Details

analyze2.7s (19.3%)

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)

sample8.8s (62.3%)

Symmetry

(sort a b)

Results

5.2s	4259×	body	2048	valid
1.7s	2466×	body	1024	valid
476.0ms	637×	body	1024	invalid
399.0ms	712×	body	512	valid
352.0ms	404×	body	2048	invalid
178.0ms	291×	body	512	invalid
113.0ms	255×	body	256	valid
110.0ms	554×	body	128	valid
48.0ms	296×	body	128	invalid
44.0ms	156×	body	256	invalid
16.0ms	10×	body	4096	valid

Compiler

Compiled 95 to 67 computations (29.5% saved)

simplify21.0ms (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

prune5.0ms (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

39.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	39.9b	(/.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)

localize11.0ms (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))))
✓	38.1b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

series324.0ms (2.3%)

Counts

4 → 144

Calls

4 calls:

261.0ms	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
28.0ms	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
22.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
12.0ms	(expm1.f64 (*.f64 eps (+.f64 a b)))

rewrite81.0ms (0.6%)

Algorithm

2×	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 → 108

Calls

4 calls:

78.0ms	(expm1.f64 (*.f64 eps (+.f64 a b)))
78.0ms	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
78.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
78.0ms	(/.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	63
1	293	63
2	4113	63
3	5908	63
0	0	0
1	0	0

simplify139.0ms (1%)

Algorithm

1×	egg-herbie

Rules

828×	`fma-def_binary64`
410×	`times-frac_binary64`
350×	`associate-/l*_binary64`
238×	`associate-/r*_binary64`
221×	`*-commutative_binary64`

Counts

252 → 212

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	556	7020
1	1978	6629
2	4932	6625
3	5215	6625

prune163.0ms (1.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	207	5	212
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	208	5	213

Error

0.0b

Counts

213 → 5

Alt Table

Status	Error	Program
	27.2b	(.f64 (/.f64 eps (expm1.f64 (.f64 eps b))) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))))
	27.6b	(.f64 (/.f64 eps (expm1.f64 (.f64 eps a))) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps b))))
	39.9b	(pow.f64 (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))) -1)
▶	8.8b	(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))))
	40.2b	(pow.f64 (cbrt.f64 (/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))) 3)

Compiler

Compiled 10849 to 3893 computations (64.1% saved)

localize15.0ms (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))
✓	7.5b	(.f64 a (.f64 eps eps))
✓	7.6b	(.f64 b (.f64 eps eps))

series61.0ms (0.4%)

Counts

4 → 120

Calls

4 calls:

27.0ms	(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))))
19.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
7.0ms	(.f64 b (.f64 eps eps))
7.0ms	(.f64 a (.f64 eps eps))

rewrite64.0ms (0.5%)

Algorithm

2×	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 → 82

Calls

4 calls:

62.0ms	(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))))
62.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
62.0ms	(.f64 a (.f64 eps eps))
62.0ms	(.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
0	0	0
1	0	0

simplify128.0ms (0.9%)

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

202 → 107

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

prune84.0ms (0.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	107	5	112

Error

0.0b

Counts

112 → 5

Alt Table

Status	Error	Program
	9.8b	(pow.f64 (cbrt.f64 (fma.f64 1/12 (.f64 (.f64 eps eps) a) (+.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)) (/.f64 1 b)))) 3)
	27.2b	(.f64 (/.f64 eps (expm1.f64 (.f64 eps b))) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))))
▶	5.5b	(+.f64 (/.f64 1 b) (/.f64 1 a))
	27.6b	(.f64 (/.f64 eps (expm1.f64 (.f64 eps a))) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps b))))
	40.2b	(pow.f64 (cbrt.f64 (/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))) 3)

Compiler

Compiled 2757 to 1429 computations (48.2% 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))

rewrite47.0ms (0.3%)

Algorithm

2×	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 → 47

Calls

1 calls:

46.0ms

(+.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
0	0	0
1	0	0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Counts

53 → 49

Iterations

Useful iterations: 0 (0.0ms)

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

prune41.0ms (0.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	48	1	49
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	49	5	54

Error

0.0b

Counts

54 → 5

Alt Table

Status	Error	Program
	27.2b	(.f64 (/.f64 eps (expm1.f64 (.f64 eps b))) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))))
✓	5.5b	(+.f64 (/.f64 1 b) (/.f64 1 a))
	27.6b	(.f64 (/.f64 eps (expm1.f64 (.f64 eps a))) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps b))))
	40.2b	(pow.f64 (cbrt.f64 (/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))) 3)
▶	12.1b	(/.f64 (/.f64 (+.f64 b a) b) a)

Compiler

Compiled 769 to 521 computations (32.2% saved)

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 b a) b)
✓	6.2b	(/.f64 (/.f64 (+.f64 b a) b) a)

series14.0ms (0.1%)

Counts

2 → 48

Calls

2 calls:

9.0ms	(/.f64 (/.f64 (+.f64 b a) b) a)
5.0ms	(/.f64 (+.f64 b a) b)

rewrite55.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

895×	`log1p-expm1-u_binary64`
895×	`expm1-log1p-u_binary64`
561×	`prod-diff_binary64`
76×	`add-sqr-sqrt_binary64`
75×	`egg-rr`

Counts

2 → 75

Calls

2 calls:

53.0ms	(/.f64 (+.f64 b a) b)
53.0ms	(/.f64 (/.f64 (+.f64 b a) b) a)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	17
1	143	17
2	2203	17
3	6588	17
0	0	0
1	0	0

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Counts

123 → 81

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	345
1	13	345
2	12	345

prune57.0ms (0.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	81	5	86

Error

Counts

86 → 5

Alt Table

Status	Error	Program
	11.2b	(pow.f64 (*.f64 a (/.f64 b (+.f64 b a))) -1)
	27.2b	(.f64 (/.f64 eps (expm1.f64 (.f64 eps b))) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))))
✓	5.5b	(+.f64 (/.f64 1 b) (/.f64 1 a))
	27.6b	(.f64 (/.f64 eps (expm1.f64 (.f64 eps a))) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps b))))
	40.2b	(pow.f64 (cbrt.f64 (/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))) 3)

Compiler

Compiled 1050 to 371 computations (64.7% saved)

regimes926.0ms (6.6%)

Accuracy

Total 0.3b remaining (94.5%)

Threshold costs 0.3b (94.5%)

Counts

105 → 3

Compiler

Compiled 7570 to 4972 computations (34.3% saved)

bsearch3.0ms (0%)

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

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
10×	`+-commutative_binary64`
8×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	136
1	61	136
2	75	136
3	85	136
4	89	136
5	90	136
6	88	136

end300.0ms (2.1%)

Compiler: Compiled 452 to 254 computations (43.8% saved)

Details

analyze2.7s (19.3%)

sample8.8s (62.3%)

simplify21.0ms (0.2%)

prune5.0ms (0%)

localize11.0ms (0.1%)

series324.0ms (2.3%)

rewrite81.0ms (0.6%)

simplify139.0ms (1%)

prune163.0ms (1.2%)

localize15.0ms (0.1%)

series61.0ms (0.4%)

rewrite64.0ms (0.5%)

simplify128.0ms (0.9%)

prune84.0ms (0.6%)

localize4.0ms (0%)

series5.0ms (0%)

rewrite47.0ms (0.3%)

simplify7.0ms (0%)

prune41.0ms (0.3%)

localize4.0ms (0%)

series14.0ms (0.1%)

rewrite55.0ms (0.4%)

simplify11.0ms (0.1%)

prune57.0ms (0.4%)

regimes926.0ms (6.6%)

bsearch3.0ms (0%)

simplify5.0ms (0%)

end300.0ms (2.1%)

Profiling