Details

analyze2.2s (16.7%)

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)

sample8.2s (62.3%)

Symmetry

(sort a b)

Results

4.9s	4205×	body	2048	valid
1.7s	2403×	body	1024	valid
375.0ms	645×	body	1024	invalid
353.0ms	766×	body	512	valid
340.0ms	400×	body	2048	invalid
137.0ms	327×	body	512	invalid
92.0ms	561×	body	128	valid
92.0ms	303×	body	256	valid
51.0ms	152×	body	256	invalid
50.0ms	320×	body	128	invalid
30.0ms	18×	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`
125×	`distribute-rgt-in_binary64`
122×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	28
1	47	28
2	108	28
3	271	28
4	989	28

Stop Event

1×	node limit

Counts

1 → 2

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

29.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	29.2b	(.f64 eps (/.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) (expm1.f64 (.f64 eps b))))

Compiler

Compiled 87 to 54 computations (37.9% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (*.f64 eps b))
✓	0.4b	(/.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) (expm1.f64 (*.f64 eps b)))
✓	11.9b	(/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a)))
✓	26.7b	(.f64 eps (/.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) (expm1.f64 (.f64 eps b))))

series387.0ms (2.9%)

Counts

4 → 132

Calls

4 calls:

187.0ms	(.f64 eps (/.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) (expm1.f64 (.f64 eps b))))
147.0ms	(/.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) (expm1.f64 (*.f64 eps b)))
47.0ms	(/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a)))
5.0ms	(expm1.f64 (*.f64 eps b))

rewrite83.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

898×	`prod-diff_binary64`
151×	`add-sqr-sqrt_binary64`
143×	`log1p-expm1-u_binary64`
143×	`expm1-log1p-u_binary64`
139×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	76
1	300	76
2	4272	76

Stop Event

1×	node limit

Counts

4 → 121

Calls

4 calls:

80.0ms	(expm1.f64 (*.f64 eps b))
80.0ms	(/.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) (expm1.f64 (*.f64 eps b)))
80.0ms	(/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a)))
80.0ms	(.f64 eps (/.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) (expm1.f64 (.f64 eps b))))

simplify102.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

688×	`fma-def_binary64`
684×	`times-frac_binary64`
610×	`associate-/l*_binary64`
237×	`*-commutative_binary64`
216×	`+-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	662	9175
1	2339	8534

Stop Event

1×	node limit

Counts

253 → 208

prune201.0ms (1.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	204	4	208
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	204	5	209

Error

0.0b

Counts

209 → 5

Alt Table

Status	Error	Program
✓	29.2b	(.f64 eps (/.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) (expm1.f64 (.f64 eps b))))
	49.0b	(.f64 (/.f64 (/.f64 eps (.f64 eps (expm1.f64 (.f64 a eps)))) b) (expm1.f64 (.f64 a eps)))
	27.2b	(/.f64 1 (/.f64 (expm1.f64 (.f64 eps b)) (.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))))))
▶	7.2b	(+.f64 (fma.f64 1/12 (.f64 a (.f64 eps eps)) (/.f64 1 b)) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))
	12.9b	(/.f64 (+.f64 a b) (*.f64 a b))

Compiler

Compiled 12883 to 4639 computations (64% 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 1 b))
✓	0.0b	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
✓	6.4b	(.f64 b (.f64 eps eps))
✓	6.9b	(.f64 a (.f64 eps eps))

series50.0ms (0.4%)

Counts

4 → 120

Calls

4 calls:

20.0ms	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (/.f64 1 b))
16.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
7.0ms	(.f64 a (.f64 eps eps))
7.0ms	(.f64 b (.f64 eps eps))

rewrite55.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

625×	`log-prod_binary64`
227×	`expm1-udef_binary64`
227×	`log1p-udef_binary64`
209×	`log-pow_binary64`
188×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	42
1	267	42
2	3209	42

Stop Event

1×	node limit

Counts

4 → 94

Calls

4 calls:

53.0ms	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (/.f64 1 b))
53.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
53.0ms	(.f64 b (.f64 eps eps))
53.0ms	(.f64 a (.f64 eps eps))

simplify129.0ms (1%)

Algorithm

1×	egg-herbie

Rules

603×	`sqr-pow_binary64`
417×	`associate-l_binary64`
364×	`*-commutative_binary64`
330×	`fabs-mul_binary64`
312×	`cube-prod_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	1290
1	32	1236
2	65	1236
3	147	1236
4	384	1236
5	1224	1236
6	1654	1236
7	2076	1236
8	2176	1236
9	2324	1236
10	2498	1236
11	2749	1236
12	3070	1236
13	3440	1236
14	3894	1236
15	4475	1236

Stop Event

1×	node limit

Counts

214 → 108

prune83.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	109	4	113

Error

0.0b

Counts

113 → 4

Alt Table

Status	Error	Program
✓	29.2b	(.f64 eps (/.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) (expm1.f64 (.f64 eps b))))
▶	5.4b	(+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))
	27.2b	(/.f64 1 (/.f64 (expm1.f64 (.f64 eps b)) (.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))))))
	12.9b	(/.f64 (+.f64 a b) (*.f64 a b))

Compiler

Compiled 2952 to 1506 computations (49% saved)

localize9.0ms (0.1%)

Local error

Found 3 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))
	6.4b	(.f64 b (.f64 eps eps))

series24.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

24.0ms

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

rewrite51.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

659×	`prod-diff_binary64`
218×	`expm1-udef_binary64`
218×	`log1p-udef_binary64`
126×	`add-sqr-sqrt_binary64`
119×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	255	20
2	3239	20

Stop Event

1×	node limit

Counts

1 → 35

Calls

1 calls:

50.0ms

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

simplify90.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

599×	`sqr-pow_binary64`
402×	`fabs-mul_binary64`
386×	`cube-prod_binary64`
274×	`pow-sqr_binary64`
254×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	660
1	31	604
2	58	604
3	118	604
4	275	604
5	838	604
6	1230	604
7	1656	604
8	1756	604
9	1891	604
10	2063	604
11	2306	604
12	2619	604
13	2989	604
14	3443	604
15	4022	604
16	4732	604

Stop Event

1×	node limit

Counts

71 → 46

prune82.0ms (0.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	100	4	104

Error

0.0b

Counts

104 → 4

Alt Table

Status	Error	Program
✓	29.2b	(.f64 eps (/.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) (expm1.f64 (.f64 eps b))))
✓	5.4b	(+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))
	27.2b	(/.f64 1 (/.f64 (expm1.f64 (.f64 eps b)) (.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))))))
▶	6.6b	(.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))) (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (*.f64 eps eps)) (/.f64 1 a)))) 2))

Compiler

Compiled 2205 to 1281 computations (41.9% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))) (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (*.f64 eps eps)) (/.f64 1 a)))) 2))
✓	0.5b	(cbrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))
✓	0.6b	(pow.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))) 2)
	6.4b	(.f64 b (.f64 eps eps))

series197.0ms (1.5%)

Counts

3 → 108

Calls

3 calls:

107.0ms

(pow.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (*.f64 b (*.f64 eps eps)) (/.f64 1 a)))) 2)

68.0ms

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

21.0ms

(*.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (*.f64 b (*.f64 eps eps)) (/.f64 1 a)))) (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (*.f64 b (*.f64 eps eps)) (/.f64 1 a)))) 2))

rewrite56.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

659×	`prod-diff_binary64`
150×	`add-sqr-sqrt_binary64`
144×	`log1p-expm1-u_binary64`
144×	`expm1-log1p-u_binary64`
143×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	67
1	336	67
2	3829	67

Stop Event

1×	node limit

Counts

3 → 75

Calls

3 calls:

54.0ms

(*.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (*.f64 b (*.f64 eps eps)) (/.f64 1 a)))) (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (*.f64 b (*.f64 eps eps)) (/.f64 1 a)))) 2))

54.0ms

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

54.0ms

(pow.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (*.f64 b (*.f64 eps eps)) (/.f64 1 a)))) 2)

simplify90.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

521×	`fma-def_binary64`
466×	`associate-/r*_binary64`
272×	`associate-l_binary64`
264×	`times-frac_binary64`
188×	`associate-*r/_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	503	8101
1	1727	7607

Stop Event

1×	node limit

Counts

183 → 215

prune446.0ms (3.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	343	1	344
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	343	5	348

Error

Counts

348 → 5

Alt Table

Status	Error	Program
	6.0b	(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))) 2) (cbrt.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))) (/.f64 1 b))
✓	5.4b	(+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))
✓	29.2b	(.f64 eps (/.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) (expm1.f64 (.f64 eps b))))
	27.2b	(/.f64 1 (/.f64 (expm1.f64 (.f64 eps b)) (.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))))))
✓	6.6b	(.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))) (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (*.f64 eps eps)) (/.f64 1 a)))) 2))

Compiler

Compiled 21987 to 15123 computations (31.2% saved)

regimes437.0ms (3.3%)

Accuracy

Total 0.8b remaining (94.7%)

Threshold costs 0.8b (94.7%)

Counts

70 → 3

Compiler

Compiled 5722 to 3784 computations (33.9% saved)

bsearch3.0ms (0%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	132
1	52	132
2	55	132

Stop Event

1×

saturated

end117.0ms (0.9%)

Remove: (sort a b)
Compiler: Compiled 484 to 284 computations (41.3% saved)

Details

analyze2.2s (16.7%)

sample8.2s (62.3%)

simplify22.0ms (0.2%)

prune4.0ms (0%)

localize14.0ms (0.1%)

series387.0ms (2.9%)

rewrite83.0ms (0.6%)

simplify102.0ms (0.8%)

prune201.0ms (1.5%)

localize15.0ms (0.1%)

series50.0ms (0.4%)

rewrite55.0ms (0.4%)

simplify129.0ms (1%)

prune83.0ms (0.6%)

localize9.0ms (0.1%)

series24.0ms (0.2%)

rewrite51.0ms (0.4%)

simplify90.0ms (0.7%)

prune82.0ms (0.6%)

localize14.0ms (0.1%)

series197.0ms (1.5%)

rewrite56.0ms (0.4%)

simplify90.0ms (0.7%)

prune446.0ms (3.4%)

regimes437.0ms (3.3%)

bsearch3.0ms (0%)

simplify4.0ms (0%)

end117.0ms (0.9%)

Profiling