Details

analyze2.3s (18.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	49.9%	50.1%	0
0%	49.9%	50.1%	1
0%	49.9%	50.1%	2
0%	49.9%	50.1%	3
0%	49.9%	50.1%	4
0%	49.9%	50.1%	5
0%	49.9%	50.1%	6
0%	49.9%	50.1%	7
0%	49.9%	50.1%	8
0.4%	49.5%	50.1%	9
0.4%	49.3%	50.3%	10
0.6%	48.9%	50.5%	11
1.1%	48.1%	50.9%	12
1.5%	47.3%	51.2%	13
1.7%	46.9%	51.5%	14

Compiler

Compiled 34 to 24 computations (29.4% saved)

sample8.3s (66.6%)

Symmetry

(sort a b)

Results

4.8s	4179×	body	2048	valid
1.8s	2453×	body	1024	valid
426.0ms	576×	body	1024	invalid
401.0ms	782×	body	512	valid
359.0ms	379×	body	2048	invalid
130.0ms	305×	body	512	invalid
93.0ms	557×	body	128	valid
80.0ms	267×	body	256	valid
47.0ms	278×	body	128	invalid
41.0ms	137×	body	256	invalid
30.0ms	18×	body	4096	valid

Compiler

Compiled 95 to 67 computations (29.5% saved)

simplify62.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

670×	`rules-20_binary64`
344×	`rules-14-rev_binary64`
338×	`rules-15-rev_binary64`
315×	`fma-def_binary64`
264×	`rules-4_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	28
1	49	28
2	104	28
3	276	28
4	773	28
5	2451	28
6	4913	28
7	4975	28

prune4.0ms (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

42.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	42.9b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

Compiler

Compiled 87 to 54 computations (37.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 eps (+.f64 a b))
✓	0.1b	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
✓	0.3b	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
✓	41.2b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

series335.0ms (2.7%)

Counts

4 → 132

Calls

4 calls:

270.0ms	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
31.0ms	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
27.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
6.0ms	(*.f64 eps (+.f64 a b))

rewrite116.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

840×	`prod-diff_binary64`
261×	`egg-rr`
142×	`add-sqr-sqrt_binary64`
134×	`log1p-expm1-u_binary64`
134×	`expm1-log1p-u_binary64`

Counts

4 → 261

Calls

4 calls:

111.0ms	(*.f64 eps (+.f64 a b))
110.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
110.0ms	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
110.0ms	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	61
1	323	61
2	4312	61
3	6071	61
0	0	0
1	0	0

simplify105.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

677×	`rules-21_binary64`
634×	`rules-20_binary64`
462×	`rules-14-rev_binary64`
135×	`fma-def_binary64`
128×	`rules-2-rev_binary64`

Counts

393 → 345

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	523	6353
1	2303	6055
2	4999	6055

prune198.0ms (1.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	343	2	345
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	343	3	346

Error

Counts

346 → 3

Alt Table

Status	Error	Program
✓	42.9b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
▶	4.7b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (+.f64 (/.f64 1 a) (.f64 1/12 (.f64 b (*.f64 eps eps))))))
	13.7b	(/.f64 (+.f64 a b) (*.f64 a b))

Compiler

Compiled 15261 to 4942 computations (67.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (+.f64 (/.f64 1 a) (.f64 1/12 (.f64 b (*.f64 eps eps))))))
✓	0.2b	(.f64 1/12 (.f64 b (*.f64 eps eps)))
✓	6.5b	(.f64 a (.f64 eps eps))
✓	6.5b	(.f64 b (.f64 eps eps))

series57.0ms (0.5%)

Counts

4 → 108

Calls

4 calls:

29.0ms	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (+.f64 (/.f64 1 a) (.f64 1/12 (.f64 b (*.f64 eps eps))))))
10.0ms	(.f64 1/12 (.f64 b (*.f64 eps eps)))
9.0ms	(.f64 a (.f64 eps eps))
8.0ms	(.f64 b (.f64 eps eps))

rewrite96.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

286×	`log1p-udef_binary64`
163×	`add-sqr-sqrt_binary64`
155×	`log1p-expm1-u_binary64`
155×	`expm1-log1p-u_binary64`
151×	`add-cbrt-cube_binary64`

Counts

4 → 138

Calls

4 calls:

93.0ms	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (+.f64 (/.f64 1 a) (.f64 1/12 (.f64 b (*.f64 eps eps))))))
93.0ms	(.f64 1/12 (.f64 b (*.f64 eps eps)))
93.0ms	(.f64 a (.f64 eps eps))
93.0ms	(.f64 b (.f64 eps eps))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	56
1	373	54
2	4947	54
3	5308	54
0	0	0
1	0	0

simplify99.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

803×	`rules-6_binary64`
592×	`rules-21_binary64`
395×	`rules-14-rev_binary64`
392×	`rules-20_binary64`
371×	`rules-6-rev_binary64`

Counts

246 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	26	1478
1	83	1301
2	344	1247
3	1445	1247
4	4723	1247
5	4873	1247
6	5007	1247

prune121.0ms (1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	162	3	165

Error

Counts

165 → 3

Alt Table

Status	Error	Program
✓	42.9b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
✓	4.7b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (+.f64 (/.f64 1 a) (.f64 1/12 (.f64 b (*.f64 eps eps))))))
▶	13.7b	(/.f64 (+.f64 a b) (*.f64 a b))

Compiler

Compiled 4272 to 2213 computations (48.2% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	12.7b	(/.f64 (+.f64 a b) (*.f64 a b))

series7.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

7.0ms

(/.f64 (+.f64 a b) (*.f64 a b))

rewrite50.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

695×	`log1p-expm1-u_binary64`
695×	`expm1-log1p-u_binary64`
615×	`prod-diff_binary64`
66×	`add-sqr-sqrt_binary64`
60×	`add-cbrt-cube_binary64`

Counts

1 → 29

Calls

1 calls:

49.0ms

(/.f64 (+.f64 a b) (*.f64 a b))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	145	10
2	1981	10
3	5648	10
0	0	0
1	0	0

simplify80.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

424×	`rules-20_binary64`
406×	`rules-9-rev_binary64`
354×	`rules-5-rev_binary64`
330×	`rules-10-rev_binary64`
281×	`rules-6_binary64`

Counts

53 → 33

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	204
1	13	204
2	21	204
3	44	204
4	122	204
5	444	204
6	1588	204
7	4585	204
8	4880	204
9	4968	204

prune19.0ms (0.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	33	0	33
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	33	3	36

Error

Counts

36 → 3

Alt Table

Status	Error	Program
✓	42.9b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
✓	4.7b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (+.f64 (/.f64 1 a) (.f64 1/12 (.f64 b (*.f64 eps eps))))))
✓	13.7b	(/.f64 (+.f64 a b) (*.f64 a b))

Compiler

Compiled 413 to 135 computations (67.3% saved)

regimes206.0ms (1.7%)

Accuracy

Total 0.5b remaining (92.8%)

Threshold costs 0.5b (92.8%)

Counts

59 → 3

Compiler

Compiled 4438 to 2820 computations (36.5% saved)

bsearch2.0ms (0%)

Compiler: Compiled 27 to 19 computations (29.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	144
1	46	144
2	45	144

end223.0ms (1.8%)

Compiler: Compiled 444 to 271 computations (39% saved)

Details

analyze2.3s (18.8%)

sample8.3s (66.6%)

simplify62.0ms (0.5%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series335.0ms (2.7%)

rewrite116.0ms (0.9%)

simplify105.0ms (0.8%)

prune198.0ms (1.6%)

localize12.0ms (0.1%)

series57.0ms (0.5%)

rewrite96.0ms (0.8%)

simplify99.0ms (0.8%)

prune121.0ms (1%)

localize4.0ms (0%)

series7.0ms (0.1%)

rewrite50.0ms (0.4%)

simplify80.0ms (0.6%)

prune19.0ms (0.2%)

regimes206.0ms (1.7%)

bsearch2.0ms (0%)

simplify3.0ms (0%)

end223.0ms (1.8%)

Profiling