Details

analyze490.0ms (17.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
50%	50%	0%	5
53.1%	46.9%	0%	6
54.7%	45.3%	0%	7
55.4%	44.5%	0%	8
55.8%	44.1%	0%	9
56%	43.9%	0%	10
56.1%	43.8%	0%	11
56.2%	43.8%	0%	12
56.2%	43.8%	0%	13
56.2%	43.7%	0%	14

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample1.4s (50.3%)

Results

630.0ms	2651×	body	1024	valid
210.0ms	1370×	body	512	valid
196.0ms	3296×	body	128	valid
151.0ms	2605×	body	128	invalid
80.0ms	664×	body	256	valid
75.0ms	275×	body	2048	valid

Compiler

Compiled 26 to 17 computations (34.6% saved)

simplify7.0ms (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

0.8b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 25 to 15 computations (40% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.7b	(/.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))

simplify70.0ms (2.6%)

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 (0.6%)

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

0.6b

Counts

41 → 3

Alt Table

Status	Error	Program
	23.9b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
▶	23.1b	(+.f64 1/2 (/.f64 1 x))
✓	0.8b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 471 to 168 computations (64.3% saved)

localize5.0ms (0.2%)

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

0.6b

Counts

3 → 3

Alt Table

Status	Error	Program
▶	23.9b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
✓	23.1b	(+.f64 1/2 (/.f64 1 x))
✓	0.8b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 28 to 21 computations (25% saved)

localize13.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (/.f64 (exp.f64 x) (expm1.f64 x)))
	0.7b	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	1.7b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))

series414.0ms (15.1%)

Counts

2 → 24

Calls

2 calls:

405.0ms	(log1p.f64 (/.f64 (exp.f64 x) (expm1.f64 x)))
9.0ms	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

1.0ms	(log1p.f64 (/.f64 (exp.f64 x) (expm1.f64 x)))
1.0ms	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))

simplify164.0ms (6%)

Algorithm

1×	egg-herbie

Rules

685×	`fma-neg_binary64`
536×	`cancel-sign-sub-inv_binary64`
419×	`fma-def_binary64`
412×	`distribute-rgt-neg-in_binary64`
331×	`sub-neg_binary64`

Counts

46 → 48

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	528
1	101	479
2	226	473
3	532	472
4	1574	472
5	3143	472
6	4718	472
7	4961	472
8	4887	472

prune54.0ms (2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	88	3	91

Error

0.6b

Counts

91 → 3

Alt Table

Status	Error	Program
✓	23.9b	(expm1.f64 (log1p.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
✓	23.1b	(+.f64 1/2 (/.f64 1 x))
✓	0.8b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 1044 to 399 computations (61.8% saved)

regimes38.0ms (1.4%)

Accuracy

Total 0.1b remaining (19.9%)

Threshold costs 0.1b (19.9%)

Counts

6 → 1

Compiler

Compiled 143 to 100 computations (30.1% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	5	8

end65.0ms (2.4%)

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

Details

analyze490.0ms (17.8%)

sample1.4s (50.3%)

simplify7.0ms (0.2%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series9.0ms (0.3%)

rewrite4.0ms (0.2%)

simplify70.0ms (2.6%)

prune17.0ms (0.6%)

localize5.0ms (0.2%)

prune3.0ms (0.1%)

localize13.0ms (0.5%)

series414.0ms (15.1%)

rewrite3.0ms (0.1%)

simplify164.0ms (6%)

prune54.0ms (2%)

regimes38.0ms (1.4%)

simplify4.0ms (0.1%)

end65.0ms (2.4%)

Profiling