Details

analyze488.0ms (19.7%)

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 (68.1%)

Results

894.0ms	2803×	body	1024	valid
293.0ms	1339×	body	512	valid
256.0ms	3140×	body	128	valid
122.0ms	314×	body	2048	valid
98.0ms	660×	body	256	valid
0.0ms	2×	body	128	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

0.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.3b	(/.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
✓	0.3b	(/.f64 (exp.f64 x) (expm1.f64 x))

series9.0ms (0.3%)

Counts

1 → 12

Calls

1 calls:

9.0ms

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

rewrite4.0ms (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:

3.0ms

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

simplify75.0ms (3%)

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

prune18.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

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

Error

0.2b

Counts

41 → 3

Alt Table

Status	Error	Program
	25.0b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
▶	20.8b	(+.f64 1/2 (/.f64 1 x))
✓	0.3b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 471 to 168 computations (64.3% saved)

localize3.0ms (0.1%)

prune3.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

0.2b

Counts

3 → 3

Alt Table

Status	Error	Program
▶	25.0b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
✓	20.8b	(+.f64 1/2 (/.f64 1 x))
✓	0.3b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 28 to 21 computations (25% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.3b	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	1.8b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))

series9.0ms (0.4%)

Counts

1 → 12

Calls

1 calls:

9.0ms

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

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 11

Calls

1 calls:

0.0ms

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

simplify77.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

1212×	`fma-neg_binary64`
773×	`fma-def_binary64`
449×	`distribute-rgt-in_binary64`
424×	`cancel-sign-sub-inv_binary64`
327×	`distribute-lft-in_binary64`

Counts

23 → 26

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	32	242
1	58	221
2	121	217
3	273	217
4	644	217
5	1382	217
6	2395	217
7	4117	217
8	4653	217
9	5002	217

prune21.0ms (0.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	66	3	69

Error

0.2b

Counts

69 → 3

Alt Table

Status	Error	Program
✓	25.0b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
✓	20.8b	(+.f64 1/2 (/.f64 1 x))
✓	0.3b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 805 to 307 computations (61.9% saved)

regimes19.0ms (0.8%)

Accuracy

Total 0.1b remaining (19.6%)

Threshold costs 0.1b (19.6%)

Counts

6 → 1

Compiler

Compiled 143 to 100 computations (30.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	5	8

end47.0ms (1.9%)

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

Details

analyze488.0ms (19.7%)

sample1.7s (68.1%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series9.0ms (0.3%)

rewrite4.0ms (0.2%)

simplify75.0ms (3%)

prune18.0ms (0.7%)

localize3.0ms (0.1%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series9.0ms (0.4%)

rewrite1.0ms (0%)

simplify77.0ms (3.1%)

prune21.0ms (0.8%)

regimes19.0ms (0.8%)

simplify2.0ms (0.1%)

end47.0ms (1.9%)

Profiling