x))
(+.f64 (*.f64 1/12 x) (/.f64 1 x))
(+.f64 (*.f64 1/12 x) (/.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 1/144 (pow.f64 x 2))
(*.f64 1/144 (pow.f64 x 2))
(*.f64 1/144 (pow.f64 x 2))
(*.f64 1/144 (pow.f64 x 2))
(*.f64 1/144 (pow.f64 x 2))
(*.f64 1/144 (pow.f64 x 2))
(*.f64 1/144 (pow.f64 x 2))
(*.f64 1/144 (pow.f64 x 2))
(*.f64 1/144 (pow.f64 x 2))
(*.f64 1/144 (pow.f64 x 2))
(*.f64 1/144 (pow.f64 x 2))
(*.f64 1/144 (pow.f64 x 2))
(/.f64 1 x)
(+.f64 (*.f64 -1/12 x) (/.f64 1 x))
(+.f64 (*.f64 -1/12 x) (/.f64 1 x))
(+.f64 (*.f64 -1/12 x) (/.f64 1 x))
(*.f64 -1/12 x)
(+.f64 (*.f64 -1/12 x) (/.f64 1 x))
(+.f64 (*.f64 -1/12 x) (/.f64 1 x))
(+.f64 (*.f64 -1/12 x) (/.f64 1 x))
(*.f64 -1/12 x)
(+.f64 (*.f64 -1/12 x) (/.f64 1 x))
(+.f64 (*.f64 -1/12 x) (/.f64 1 x))
(+.f64 (*.f64 -1/12 x) (/.f64 1 x))

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 1 x))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.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 1/12 x)
(*.f64 x 1/12)
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(*.f64 1/12 x)
(*.f64 x 1/12)
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(/.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 1 x))
(fma.f64 -1/12 x (/.f64 1 x))
(fma.f64 x -1/12 (/.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 -1/12 x)
(*.f64 x -1/12)
(+.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 1 x))
(fma.f64 -1/12 x (/.f64 1 x))
(fma.f64 x -1/12 (/.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 -1/12 x)
(*.f64 x -1/12)
(+.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 1 x))
(fma.f64 -1/12 x (/.f64 1 x))
(fma.f64 x -1/12 (/.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))

eval208.0ms (4.5%)

Compiler: Compiled 9921 to 7064 computations (28.8% saved)

prune72.0ms (1.6%)

Pruning

10 alts after pruning (2 fresh and 8 done)

	Pruned	Kept	Total
New	509	2	511
Fresh	0	0	0
Picked	0	1	1
Done	1	7	8
Total	510	10	520

Error

0.6b

Counts

520 → 10

Alt Table

Click to see full alt table

Status	Error	Program
▶	42.3b	(.f64 (.f64 x 1/12) (exp.f64 x))
✓	0.8b	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	20.9b	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
✓	20.6b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
✓	0.8b	(*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))
✓	20.6b	(+.f64 (/.f64 1 x) 1/2)
▶	42.6b	(*.f64 -1/2 (exp.f64 x))
✓	20.5b	(/.f64 1 x)
✓	43.2b	(+.f64 1/2 (/.f64 (-.f64 (pow.f64 x -2) (.f64 1/144 (.f64 x x))) (-.f64 (/.f64 1 x) (*.f64 1/12 x))))
✓	1.1b	(.f64 (-.f64 (+.f64 (.f64 1/12 x) (/.f64 1 x)) 1/2) (exp.f64 x))

Compiler

Compiled 95 to 73 computations (23.2% saved)

localize4.0ms (0.1%)

Compiler: Compiled 9 to 5 computations (44.4% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 14 to 8 computations (42.9% saved)

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite46.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

535×	`pow1_binary64`
517×	`add-sqr-sqrt_binary64`
494×	`add-log-exp_binary64`
494×	`log1p-expm1-u_binary64`
494×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	118	13
2	1356	13

Stop Event

1×	node limit

Counts

2 → 22

Calls

Call 1

Inputs
(*.f64 x 1/12)
(.f64 (.f64 x 1/12) (exp.f64 x))

Outputs

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

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

simplify71.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1011×	`fma-def_binary64`
660×	`associate-/l/_binary64`
563×	`distribute-lft-out_binary64`
488×	`associate-/r/_binary64`
428×	`*-commutative_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	22	177
1	57	169
2	135	169
3	399	167
4	1395	163
5	3399	163
6	4164	163
7	4468	163
8	5119	163

Stop Event

1×	node limit

Counts

46 → 31

Calls

Call 1

Inputs
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(+.f64 (.f64 1/12 (pow.f64 x 2)) (.f64 1/12 x))
(+.f64 (.f64 1/12 (pow.f64 x 2)) (+.f64 (.f64 1/12 x) (*.f64 1/24 (pow.f64 x 3))))
(+.f64 (.f64 1/72 (pow.f64 x 4)) (+.f64 (.f64 1/12 (pow.f64 x 2)) (+.f64 (.f64 1/12 x) (.f64 1/24 (pow.f64 x 3)))))
(.f64 1/12 (.f64 (exp.f64 x) x))
(.f64 1/12 (.f64 (exp.f64 x) x))
(.f64 1/12 (.f64 (exp.f64 x) x))
(.f64 1/12 (.f64 (exp.f64 x) x))
(.f64 1/12 (.f64 (exp.f64 x) x))
(.f64 1/12 (.f64 (exp.f64 x) x))
(.f64 1/12 (.f64 (exp.f64 x) x))
(.f64 1/12 (.f64 (exp.f64 x) x))

Outputs
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(+.f64 (.f64 1/12 (pow.f64 x 2)) (.f64 1/12 x))
(.f64 1/12 (+.f64 (.f64 x x) x))
(*.f64 1/12 (fma.f64 x x x))
(+.f64 (.f64 1/12 (pow.f64 x 2)) (+.f64 (.f64 1/12 x) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 1/12 (.f64 x x) (fma.f64 1/12 x (.f64 1/24 (pow.f64 x 3))))
(fma.f64 1/12 (fma.f64 x x x) (*.f64 1/24 (pow.f64 x 3)))
(.f64 x (+.f64 1/12 (.f64 x (fma.f64 x 1/24 1/12))))
(*.f64 x (fma.f64 x (fma.f64 x 1/24 1/12) 1/12))
(+.f64 (.f64 1/72 (pow.f64 x 4)) (+.f64 (.f64 1/12 (pow.f64 x 2)) (+.f64 (.f64 1/12 x) (.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/72 (pow.f64 x 4) (fma.f64 1/12 (.f64 x x) (fma.f64 1/12 x (.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/72 (pow.f64 x 4) (fma.f64 1/12 (fma.f64 x x x) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 1/12 (fma.f64 x x x) (.f64 (pow.f64 x 3) (+.f64 1/24 (.f64 x 1/72))))
(fma.f64 (pow.f64 x 3) (fma.f64 x 1/72 1/24) (*.f64 1/12 (fma.f64 x x x)))
(.f64 1/12 (.f64 (exp.f64 x) x))
(.f64 1/12 (.f64 x (exp.f64 x)))
(.f64 (.f64 1/12 x) (exp.f64 x))
(.f64 1/12 (.f64 (exp.f64 x) x))
(.f64 1/12 (.f64 x (exp.f64 x)))
(.f64 (.f64 1/12 x) (exp.f64 x))
(.f64 1/12 (.f64 (exp.f64 x) x))
(.f64 1/12 (.f64 x (exp.f64 x)))
(.f64 (.f64 1/12 x) (exp.f64 x))
(.f64 1/12 (.f64 (exp.f64 x) x))
(.f64 1/12 (.f64 x (exp.f64 x)))
(.f64 (.f64 1/12 x) (exp.f64 x))
(.f64 1/12 (.f64 (exp.f64 x) x))
(.f64 1/12 (.f64 x (exp.f64 x)))
(.f64 (.f64 1/12 x) (exp.f64 x))
(.f64 1/12 (.f64 (exp.f64 x) x))
(.f64 1/12 (.f64 x (exp.f64 x)))
(.f64 (.f64 1/12 x) (exp.f64 x))
(.f64 1/12 (.f64 (exp.f64 x) x))
(.f64 1/12 (.f64 x (exp.f64 x)))
(.f64 (.f64 1/12 x) (exp.f64 x))
(.f64 1/12 (.f64 (exp.f64 x) x))
(.f64 1/12 (.f64 x (exp.f64 x)))
(.f64 (.f64 1/12 x) (exp.f64 x))

eval7.0ms (0.2%)

Compiler: Compiled 284 to 188 computations (33.8% saved)

prune16.0ms (0.3%)

Pruning

11 alts after pruning (1 fresh and 10 done)

	Pruned	Kept	Total
New	30	1	31
Fresh	0	0	0
Picked	0	1	1
Done	0	9	9
Total	30	11	41

Error

0.6b

Counts

41 → 11

Alt Table

Click to see full alt table

Status	Error	Program
	42.9b	(-.f64 (+.f64 1 (.f64 x (.f64 1/12 (exp.f64 x)))) 1)
✓	20.6b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
✓	42.3b	(.f64 (.f64 x 1/12) (exp.f64 x))
✓	0.8b	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	20.9b	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
✓	0.8b	(*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))
✓	20.6b	(+.f64 (/.f64 1 x) 1/2)
✓	42.6b	(*.f64 -1/2 (exp.f64 x))
✓	20.5b	(/.f64 1 x)
✓	43.2b	(+.f64 1/2 (/.f64 (-.f64 (pow.f64 x -2) (.f64 1/144 (.f64 x x))) (-.f64 (/.f64 1 x) (*.f64 1/12 x))))
✓	1.1b	(.f64 (-.f64 (+.f64 (.f64 1/12 x) (/.f64 1 x)) 1/2) (exp.f64 x))

Compiler

Compiled 106 to 82 computations (22.6% saved)

regimes42.0ms (0.9%)

Counts

13 → 1

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(*.f64 -1/2 (exp.f64 x))
(.f64 (.f64 x 1/12) (exp.f64 x))
(*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x))
(-.f64 (+.f64 1 (.f64 x (.f64 1/12 (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 1/2 (/.f64 (-.f64 (pow.f64 x -2) (.f64 1/144 (.f64 x x))) (-.f64 (/.f64 1 x) (*.f64 1/12 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 (/.f64 1 (expm1.f64 x)) (exp.f64 x))

Calls

4 calls:

15.0ms	x
9.0ms	(exp.f64 x)
5.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
5.0ms	(exp.f64 x)

Results

Error	Segments	Branch
0.8b	1	`x`
0.8b	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))`
0.8b	1	`(exp.f64 x)`
0.8b	1	`(exp.f64 x)`

Compiler

Compiled 127 to 84 computations (33.9% saved)

regimes26.0ms (0.6%)

Counts

11 → 1

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(*.f64 -1/2 (exp.f64 x))
(.f64 (.f64 x 1/12) (exp.f64 x))
(*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x))
(-.f64 (+.f64 1 (.f64 x (.f64 1/12 (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 1/2 (/.f64 (-.f64 (pow.f64 x -2) (.f64 1/144 (.f64 x x))) (-.f64 (/.f64 1 x) (*.f64 1/12 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))

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

Calls

2 calls:

14.0ms	x
6.0ms	(exp.f64 x)

Results

Error	Segments	Branch
0.8b	1	`x`
0.8b	1	`(exp.f64 x)`

Compiler

Compiled 102 to 71 computations (30.4% saved)

regimes24.0ms (0.5%)

Counts

10 → 1

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(*.f64 -1/2 (exp.f64 x))
(.f64 (.f64 x 1/12) (exp.f64 x))
(*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x))
(-.f64 (+.f64 1 (.f64 x (.f64 1/12 (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 1/2 (/.f64 (-.f64 (pow.f64 x -2) (.f64 1/144 (.f64 x x))) (-.f64 (/.f64 1 x) (*.f64 1/12 x))))

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

Calls

2 calls:

13.0ms	x
5.0ms	(exp.f64 x)

Results

Error	Segments	Branch
1.1b	1	`x`
1.1b	1	`(exp.f64 x)`

Compiler

Compiled 97 to 69 computations (28.9% saved)

regimes20.0ms (0.4%)

Counts

7 → 1

Calls

Call 1

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

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

Calls

2 calls:

11.0ms	x
4.0ms	(exp.f64 x)

Results

Error	Segments	Branch
1.4b	1	`x`
1.4b	1	`(exp.f64 x)`

Compiler

Compiled 51 to 35 computations (31.4% saved)

regimes29.0ms (0.6%)

Counts

5 → 2

Calls

Call 1

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

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

Calls

2 calls:

19.0ms	x
7.0ms	(exp.f64 x)

Results

Error	Segments	Branch
1.0b	2	`x`
1.0b	2	`(exp.f64 x)`

Compiler

Compiled 33 to 23 computations (30.3% saved)

bsearch33.0ms (0.7%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
32.0ms	-9.921221077946356	-0.034814003071015134

Compiler

Compiled 12 to 8 computations (33.3% saved)

regimes28.0ms (0.6%)

Counts

4 → 2

Calls

Call 1

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

2 calls:

19.0ms	x
7.0ms	(exp.f64 x)

Results

Error	Segments	Branch
1.0b	2	`x`
1.0b	2	`(exp.f64 x)`

Compiler

Compiled 27 to 20 computations (25.9% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	4.9121139409528924e-5	0.9657850326031281

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes10.0ms (0.2%)

Accuracy

Total -0.6b remaining (-3%)

Threshold costs -0.6b (-3%)

Counts

3 → 1

Calls

Call 1

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

Outputs
(/.f64 1 x)

Calls

1 calls:

8.0ms

Results

Error	Segments	Branch
20.5b	1	`x`

Compiler

Compiled 20 to 15 computations (25% saved)

simplify12.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
4×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	108
1	42	108
2	44	108

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))
(/.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))
(if (<=.f64 x -698143867964055/70368744177664) (.f64 (.f64 x 1/12) (exp.f64 x)) (+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x))))
(if (<=.f64 (exp.f64 x) 7378697629483821/147573952589676412928) (.f64 -1/2 (exp.f64 x)) (+.f64 1/2 (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(/.f64 1 x)

Outputs
(*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))
(/.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 1 x) (.f64 x 1/12)) -1/2))
(*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x))
(*.f64 (exp.f64 x) (+.f64 (/.f64 1 x) -1/2))
(if (<=.f64 x -698143867964055/70368744177664) (.f64 (.f64 x 1/12) (exp.f64 x)) (+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x))))
(if (<=.f64 x -698143867964055/70368744177664) (.f64 (exp.f64 x) (.f64 x 1/12)) (+.f64 (+.f64 (/.f64 1 x) (*.f64 x 1/12)) 1/2))
(if (<=.f64 (exp.f64 x) 7378697629483821/147573952589676412928) (.f64 -1/2 (exp.f64 x)) (+.f64 1/2 (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(if (<=.f64 (exp.f64 x) 7378697629483821/147573952589676412928) (.f64 (exp.f64 x) -1/2) (+.f64 (+.f64 (/.f64 1 x) (.f64 x 1/12)) 1/2))
(/.f64 1 x)

Compiler

Compiled 79 to 59 computations (25.3% saved)

soundness15.0ms (0.3%)

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

Compiler

Compiled 14 to 9 computations (35.7% saved)

end103.0ms (2.2%)

Compiler: Compiled 73 to 47 computations (35.6% saved)

Details

analyze272.0ms (5.9%)

sample1.6s (34.5%)

preprocess19.0ms (0.4%)

simplify6.0ms (0.1%)

eval1.0ms (0%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series2.0ms (0%)

rewrite52.0ms (1.1%)

simplify177.0ms (3.8%)

eval7.0ms (0.2%)

prune10.0ms (0.2%)

localize8.0ms (0.2%)

series3.0ms (0.1%)

rewrite51.0ms (1.1%)

simplify122.0ms (2.6%)

localize3.0ms (0.1%)

localize5.0ms (0.1%)

localize11.0ms (0.2%)

series4.0ms (0.1%)

rewrite80.0ms (1.7%)

simplify11.0ms (0.2%)

localize24.0ms (0.5%)

series3.0ms (0.1%)

rewrite82.0ms (1.8%)

simplify183.0ms (4%)

eval326.0ms (7.1%)

prune102.0ms (2.2%)

localize34.0ms (0.7%)

series5.0ms (0.1%)

rewrite112.0ms (2.4%)

simplify89.0ms (1.9%)

localize19.0ms (0.4%)

series4.0ms (0.1%)

rewrite59.0ms (1.3%)

simplify84.0ms (1.8%)

localize30.0ms (0.6%)

series6.0ms (0.1%)

rewrite94.0ms (2%)

simplify140.0ms (3%)

eval208.0ms (4.5%)

prune72.0ms (1.6%)

localize4.0ms (0.1%)

localize6.0ms (0.1%)

series3.0ms (0.1%)

rewrite46.0ms (1%)

simplify71.0ms (1.5%)

eval7.0ms (0.2%)

prune16.0ms (0.3%)

regimes42.0ms (0.9%)

regimes26.0ms (0.6%)

regimes24.0ms (0.5%)

regimes20.0ms (0.4%)

regimes29.0ms (0.6%)

bsearch33.0ms (0.7%)

regimes28.0ms (0.6%)

bsearch0.0ms (0%)

regimes10.0ms (0.2%)

simplify12.0ms (0.3%)

soundness15.0ms (0.3%)

end103.0ms (2.2%)

Profiling