Details

analyze2.8s (19.8%)

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)

sample8.7s (62.3%)

Symmetry

(sort a b)

Results

5.1s	4196×	body	2048	valid
1.9s	2510×	body	1024	valid
451.0ms	416×	body	2048	invalid
410.0ms	655×	body	1024	invalid
359.0ms	736×	body	512	valid
122.0ms	280×	body	512	invalid
100.0ms	522×	body	128	valid
90.0ms	274×	body	256	valid
54.0ms	297×	body	128	invalid
44.0ms	141×	body	256	invalid
33.0ms	18×	body	4096	valid

Compiler

Compiled 95 to 67 computations (29.5% saved)

simplify24.0ms (0.2%)

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

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

43.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	43.8b	(/.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 eps (expm1.f64 (.f64 eps (+.f64 a b))))
✓	0.3b	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
✓	41.9b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

series261.0ms (1.9%)

Counts

4 → 144

Calls

4 calls:

199.0ms	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
26.0ms	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
24.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
12.0ms	(expm1.f64 (*.f64 eps (+.f64 a 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 eps (expm1.f64 (.f64 eps (+.f64 a b))))
3.0ms	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
0.0ms	(expm1.f64 (*.f64 eps (+.f64 a b)))

simplify133.0ms (1%)

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 → 229

Iterations

Useful iterations: 1 (0.0ms)

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

prune161.0ms (1.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	226	3	229
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	227	3	230

Error

0.0b

Counts

230 → 3

Alt Table

Status	Error	Program
▶	3.7b	(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))))
	12.8b	(/.f64 (+.f64 a b) (*.f64 a b))
	31.2b	(.f64 (/.f64 eps (expm1.f64 (.f64 eps a))) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps b))))

Compiler

Compiled 11404 to 3825 computations (66.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.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))
✓	6.0b	(.f64 b (.f64 eps eps))
✓	8.2b	(.f64 a (.f64 eps eps))

series67.0ms (0.5%)

Counts

4 → 120

Calls

4 calls:

24.0ms	(+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))
22.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
14.0ms	(.f64 a (.f64 eps eps))
8.0ms	(.f64 b (.f64 eps eps))

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
14×	`pow1_binary64`

Counts

4 → 81

Calls

4 calls:

5.0ms	(+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))
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))

simplify112.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

562×	`associate-+l+_binary64`
523×	`associate-l_binary64`
384×	`associate-r_binary64`
262×	`cancel-sign-sub-inv_binary64`
220×	`unswap-sqr_binary64`

Counts

201 → 131

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	105	2505
1	236	2362
2	656	2362
3	2257	2360
4	4524	2360
5	5001	2360

prune100.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	130	4	134

Error

Counts

134 → 4

Alt Table

Status	Error	Program
✓	3.7b	(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))))
▶	4.3b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (.f64 (.f64 (cbrt.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))) (cbrt.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))) (cbrt.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))))
	12.8b	(/.f64 (+.f64 a b) (*.f64 a b))
	31.2b	(.f64 (/.f64 eps (expm1.f64 (.f64 eps a))) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps b))))

Compiler

Compiled 3703 to 1754 computations (52.6% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (cbrt.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))) (cbrt.f64 (fma.f64 1/12 (.f64 b (*.f64 eps eps)) (/.f64 1 a))))
✓	0.6b	(cbrt.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))
	6.0b	(.f64 b (.f64 eps eps))
	8.2b	(.f64 a (.f64 eps eps))

series107.0ms (0.8%)

Counts

2 → 72

Calls

2 calls:

61.0ms	(.f64 (cbrt.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))) (cbrt.f64 (fma.f64 1/12 (.f64 b (*.f64 eps eps)) (/.f64 1 a))))
46.0ms	(cbrt.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))

rewrite9.0ms (0.1%)

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 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))) (cbrt.f64 (fma.f64 1/12 (.f64 b (*.f64 eps eps)) (/.f64 1 a))))
1.0ms	(cbrt.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))

simplify263.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

544×	`fma-neg_binary64`
413×	`cancel-sign-sub-inv_binary64`
252×	`associate-/r*_binary64`
220×	`exp-prod_binary64`
213×	`unswap-sqr_binary64`

Counts

127 → 152

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	308	6165
1	944	5933
2	3080	5552
3	4569	5350
4	4831	5192
5	4448	4798
6	4214	4708
7	4903	4708
8	4923	4708

prune573.0ms (4.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	400	0	400
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	400	4	404

Error

Counts

404 → 4

Alt Table

Status	Error	Program
✓	3.7b	(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))))
✓	4.3b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (.f64 (.f64 (cbrt.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))) (cbrt.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))) (cbrt.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))))
▶	12.8b	(/.f64 (+.f64 a b) (*.f64 a b))
	31.2b	(.f64 (/.f64 eps (expm1.f64 (.f64 eps a))) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps b))))

Compiler

Compiled 24619 to 13576 computations (44.9% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	13.3b	(/.f64 (+.f64 a b) (*.f64 a b))

series8.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

7.0ms

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

rewrite7.0ms (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:

6.0ms

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

simplify81.0ms (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 → 33

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

prune48.0ms (0.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	33	0	33
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	33	4	37

Error

Counts

37 → 4

Alt Table

Status	Error	Program
✓	3.7b	(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))))
✓	4.3b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (.f64 (.f64 (cbrt.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))) (cbrt.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))) (cbrt.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))))
✓	12.8b	(/.f64 (+.f64 a b) (*.f64 a b))
	31.2b	(.f64 (/.f64 eps (expm1.f64 (.f64 eps a))) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps b))))

Compiler

Compiled 530 to 185 computations (65.1% saved)

regimes359.0ms (2.6%)

Accuracy

Total 0.2b remaining (76.2%)

Threshold costs 0.2b (76.2%)

Counts

92 → 3

Compiler

Compiled 8238 to 5184 computations (37.1% saved)

bsearch4.0ms (0%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
5×	`+-commutative_binary64`
3×	`sub-neg_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	132
1	52	132
2	55	132
3	53	132

end112.0ms (0.8%)

Remove: (sort a b)
Compiler: Compiled 460 to 262 computations (43% saved)

Details

analyze2.8s (19.8%)

sample8.7s (62.3%)

simplify24.0ms (0.2%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series261.0ms (1.9%)

rewrite14.0ms (0.1%)

simplify133.0ms (1%)

prune161.0ms (1.2%)

localize11.0ms (0.1%)

series67.0ms (0.5%)

rewrite18.0ms (0.1%)

simplify112.0ms (0.8%)

prune100.0ms (0.7%)

localize14.0ms (0.1%)

series107.0ms (0.8%)

rewrite9.0ms (0.1%)

simplify263.0ms (1.9%)

prune573.0ms (4.1%)

localize4.0ms (0%)

series8.0ms (0.1%)

rewrite7.0ms (0.1%)

simplify81.0ms (0.6%)

prune48.0ms (0.3%)

regimes359.0ms (2.6%)

bsearch4.0ms (0%)

simplify4.0ms (0%)

end112.0ms (0.8%)

Profiling