Details

analyze477.0ms (19.3%)

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 (66.7%)

Results

887.0ms	2806×	body	1024	valid
287.0ms	1337×	body	512	valid
244.0ms	3147×	body	128	valid
104.0ms	283×	body	2048	valid
101.0ms	683×	body	256	valid
1.0ms	2×	body	2048	invalid

Compiler

Compiled 26 to 17 computations (34.6% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

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)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series8.0ms (0.3%)

Counts

1 → 12

Calls

1 calls:

8.0ms

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

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
3×	`associate-/r*_binary64`

Counts

1 → 29

Calls

1 calls:

4.0ms

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

simplify66.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

825×	`fma-def_binary64`
587×	`div-sub_binary64`
548×	`times-frac_binary64`
500×	`fma-neg_binary64`
317×	`distribute-rgt-in_binary64`

Counts

41 → 40

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	66	559
1	130	521
2	292	519
3	609	519
4	1403	519
5	4001	519
6	5294	519

prune17.0ms (0.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	39	1	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	39	2	41

Error

Counts

41 → 2

Alt Table

Status	Error	Program
▶	22.1b	(+.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 471 to 168 computations (64.3% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	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 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)

series8.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(fma.f64 (pow.f64 x 3) -1/720 1/2)
2.0ms	(fma.f64 x 1/12 (fma.f64 (pow.f64 x 3) -1/720 1/2))
2.0ms	(+.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 (pow.f64 x 3) -1/720 1/2)))

rewrite8.0ms (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:

5.0ms	(+.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))

simplify87.0ms (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

prune59.0ms (2.4%)

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
✓	22.1b	(+.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 1589 to 1247 computations (21.5% saved)

regimes25.0ms (1%)

Accuracy

Total 0.0b remaining (3.4%)

Threshold costs 0.0b (3.4%)

Counts

11 → 1

Compiler

Compiled 311 to 226 computations (27.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	10	11
2	9	11

end42.0ms (1.7%)

Compiler: Compiled 36 to 27 computations (25% saved)

Details

analyze477.0ms (19.3%)

sample1.7s (66.7%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series8.0ms (0.3%)

rewrite6.0ms (0.2%)

simplify66.0ms (2.7%)

prune17.0ms (0.7%)

localize8.0ms (0.3%)

series8.0ms (0.3%)

rewrite8.0ms (0.3%)

simplify87.0ms (3.5%)

prune59.0ms (2.4%)

regimes25.0ms (1%)

simplify2.0ms (0.1%)

end42.0ms (1.7%)

Profiling