Details

analyze497.0ms (18.9%)

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
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample1.7s (66.1%)

Results

926.0ms	2800×	body	1024	valid
300.0ms	1358×	body	512	valid
281.0ms	3193×	body	128	valid
109.0ms	653×	body	256	valid
98.0ms	252×	body	2048	valid
1.0ms	2×	body	2048	invalid
0.0ms	1×	body	128	invalid

Compiler

Compiled 26 to 17 computations (34.6% saved)

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	12	8
2	13	8
3	11	8

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 25 to 15 computations (40% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series12.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

9.0ms	(/.f64 (exp.f64 x) (expm1.f64 x))
3.0ms	(expm1.f64 x)

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 40

Calls

2 calls:

3.0ms	(/.f64 (exp.f64 x) (expm1.f64 x))
0.0ms	(expm1.f64 x)

simplify77.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

942×	`fma-neg_binary64`
666×	`times-frac_binary64`
570×	`fma-def_binary64`
504×	`cancel-sign-sub-inv_binary64`
262×	`associate-l_binary64`

Counts

64 → 59

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	688
1	165	643
2	385	641
3	904	635
4	2629	635
5	4940	635
6	5241	635

prune29.0ms (1.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	58	2	60

Error

Counts

60 → 2

Alt Table

Status	Error	Program
▶	21.2b	(+.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 (pow.f64 x 3) -1/720 1/2)))
✓	0.0b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 659 to 252 computations (61.8% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series9.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(fma.f64 (pow.f64 x 3) -1/720 1/2)
3.0ms	(fma.f64 x 1/12 (fma.f64 (pow.f64 x 3) -1/720 1/2))
3.0ms	(+.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 (pow.f64 x 3) -1/720 1/2)))

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`fma-def_binary64`
13×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`

Counts

3 → 49

Calls

3 calls:

6.0ms	(+.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 (pow.f64 x 3) -1/720 1/2)))
0.0ms	(fma.f64 (pow.f64 x 3) -1/720 1/2)
0.0ms	(fma.f64 x 1/12 (fma.f64 (pow.f64 x 3) -1/720 1/2))

simplify91.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

424×	`times-frac_binary64`
415×	`sub-neg_binary64`
402×	`exp-prod_binary64`
311×	`cancel-sign-sub-inv_binary64`
287×	`*-commutative_binary64`

Counts

85 → 82

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	1121
1	149	977
2	368	977
3	1874	975
4	3216	975
5	4923	975
6	5036	975

prune55.0ms (2.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	82	2	84

Error

Counts

84 → 2

Alt Table

Status	Error	Program
✓	21.2b	(+.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 (pow.f64 x 3) -1/720 1/2)))
✓	0.0b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 1573 to 1235 computations (21.5% saved)

regimes41.0ms (1.6%)

Accuracy

Total 0.0b remaining (3.9%)

Threshold costs 0.0b (3.9%)

Counts

18 → 1

Compiler

Compiled 521 to 373 computations (28.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	5	8

end43.0ms (1.6%)

Compiler: Compiled 32 to 23 computations (28.1% saved)

Details

analyze497.0ms (18.9%)

sample1.7s (66.1%)

simplify7.0ms (0.3%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series12.0ms (0.5%)

rewrite5.0ms (0.2%)

simplify77.0ms (2.9%)

prune29.0ms (1.1%)

localize9.0ms (0.3%)

series9.0ms (0.3%)

rewrite9.0ms (0.3%)

simplify91.0ms (3.5%)

prune55.0ms (2.1%)

regimes41.0ms (1.6%)

simplify3.0ms (0.1%)

end43.0ms (1.6%)

Profiling