Details

analyze2.4s (19.5%)

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)

sample286.0ms (2.4%)

Algorithm

1×

intervals

Symmetry

(sort a b)

Results

125.0ms	136×	body	2048	valid
32.0ms	70×	body	1024	valid
24.0ms	24×	body	512	valid
7.0ms	11×	body	2048	overflowed
7.0ms	298×	pre	128	true
5.0ms	14×	body	1024	overflowed
2.0ms	8×	body	256	valid
2.0ms	18×	body	128	valid
1.0ms	4×	body	512	overflowed
1.0ms	9×	body	128	overflowed
1.0ms	4×	body	256	overflowed

Compiler

Compiled 64 to 46 computations (28.1% 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

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

42.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	42.8b	(/.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)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (*.f64 eps a))
✓	0.1b	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
✓	0.1b	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
✓	41.0b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

series336.0ms (2.8%)

Counts

4 → 132

Calls

4 calls:

271.0ms	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
30.0ms	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
28.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
6.0ms	(expm1.f64 (*.f64 eps a))

rewrite13.0ms (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:

4.0ms	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
3.0ms	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
3.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
0.0ms	(expm1.f64 (*.f64 eps a))

simplify138.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

692×	`fma-def_binary64`
622×	`times-frac_binary64`
470×	`associate-/l*_binary64`
249×	`*-commutative_binary64`
163×	`+-commutative_binary64`

Counts

206 → 213

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	613	8300
1	2021	7554
2	5057	7554

prune152.0ms (1.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	210	3	213
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	211	3	214

Error

0.0b

Counts

214 → 3

Alt Table

Status	Error	Program
▶	5.5b	(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))))
	15.4b	(/.f64 (+.f64 a b) (*.f64 a b))
	29.8b	(.f64 (/.f64 eps (expm1.f64 (.f64 eps a))) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps b))))

Compiler

Compiled 10503 to 3485 computations (66.8% saved)

localize15.0ms (0.1%)

Local error

Found 4 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))
✓	5.7b	(.f64 b (.f64 eps eps))
✓	6.0b	(.f64 a (.f64 eps eps))

series67.0ms (0.6%)

Counts

4 → 120

Calls

4 calls:

26.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
25.0ms	(+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))
8.0ms	(.f64 a (.f64 eps eps))
8.0ms	(.f64 b (.f64 eps eps))

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
14×	`pow1_binary64`

Counts

4 → 81

Calls

4 calls:

5.0ms	(+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))
4.0ms	(.f64 a (.f64 eps eps))
4.0ms	(.f64 b (.f64 eps eps))
0.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))

simplify119.0ms (1%)

Algorithm

1×	egg-herbie

Rules

562×	`associate-+l+_binary64`
523×	`associate-l_binary64`
384×	`associate-r_binary64`
262×	`cancel-sign-sub-inv_binary64`
220×	`unswap-sqr_binary64`

Counts

201 → 131

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	105	2505
1	236	2362
2	656	2362
3	2257	2360
4	4524	2360
5	5001	2360

prune104.0ms (0.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	129	2	131
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	129	5	134

Error

0.0b

Counts

134 → 5

Alt Table

Status	Error	Program
	29.8b	(.f64 (/.f64 eps (expm1.f64 (.f64 eps a))) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps b))))
	33.3b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (.f64 (sqrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))) (sqrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (*.f64 eps eps)) (/.f64 1 a))))))
✓	5.5b	(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))))
	15.4b	(/.f64 (+.f64 a b) (*.f64 a b))
▶	6.1b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (.f64 (.f64 (cbrt.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))) (cbrt.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))) (cbrt.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))))

Compiler

Compiled 3785 to 1804 computations (52.3% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (cbrt.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))) (cbrt.f64 (fma.f64 1/12 (.f64 b (*.f64 eps eps)) (/.f64 1 a))))
✓	0.6b	(cbrt.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))
	5.7b	(.f64 b (.f64 eps eps))
	6.0b	(.f64 a (.f64 eps eps))

series132.0ms (1.1%)

Counts

2 → 72

Calls

2 calls:

74.0ms	(.f64 (cbrt.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))) (cbrt.f64 (fma.f64 1/12 (.f64 b (*.f64 eps eps)) (/.f64 1 a))))
57.0ms	(cbrt.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`

Counts

2 → 55

Calls

2 calls:

5.0ms	(.f64 (cbrt.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))) (cbrt.f64 (fma.f64 1/12 (.f64 b (*.f64 eps eps)) (/.f64 1 a))))
1.0ms	(cbrt.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))

simplify276.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

544×	`fma-neg_binary64`
413×	`cancel-sign-sub-inv_binary64`
252×	`associate-/r*_binary64`
220×	`exp-prod_binary64`
213×	`unswap-sqr_binary64`

Counts

127 → 152

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	308	6165
1	944	5933
2	3080	5552
3	4569	5350
4	4831	5192
5	4448	4798
6	4214	4708
7	4903	4708
8	4923	4708

prune505.0ms (4.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	400	0	400
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	400	5	405

Error

0.0b

Counts

405 → 5

Alt Table

Status	Error	Program
	29.8b	(.f64 (/.f64 eps (expm1.f64 (.f64 eps a))) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps b))))
	33.3b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (.f64 (sqrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))) (sqrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (*.f64 eps eps)) (/.f64 1 a))))))
✓	5.5b	(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))))
▶	15.4b	(/.f64 (+.f64 a b) (*.f64 a b))
✓	6.1b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (.f64 (.f64 (cbrt.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))) (cbrt.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))) (cbrt.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))))

Compiler

Compiled 24701 to 13626 computations (44.8% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	15.7b	(/.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))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64`
6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
4×	`associate-/l*_binary64`
4×	`times-frac_binary64`

Counts

1 → 27

Calls

1 calls:

10.0ms

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

simplify80.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

581×	`associate-/r*_binary64`
450×	`sub-neg_binary64`
441×	`associate-/r/_binary64`
370×	`fma-def_binary64`
349×	`distribute-rgt-in_binary64`

Counts

51 → 33

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	57	613
1	152	550
2	469	550
3	1544	550
4	3494	550
5	3895	550
6	4902	550
7	5491	550

prune22.0ms (0.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	32	1	33
Fresh	1	1	2
Picked	0	1	1
Done	1	1	2
Total	34	4	38

Error

Counts

38 → 4

Alt Table

Status	Error	Program
	8.8b	(/.f64 1 (/.f64 a (/.f64 (+.f64 a b) b)))
	29.8b	(.f64 (/.f64 eps (expm1.f64 (.f64 eps a))) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps b))))
✓	5.5b	(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))))
✓	15.4b	(/.f64 (+.f64 a b) (*.f64 a b))

Compiler

Compiled 493 to 165 computations (66.5% saved)

regimes339.0ms (2.8%)

Accuracy

Total 0.1b remaining (72.6%)

Threshold costs 0.1b (72.6%)

Counts

80 → 3

Compiler

Compiled 7078 to 4480 computations (36.7% saved)

bsearch3.0ms (0%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-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	43	142
1	56	142
2	59	142
3	57	142

end9.0ms (0.1%)

Compiler: Compiled 288 to 162 computations (43.8% saved)

sample7.0s (58.1%)

Algorithm

1×

intervals

Results

3.8s	4141×	body	2048	valid
1.1s	2349×	body	1024	valid
253.0ms	732×	body	512	valid
234.0ms	562×	body	1024	overflowed
215.0ms	9693×	pre	128	true
202.0ms	349×	body	2048	overflowed
90.0ms	310×	body	512	overflowed
79.0ms	543×	body	128	valid
42.0ms	220×	body	256	valid
39.0ms	171×	body	256	overflowed
30.0ms	15×	body	4096	valid
27.0ms	297×	body	128	overflowed
3.0ms	4×	body	2048	invalid

Compiler

Compiled 200 to 123 computations (38.5% saved)

Details

analyze2.4s (19.5%)

sample286.0ms (2.4%)

simplify21.0ms (0.2%)

prune4.0ms (0%)

localize18.0ms (0.1%)

series336.0ms (2.8%)

rewrite13.0ms (0.1%)

simplify138.0ms (1.1%)

prune152.0ms (1.3%)

localize15.0ms (0.1%)

series67.0ms (0.6%)

rewrite18.0ms (0.1%)

simplify119.0ms (1%)

prune104.0ms (0.9%)

localize18.0ms (0.1%)

series132.0ms (1.1%)

rewrite10.0ms (0.1%)

simplify276.0ms (2.3%)

prune505.0ms (4.2%)

localize4.0ms (0%)

series7.0ms (0.1%)

rewrite11.0ms (0.1%)

simplify80.0ms (0.7%)

prune22.0ms (0.2%)

regimes339.0ms (2.8%)

bsearch3.0ms (0%)

simplify4.0ms (0%)

end9.0ms (0.1%)

sample7.0s (58.1%)

Profiling