Details

analyze2.6s (12.8%)

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)

sample219.0ms (1.1%)

Algorithm

1×

intervals

Results

102.0ms	128×	body	2048	valid
40.0ms	77×	body	1024	valid
9.0ms	8×	body	512	overflowed
9.0ms	307×	pre	128	true
8.0ms	22×	body	1024	overflowed
8.0ms	28×	body	512	valid
6.0ms	12×	body	2048	overflowed
2.0ms	1×	body	4096	valid
2.0ms	11×	body	256	valid
1.0ms	11×	body	128	valid
1.0ms	6×	body	128	overflowed
0.0ms	3×	body	256	overflowed

Compiler

Compiled 64 to 46 computations (28.1% saved)

simplify25.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

986×	`times-frac_binary64`
580×	`associate-/l*_binary64`
372×	`fma-def_binary64`
126×	`distribute-rgt-in_binary64`
122×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	28
1	47	28
2	108	28
3	254	28
4	897	28
5	5292	28

prune6.0ms (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

41.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	41.3b	(/.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	(expm1.f64 (*.f64 eps (+.f64 a b)))
✓	0.1b	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
✓	0.1b	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
✓	39.6b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

4.0ms	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
3.0ms	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
3.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
0.0ms	(expm1.f64 (*.f64 eps (+.f64 a b)))

series481.0ms (2.4%)

Counts

4 → 144

Calls

4 calls:

360.0ms	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
52.0ms	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
40.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
27.0ms	(expm1.f64 (*.f64 eps (+.f64 a b)))

simplify156.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

828×	`fma-def_binary64`
622×	`times-frac_binary64`
470×	`associate-/l*_binary64`
249×	`*-commutative_binary64`
191×	`+-commutative_binary64`

Counts

218 → 424

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	646	8872
1	2166	8105
2	5325	8105

prune177.0ms (0.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	419	5	424
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	420	5	425

Error

0.0b

Counts

425 → 5

Alt Table

Status	Error	Program
	41.3b	(/.f64 1 (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))))
	51.1b	(/.f64 (.f64 (sqrt.f64 eps) (.f64 (sqrt.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) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))
	52.5b	(/.f64 (.f64 (sqrt.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))) (sqrt.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))
	13.8b	(/.f64 (+.f64 a b) (*.f64 a b))

Compiler

Compiled 11398 to 3877 computations (66% saved)

localize11.0ms (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) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))
✓	0.0b	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
✓	7.3b	(.f64 b (.f64 eps eps))
✓	7.6b	(.f64 a (.f64 eps eps))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
14×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`

Counts

4 → 62

Calls

4 calls:

4.0ms	(.f64 a (.f64 eps eps))
4.0ms	(.f64 b (.f64 eps eps))
0.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
0.0ms	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))

series219.0ms (1.1%)

Counts

4 → 120

Calls

4 calls:

83.0ms	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))
66.0ms	(.f64 a (.f64 eps eps))
45.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
24.0ms	(.f64 b (.f64 eps eps))

simplify117.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

766×	`unswap-sqr_binary64`
610×	`fma-def_binary64`
470×	`associate-l_binary64`
333×	`associate-r_binary64`
295×	`associate-+r+_binary64`

Counts

182 → 349

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	103	2698
1	202	2339
2	549	2269
3	1651	2269
4	3788	2269
5	5058	2269

prune100.0ms (0.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	348	1	349
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	348	6	354

Error

Counts

354 → 6

Alt Table

Status	Error	Program
▶	6.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 eps (.f64 (+.f64 a b) (.f64 eps 1/12)) (+.f64 (/.f64 1 a) (/.f64 1 b)))) (cbrt.f64 (fma.f64 eps (.f64 (+.f64 a b) (.f64 eps 1/12)) (+.f64 (/.f64 1 a) (/.f64 1 b))))) (cbrt.f64 (fma.f64 eps (.f64 (+.f64 a b) (.f64 eps 1/12)) (+.f64 (/.f64 1 a) (/.f64 1 b)))))
✓	4.7b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))
	41.3b	(/.f64 1 (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))))
	51.1b	(/.f64 (.f64 (sqrt.f64 eps) (.f64 (sqrt.f64 eps) (expm1.f64 (.f64 eps (+.f64 a b))))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))
	52.5b	(/.f64 (.f64 (sqrt.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))) (sqrt.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))
	13.8b	(/.f64 (+.f64 a b) (*.f64 a b))

Compiler

Compiled 3323 to 1632 computations (50.9% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (cbrt.f64 (fma.f64 eps (.f64 (+.f64 a b) (.f64 eps 1/12)) (+.f64 (/.f64 1 a) (/.f64 1 b)))) (cbrt.f64 (fma.f64 eps (.f64 (+.f64 a b) (*.f64 eps 1/12)) (+.f64 (/.f64 1 a) (/.f64 1 b)))))
	0.6b	(cbrt.f64 (fma.f64 eps (.f64 (+.f64 a b) (.f64 eps 1/12)) (+.f64 (/.f64 1 a) (/.f64 1 b))))
	0.6b	(cbrt.f64 (fma.f64 eps (.f64 (+.f64 a b) (.f64 eps 1/12)) (+.f64 (/.f64 1 a) (/.f64 1 b))))
✓	0.6b	(cbrt.f64 (fma.f64 eps (.f64 (+.f64 a b) (.f64 eps 1/12)) (+.f64 (/.f64 1 a) (/.f64 1 b))))

rewrite10.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`

Counts

2 → 55

Calls

2 calls:

5.0ms

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

1.0ms

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

series470.0ms (2.3%)

Counts

2 → 72

Calls

2 calls:

331.0ms

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

137.0ms

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

simplify291.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

795×	`times-frac_binary64`
404×	`*-commutative_binary64`
299×	`+-commutative_binary64`
260×	`fma-def_binary64`
218×	`associate-+r+_binary64`

Counts

127 → 247

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1089	17766
1	3807	17538
2	5087	17538

prune1.9s (9.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	532	0	532
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	532	6	538

Error

Counts

538 → 6

Alt Table

Status	Error	Program
✓	6.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 eps (.f64 (+.f64 a b) (.f64 eps 1/12)) (+.f64 (/.f64 1 a) (/.f64 1 b)))) (cbrt.f64 (fma.f64 eps (.f64 (+.f64 a b) (.f64 eps 1/12)) (+.f64 (/.f64 1 a) (/.f64 1 b))))) (cbrt.f64 (fma.f64 eps (.f64 (+.f64 a b) (.f64 eps 1/12)) (+.f64 (/.f64 1 a) (/.f64 1 b)))))
✓	4.7b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))
	41.3b	(/.f64 1 (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))))
	51.1b	(/.f64 (.f64 (sqrt.f64 eps) (.f64 (sqrt.f64 eps) (expm1.f64 (.f64 eps (+.f64 a b))))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))
	52.5b	(/.f64 (.f64 (sqrt.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))) (sqrt.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))
▶	13.8b	(/.f64 (+.f64 a b) (*.f64 a b))

Compiler

Compiled 54385 to 37591 computations (30.9% saved)

localize8.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	14.5b	(/.f64 (+.f64 a b) (*.f64 a b))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64`
6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
4×	`associate-/l*_binary64`
4×	`times-frac_binary64`

Counts

1 → 27

Calls

1 calls:

8.0ms

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

series46.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

46.0ms

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

simplify128.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

581×	`associate-/r*_binary64`
450×	`sub-neg_binary64`
441×	`associate-/r/_binary64`
370×	`fma-def_binary64`
349×	`distribute-rgt-in_binary64`

Counts

51 → 80

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	57	613
1	152	550
2	469	550
3	1544	550
4	3494	550
5	3895	550
6	4902	550
7	5491	550

prune41.0ms (0.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	80	6	86

Error

Counts

86 → 6

Alt Table

Status	Error	Program
✓	6.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 eps (.f64 (+.f64 a b) (.f64 eps 1/12)) (+.f64 (/.f64 1 a) (/.f64 1 b)))) (cbrt.f64 (fma.f64 eps (.f64 (+.f64 a b) (.f64 eps 1/12)) (+.f64 (/.f64 1 a) (/.f64 1 b))))) (cbrt.f64 (fma.f64 eps (.f64 (+.f64 a b) (.f64 eps 1/12)) (+.f64 (/.f64 1 a) (/.f64 1 b)))))
✓	4.7b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))
	51.1b	(/.f64 (.f64 (sqrt.f64 eps) (.f64 (sqrt.f64 eps) (expm1.f64 (.f64 eps (+.f64 a b))))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))
	52.5b	(/.f64 (.f64 (sqrt.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))) (sqrt.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))
✓	13.8b	(/.f64 (+.f64 a b) (*.f64 a b))
	9.2b	(/.f64 (/.f64 (+.f64 a b) a) b)

Compiler

Compiled 583 to 216 computations (63% saved)

regimes747.0ms (3.7%)

Accuracy

Total 0.3b remaining (85.6%)

Threshold costs 0.3b (85.6%)

Compiler

Compiled 9762 to 5992 computations (38.6% saved)

bsearch9.0ms (0%)

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

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
5×	`+-commutative_binary64`
3×	`sub-neg_binary64`
1×	`*-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	145
1	60	145
2	63	145
3	61	145

end16.0ms (0.1%)

Compiler: Compiled 294 to 159 computations (45.9% saved)

sample12.4s (61.4%)

Algorithm

1×

intervals

Results

6.8s	4105×	body	2048	valid
2.1s	2387×	body	1024	valid
434.0ms	603×	body	1024	overflowed
426.0ms	380×	body	2048	overflowed
379.0ms	689×	body	512	valid
349.0ms	9696×	pre	128	true
170.0ms	283×	body	512	overflowed
89.0ms	558×	body	128	valid
86.0ms	248×	body	256	valid
47.0ms	291×	body	128	overflowed
41.0ms	136×	body	256	overflowed
32.0ms	13×	body	4096	valid
4.0ms	3×	body	2048	invalid

Compiler

Compiled 292 to 173 computations (40.8% saved)

Details

analyze2.6s (12.8%)

sample219.0ms (1.1%)

simplify25.0ms (0.1%)

prune6.0ms (0%)

localize12.0ms (0.1%)

rewrite14.0ms (0.1%)

series481.0ms (2.4%)

simplify156.0ms (0.8%)

prune177.0ms (0.9%)

localize11.0ms (0.1%)

rewrite12.0ms (0.1%)

series219.0ms (1.1%)

simplify117.0ms (0.6%)

prune100.0ms (0.5%)

localize16.0ms (0.1%)

rewrite10.0ms (0%)

series470.0ms (2.3%)

simplify291.0ms (1.4%)

prune1.9s (9.2%)

localize8.0ms (0%)

rewrite11.0ms (0.1%)

series46.0ms (0.2%)

simplify128.0ms (0.6%)

prune41.0ms (0.2%)

regimes747.0ms (3.7%)

bsearch9.0ms (0%)

simplify9.0ms (0%)

end16.0ms (0.1%)

sample12.4s (61.4%)

Profiling