Details

analyze2.7s (20.6%)

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)

sample8.5s (64.7%)

Symmetry

(sort a b)

Results

4.8s	4101×	body	2048	valid
1.9s	2516×	body	1024	valid
435.0ms	632×	body	1024	invalid
435.0ms	410×	body	2048	invalid
371.0ms	804×	body	512	valid
127.0ms	284×	body	512	invalid
95.0ms	573×	body	128	valid
77.0ms	246×	body	256	valid
51.0ms	150×	body	256	invalid
50.0ms	314×	body	128	invalid
25.0ms	16×	body	4096	valid

Compiler

Compiled 95 to 67 computations (29.5% saved)

simplify26.0ms (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

39.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	39.0b	(/.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 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
✓	0.1b	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
✓	37.3b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

series435.0ms (3.3%)

Counts

4 → 144

Calls

4 calls:

363.0ms	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
30.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
28.0ms	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
14.0ms	(expm1.f64 (*.f64 eps (+.f64 a b)))

rewrite87.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

104× egg-rr

Counts

4 → 104

Calls

2 calls:

84.0ms

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

0.0ms

()

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

simplify140.0ms (1.1%)

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

248 → 208

Iterations

Useful iterations: 2 (0.0ms)

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

prune156.0ms (1.2%)

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
	46.0b	(cbrt.f64 (pow.f64 (/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))) 3))
	38.9b	(pow.f64 (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))) -1)
▶	6.7b	(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))))
✓	39.0b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
	17.1b	(/.f64 (+.f64 a b) (*.f64 a b))

Compiler

Compiled 10734 to 3866 computations (64% 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))
✓	5.7b	(.f64 a (.f64 eps eps))
✓	8.2b	(.f64 b (.f64 eps eps))

series69.0ms (0.5%)

Counts

4 → 120

Calls

4 calls:

30.0ms	(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))))
21.0ms	(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))

rewrite65.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

78× egg-rr

Counts

4 → 78

Calls

2 calls:

63.0ms

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

()

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

simplify131.0ms (1%)

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

prune73.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	105	4	109

Error

0.0b

Counts

109 → 4

Alt Table

Status	Error	Program
	46.0b	(cbrt.f64 (pow.f64 (/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))) 3))
✓	39.0b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
	17.1b	(/.f64 (+.f64 a b) (*.f64 a b))
▶	3.7b	(+.f64 (/.f64 1 b) (/.f64 1 a))

Compiler

Compiled 2597 to 1339 computations (48.4% 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))

rewrite45.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

46× egg-rr

Counts

1 → 46

Calls

2 calls:

45.0ms	((+.f64 (/.f64 1 b) (/.f64 1 a)))
0.0ms	()

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 (0.1%)

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

prune27.0ms (0.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	48	0	48
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	48	4	52

Error

0.0b

Counts

52 → 4

Alt Table

Status	Error	Program
	46.0b	(cbrt.f64 (pow.f64 (/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))) 3))
✓	39.0b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
▶	17.1b	(/.f64 (+.f64 a b) (*.f64 a b))
✓	3.7b	(+.f64 (/.f64 1 b) (/.f64 1 a))

Compiler

Compiled 699 to 477 computations (31.8% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	16.1b	(/.f64 (+.f64 a b) (*.f64 a b))

series7.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

7.0ms

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

rewrite48.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

40× egg-rr

Counts

1 → 40

Calls

2 calls:

47.0ms	((/.f64 (+.f64 a b) (*.f64 a b)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	136	10
2	2016	10
3	6180	10
0	0	0
1	0	0

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Counts

64 → 44

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	204
1	10	204
2	9	204

prune17.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	44	0	44
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	44	4	48

Error

0.0b

Counts

48 → 4

Alt Table

Status	Error	Program
	46.0b	(cbrt.f64 (pow.f64 (/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))) 3))
✓	39.0b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
✓	17.1b	(/.f64 (+.f64 a b) (*.f64 a b))
✓	3.7b	(+.f64 (/.f64 1 b) (/.f64 1 a))

Compiler

Compiled 592 to 206 computations (65.2% saved)

regimes304.0ms (2.3%)

Accuracy

Total 0.0b remaining (51.4%)

Threshold costs 0.0b (51.4%)

Counts

54 → 3

Compiler

Compiled 4570 to 2868 computations (37.2% saved)

bsearch2.0ms (0%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	152
1	60	152
2	63	152
3	61	152

end237.0ms (1.8%)

Compiler: Compiled 477 to 271 computations (43.2% saved)

Details

analyze2.7s (20.6%)

sample8.5s (64.7%)

simplify26.0ms (0.2%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series435.0ms (3.3%)

rewrite87.0ms (0.7%)

simplify140.0ms (1.1%)

prune156.0ms (1.2%)

localize11.0ms (0.1%)

series69.0ms (0.5%)

rewrite65.0ms (0.5%)

simplify131.0ms (1%)

prune73.0ms (0.6%)

localize4.0ms (0%)

series5.0ms (0%)

rewrite45.0ms (0.3%)

simplify7.0ms (0.1%)

prune27.0ms (0.2%)

localize4.0ms (0%)

series7.0ms (0.1%)

rewrite48.0ms (0.4%)

simplify8.0ms (0.1%)

prune17.0ms (0.1%)

regimes304.0ms (2.3%)

bsearch2.0ms (0%)

simplify4.0ms (0%)

end237.0ms (1.8%)

Profiling