Details

analyze2.3s (17.7%)

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)

sample8.9s (68.1%)

Symmetry

(sort a b)

Results

5.0s	4151×	body	2048	valid
2.1s	2490×	body	1024	valid
596.0ms	619×	body	1024	invalid
378.0ms	782×	body	512	valid
351.0ms	393×	body	2048	invalid
159.0ms	347×	body	512	invalid
109.0ms	262×	body	256	valid
106.0ms	560×	body	128	valid
53.0ms	321×	body	128	invalid
42.0ms	139×	body	256	invalid
20.0ms	11×	body	4096	valid

Compiler

Compiled 95 to 67 computations (29.5% saved)

simplify22.0ms (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

37.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	37.1b	(/.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)))
✓	35.8b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

series382.0ms (2.9%)

Counts

4 → 144

Calls

4 calls:

310.0ms	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
29.0ms	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
28.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
15.0ms	(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:

5.0ms	(/.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)))

simplify122.0ms (0.9%)

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

prune159.0ms (1.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	225	4	229
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	226	4	230

Error

0.0b

Counts

230 → 4

Alt Table

Status	Error	Program
	11.5b	(/.f64 (+.f64 a b) (*.f64 a b))
	25.4b	(.f64 (/.f64 eps (expm1.f64 (.f64 eps a))) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps b))))
▶	7.6b	(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))))
	37.1b	(/.f64 1 (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))))

Compiler

Compiled 11450 to 3855 computations (66.3% 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))
✓	6.0b	(.f64 a (.f64 eps eps))
✓	7.4b	(.f64 b (.f64 eps eps))

series67.0ms (0.5%)

Counts

4 → 120

Calls

4 calls:

29.0ms	(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))))
20.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
9.0ms	(.f64 b (.f64 eps eps))
8.0ms	(.f64 a (.f64 eps eps))

rewrite11.0ms (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 b (.f64 eps eps))
4.0ms	(.f64 a (.f64 eps eps))
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))))
0.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))

simplify93.0ms (0.7%)

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 → 122

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

prune79.0ms (0.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	123	3	126

Error

0.0b

Counts

126 → 3

Alt Table

Status	Error	Program
	25.4b	(.f64 (/.f64 eps (expm1.f64 (.f64 eps a))) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps b))))
	9.1b	(.f64 (.f64 (cbrt.f64 (fma.f64 eps (.f64 (+.f64 b a) (.f64 eps 1/12)) (+.f64 (/.f64 1 a) (/.f64 1 b)))) (cbrt.f64 (fma.f64 eps (.f64 (+.f64 b a) (.f64 eps 1/12)) (+.f64 (/.f64 1 a) (/.f64 1 b))))) (cbrt.f64 (fma.f64 eps (.f64 (+.f64 b a) (.f64 eps 1/12)) (+.f64 (/.f64 1 a) (/.f64 1 b)))))
▶	2.9b	(+.f64 (/.f64 1 b) (/.f64 1 a))

Compiler

Compiled 3164 to 1548 computations (51.1% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1 b) (/.f64 1 a))

series5.0ms (0%)

Counts

1 → 6

Calls

1 calls:

5.0ms

(+.f64 (/.f64 1 b) (/.f64 1 a))

rewrite62.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
15×	`times-frac_binary64`
13×	`fma-def_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`

Counts

1 → 34

Calls

1 calls:

61.0ms

(+.f64 (/.f64 1 b) (/.f64 1 a))

simplify117.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

450×	`fma-neg_binary64`
421×	`div-sub_binary64`
357×	`fma-def_binary64`
329×	`sub-neg_binary64`
281×	`distribute-rgt-in_binary64`

Counts

40 → 37

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	36	332
1	106	302
2	241	301
3	565	301
4	1313	301
5	2794	301
6	4202	301
7	4546	301
8	4845	301
9	4973	301
10	4870	301

prune31.0ms (0.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	36	1	37
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	37	3	40

Error

0.0b

Counts

40 → 3

Alt Table

Status	Error	Program
	25.4b	(.f64 (/.f64 eps (expm1.f64 (.f64 eps a))) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps b))))
▶	13.6b	(fma.f64 (sqrt.f64 (/.f64 1 b)) (sqrt.f64 (/.f64 1 b)) (/.f64 1 a))
✓	2.9b	(+.f64 (/.f64 1 b) (/.f64 1 a))

Compiler

Compiled 599 to 442 computations (26.2% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 b))
✓	0.2b	(fma.f64 (sqrt.f64 (/.f64 1 b)) (sqrt.f64 (/.f64 1 b)) (/.f64 1 a))

series24.0ms (0.2%)

Counts

2 → 14

Calls

2 calls:

16.0ms	(fma.f64 (sqrt.f64 (/.f64 1 b)) (sqrt.f64 (/.f64 1 b)) (/.f64 1 a))
7.0ms	(sqrt.f64 (/.f64 1 b))

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`sqrt-prod_binary64`
13×	`add-sqr-sqrt_binary64`
11×	`times-frac_binary64`
10×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`

Counts

2 → 40

Calls

2 calls:

2.0ms	(sqrt.f64 (/.f64 1 b))
0.0ms	(fma.f64 (sqrt.f64 (/.f64 1 b)) (sqrt.f64 (/.f64 1 b)) (/.f64 1 a))

simplify91.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

700×	`distribute-rgt-in_binary64`
486×	`associate-/l*_binary64`
446×	`distribute-rgt-out_binary64`
426×	`associate-*l/_binary64`
408×	`distribute-lft-in_binary64`

Counts

54 → 53

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	51	529
1	58	505
2	86	505
3	154	505
4	341	505
5	917	505
6	1790	505
7	2751	505
8	4580	505
9	4782	505
10	4897	505

prune65.0ms (0.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	85	3	88

Error

0.0b

Counts

88 → 3

Alt Table

Status	Error	Program
	25.4b	(.f64 (/.f64 eps (expm1.f64 (.f64 eps a))) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps b))))
✓	13.6b	(fma.f64 (sqrt.f64 (/.f64 1 b)) (sqrt.f64 (/.f64 1 b)) (/.f64 1 a))
✓	2.9b	(+.f64 (/.f64 1 b) (/.f64 1 a))

Compiler

Compiled 1462 to 1109 computations (24.1% saved)

regimes243.0ms (1.9%)

Accuracy

Total 0.1b remaining (75%)

Threshold costs 0.1b (75%)

Counts

68 → 3

Compiler

Compiled 5106 to 3544 computations (30.6% saved)

bsearch4.0ms (0%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`*-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	42	142
1	57	142
2	60	142
3	58	142

end223.0ms (1.7%)

Compiler: Compiled 430 to 249 computations (42.1% saved)

Details

analyze2.3s (17.7%)

sample8.9s (68.1%)

simplify22.0ms (0.2%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series382.0ms (2.9%)

rewrite14.0ms (0.1%)

simplify122.0ms (0.9%)

prune159.0ms (1.2%)

localize11.0ms (0.1%)

series67.0ms (0.5%)

rewrite11.0ms (0.1%)

simplify93.0ms (0.7%)

prune79.0ms (0.6%)

localize4.0ms (0%)

series5.0ms (0%)

rewrite62.0ms (0.5%)

simplify117.0ms (0.9%)

prune31.0ms (0.2%)

localize9.0ms (0.1%)

series24.0ms (0.2%)

rewrite4.0ms (0%)

simplify91.0ms (0.7%)

prune65.0ms (0.5%)

regimes243.0ms (1.9%)

bsearch4.0ms (0%)

simplify4.0ms (0%)

end223.0ms (1.7%)

Profiling