Details

analyze4.6s (21.5%)

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)

sample14.2s (66.4%)

Symmetry

(sort a b)

Results

8.3s	4175×	body	2048	valid
3.1s	2467×	body	1024	valid
671.0ms	756×	body	512	valid
613.0ms	618×	body	1024	invalid
563.0ms	416×	body	2048	invalid
217.0ms	291×	body	512	invalid
169.0ms	587×	body	128	valid
140.0ms	255×	body	256	valid
93.0ms	271×	body	128	invalid
68.0ms	139×	body	256	invalid
48.0ms	16×	body	4096	valid

Compiler

Compiled 95 to 67 computations (29.5% saved)

simplify51.0ms (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

prune7.0ms (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

40.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	40.5b	(/.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)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (*.f64 eps 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))))
✓	38.9b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

series388.0ms (1.8%)

Counts

4 → 132

Calls

4 calls:

275.0ms	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
56.0ms	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
47.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
9.0ms	(expm1.f64 (*.f64 eps b))

rewrite156.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

916×	`prod-diff_binary64`
149×	`add-sqr-sqrt_binary64`
141×	`associate-r_binary64`
141×	`log1p-expm1-u_binary64`
141×	`expm1-log1p-u_binary64`

Counts

4 → 104

Calls

4 calls:

151.0ms	(expm1.f64 (*.f64 eps b))
151.0ms	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
151.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
151.0ms	(/.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	60
1	293	60
2	4113	60
3	5908	60

simplify137.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

692×	`fma-def_binary64`
492×	`associate-l_binary64`
410×	`times-frac_binary64`
350×	`associate-/l*_binary64`
238×	`associate-/r*_binary64`

Counts

236 → 192

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	522	6487
1	1833	6111
2	5323	6111

prune231.0ms (1.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	187	5	192
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	188	5	193

Error

0.0b

Counts

193 → 5

Alt Table

Status	Error	Program
	29.1b	(.f64 (/.f64 eps (expm1.f64 (.f64 eps b))) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))))
	34.9b	(.f64 (/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (expm1.f64 (.f64 eps a))) (/.f64 1 (expm1.f64 (*.f64 eps b))))
▶	6.8b	(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))))
	17.8b	(/.f64 (+.f64 a b) (*.f64 a b))
	40.6b	(pow.f64 (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))) -1)

Compiler

Compiled 9854 to 3558 computations (63.9% saved)

localize22.0ms (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))))
✓	0.1b	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
✓	7.0b	(.f64 a (.f64 eps eps))
✓	7.1b	(.f64 b (.f64 eps eps))

series110.0ms (0.5%)

Counts

4 → 120

Calls

4 calls:

47.0ms	(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))))
33.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
15.0ms	(.f64 b (.f64 eps eps))
14.0ms	(.f64 a (.f64 eps eps))

rewrite93.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

743×	`prod-diff_binary64`
148×	`add-sqr-sqrt_binary64`
139×	`log1p-expm1-u_binary64`
139×	`expm1-log1p-u_binary64`
137×	`add-cbrt-cube_binary64`

Counts

4 → 78

Calls

4 calls:

90.0ms	(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))))
90.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
90.0ms	(.f64 a (.f64 eps eps))
90.0ms	(.f64 b (.f64 eps eps))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	58
1	298	58
2	3557	58
3	4925	58

simplify162.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

731×	`distribute-rgt-out_binary64`
626×	`associate-l_binary64`
552×	`fma-def_binary64`
484×	`*-commutative_binary64`
362×	`distribute-rgt-in_binary64`

Counts

198 → 104

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	26	1742
1	65	1511
2	140	1461
3	295	1461
4	616	1461
5	1529	1461
6	2768	1461
7	3790	1461
8	4997	1461
9	4996	1461
10	4947	1461

prune83.0ms (0.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	105	4	109

Error

0.0b

Counts

109 → 4

Alt Table

Status	Error	Program
▶	2.7b	(+.f64 (/.f64 1 b) (/.f64 1 a))
	29.1b	(.f64 (/.f64 eps (expm1.f64 (.f64 eps b))) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))))
	34.9b	(.f64 (/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (expm1.f64 (.f64 eps a))) (/.f64 1 (expm1.f64 (*.f64 eps b))))
	17.8b	(/.f64 (+.f64 a b) (*.f64 a b))

Compiler

Compiled 2616 to 1350 computations (48.4% saved)

localize7.0ms (0%)

Local error

Found 1 expressions with local error:

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

series18.0ms (0.1%)

Counts

1 → 6

Calls

1 calls:

18.0ms

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

rewrite91.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

795×	`log1p-expm1-u_binary64`
795×	`expm1-log1p-u_binary64`
702×	`prod-diff_binary64`
79×	`add-sqr-sqrt_binary64`
73×	`add-cbrt-cube_binary64`

Counts

1 → 46

Calls

1 calls:

89.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	156	10
2	2002	10
3	6195	10

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Counts

52 → 48

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	24
1	8	24
2	7	24

prune61.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	47	1	48
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	49	3	52

Error

0.0b

Counts

52 → 3

Alt Table

Status	Error	Program
✓	2.7b	(+.f64 (/.f64 1 b) (/.f64 1 a))
	29.1b	(.f64 (/.f64 eps (expm1.f64 (.f64 eps b))) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))))
▶	18.3b	(.f64 (+.f64 b a) (/.f64 1 (.f64 b a)))

Compiler

Compiled 676 to 462 computations (31.7% saved)

localize10.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.6b	(/.f64 1 (*.f64 b a))
✓	16.4b	(.f64 (+.f64 b a) (/.f64 1 (.f64 b a)))

series34.0ms (0.2%)

Counts

2 → 48

Calls

2 calls:

19.0ms	(/.f64 1 (*.f64 b a))
15.0ms	(.f64 (+.f64 b a) (/.f64 1 (.f64 b a)))

rewrite89.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

882×	`expm1-log1p-u_binary64`
583×	`prod-diff_binary64`
85×	`add-sqr-sqrt_binary64`
80×	`log1p-expm1-u_binary64`
78×	`add-cbrt-cube_binary64`

Counts

2 → 76

Calls

2 calls:

87.0ms	(/.f64 1 (*.f64 b a))
87.0ms	(.f64 (+.f64 b a) (/.f64 1 (.f64 b a)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	172	17
2	2231	17
3	4934	17

simplify24.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`associate-/r*_binary64`
1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Counts

124 → 81

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	372
1	14	372
2	15	372
3	14	372

prune67.0ms (0.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	81	3	84

Error

0.0b

Counts

84 → 3

Alt Table

Status	Error	Program
✓	2.7b	(+.f64 (/.f64 1 b) (/.f64 1 a))
	29.1b	(.f64 (/.f64 eps (expm1.f64 (.f64 eps b))) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))))
✓	18.3b	(.f64 (+.f64 b a) (/.f64 1 (.f64 b a)))

Compiler

Compiled 1082 to 433 computations (60% saved)

regimes541.0ms (2.5%)

Accuracy

Total 0.0b remaining (34.5%)

Threshold costs 0.0b (34.5%)

Counts

64 → 3

Compiler

Compiled 5186 to 3412 computations (34.2% saved)

bsearch3.0ms (0%)

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

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
5×	`+-commutative_binary64`
3×	`sub-neg_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	132
1	51	132
2	54	132
3	52	132

end147.0ms (0.7%)

Remove: (sort a b)
Compiler: Compiled 399 to 229 computations (42.6% saved)

Details

analyze4.6s (21.5%)

sample14.2s (66.4%)

simplify51.0ms (0.2%)

prune7.0ms (0%)

localize19.0ms (0.1%)

series388.0ms (1.8%)

rewrite156.0ms (0.7%)

simplify137.0ms (0.6%)

prune231.0ms (1.1%)

localize22.0ms (0.1%)

series110.0ms (0.5%)

rewrite93.0ms (0.4%)

simplify162.0ms (0.8%)

prune83.0ms (0.4%)

localize7.0ms (0%)

series18.0ms (0.1%)

rewrite91.0ms (0.4%)

simplify12.0ms (0.1%)

prune61.0ms (0.3%)

localize10.0ms (0%)

series34.0ms (0.2%)

rewrite89.0ms (0.4%)

simplify24.0ms (0.1%)

prune67.0ms (0.3%)

regimes541.0ms (2.5%)

bsearch3.0ms (0%)

simplify6.0ms (0%)

end147.0ms (0.7%)

Profiling