Details

analyze2.7s (18.1%)

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)

sample8.6s (58.1%)

Symmetry

(sort a b)

Results

5.2s	4290×	body	2048	valid
1.7s	2430×	body	1024	valid
394.0ms	724×	body	512	valid
388.0ms	604×	body	1024	invalid
377.0ms	390×	body	2048	invalid
126.0ms	288×	body	512	invalid
91.0ms	543×	body	128	valid
86.0ms	252×	body	256	valid
63.0ms	171×	body	256	invalid
56.0ms	333×	body	128	invalid
28.0ms	17×	body	4096	valid

Compiler

Compiled 95 to 67 computations (29.5% saved)

simplify22.0ms (0.1%)

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

39.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	39.8b	(/.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)

localize14.0ms (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))))
✓	38.2b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

series338.0ms (2.3%)

Counts

4 → 132

Calls

4 calls:

274.0ms	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
31.0ms	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
27.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
6.0ms	(expm1.f64 (*.f64 eps b))

rewrite15.0ms (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 b))

simplify131.0ms (0.9%)

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	612	8300
1	2021	7554
2	5059	7554

prune173.0ms (1.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	206	7	213
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	207	7	214

Error

0.0b

Counts

214 → 7

Alt Table

Status	Error	Program
	27.5b	(.f64 (/.f64 eps (expm1.f64 (.f64 eps a))) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps b))))
▶	7.1b	(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))))
	49.3b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (fma.f64 b eps (.f64 1/2 (.f64 (.f64 eps eps) (.f64 b b))))))
	12.2b	(/.f64 (+.f64 a b) (*.f64 a b))
	27.5b	(/.f64 (.f64 (/.f64 eps (expm1.f64 (.f64 a eps))) (expm1.f64 (.f64 (+.f64 a b) eps))) (expm1.f64 (.f64 eps b)))
	38.8b	(/.f64 eps (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (expm1.f64 (.f64 eps (+.f64 a b)))))
	40.1b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (.f64 (expm1.f64 (.f64 eps a)) (.f64 (cbrt.f64 (expm1.f64 (.f64 eps b))) (cbrt.f64 (expm1.f64 (.f64 eps b))))) (cbrt.f64 (expm1.f64 (*.f64 eps b)))))

Compiler

Compiled 10713 to 3604 computations (66.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
✓	0.0b	(+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))
✓	7.5b	(.f64 a (.f64 eps eps))
✓	8.5b	(.f64 b (.f64 eps eps))

series60.0ms (0.4%)

Counts

4 → 120

Calls

4 calls:

22.0ms	(+.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))
8.0ms	(.f64 b (.f64 eps eps))
8.0ms	(.f64 a (.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:

6.0ms	(+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))
4.0ms	(.f64 b (.f64 eps eps))
4.0ms	(.f64 a (.f64 eps eps))
0.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))

simplify103.0ms (0.7%)

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 → 130

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

prune116.0ms (0.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	129	8	137

Error

0.0b

Counts

137 → 8

Alt Table

Status	Error	Program
	27.5b	(.f64 (/.f64 eps (expm1.f64 (.f64 eps a))) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps b))))
✓	7.1b	(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))))
▶	8.3b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (.f64 (.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))) (cbrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))) (cbrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))))
	49.3b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (fma.f64 b eps (.f64 1/2 (.f64 (.f64 eps eps) (.f64 b b))))))
	12.2b	(/.f64 (+.f64 a b) (*.f64 a b))
	27.5b	(/.f64 (.f64 (/.f64 eps (expm1.f64 (.f64 a eps))) (expm1.f64 (.f64 (+.f64 a b) eps))) (expm1.f64 (.f64 eps b)))
	38.8b	(/.f64 eps (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (expm1.f64 (.f64 eps (+.f64 a b)))))
	40.1b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (.f64 (expm1.f64 (.f64 eps a)) (.f64 (cbrt.f64 (expm1.f64 (.f64 eps b))) (cbrt.f64 (expm1.f64 (.f64 eps b))))) (cbrt.f64 (expm1.f64 (*.f64 eps b)))))

Compiler

Compiled 3895 to 1862 computations (52.2% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))
✓	0.5b	(.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))) (cbrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (*.f64 eps eps)) (/.f64 1 a)))))
	7.5b	(.f64 a (.f64 eps eps))
	8.5b	(.f64 b (.f64 eps eps))

series307.0ms (2.1%)

Counts

2 → 72

Calls

2 calls:

215.0ms

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

92.0ms

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

rewrite32.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64`
41×	`cbrt-prod_binary64`
19×	`add-sqr-sqrt_binary64`
18×	`distribute-lft-out_binary64`
14×	`swap-sqr_binary64`

Counts

2 → 79

Calls

2 calls:

13.0ms

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

8.0ms

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

simplify186.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

677×	`fma-def_binary64`
527×	`associate-/r*_binary64`
240×	`times-frac_binary64`
226×	`*-commutative_binary64`
144×	`+-commutative_binary64`

Counts

151 → 229

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	687	13176
1	2222	12078
2	5142	12078

prune951.0ms (6.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	538	1	539
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	538	9	547

Error

0.0b

Counts

547 → 9

Alt Table

Status	Error	Program
	27.5b	(.f64 (/.f64 eps (expm1.f64 (.f64 eps a))) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps b))))
✓	7.1b	(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))))
✓	8.3b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (.f64 (.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))) (cbrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))) (cbrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))))
	49.3b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (fma.f64 b eps (.f64 1/2 (.f64 (.f64 eps eps) (.f64 b b))))))
▶	12.2b	(/.f64 (+.f64 a b) (*.f64 a b))
	27.5b	(/.f64 (.f64 (/.f64 eps (expm1.f64 (.f64 a eps))) (expm1.f64 (.f64 (+.f64 a b) eps))) (expm1.f64 (.f64 eps b)))
	49.3b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (.f64 (fma.f64 1/18 (.f64 (.f64 b (.f64 eps eps)) (cbrt.f64 a)) (fma.f64 2/3 (/.f64 (cbrt.f64 a) b) (cbrt.f64 (/.f64 1 (.f64 a a))))) (cbrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (*.f64 eps eps)) (/.f64 1 a))))))
	38.8b	(/.f64 eps (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (expm1.f64 (.f64 eps (+.f64 a b)))))
	40.1b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (.f64 (expm1.f64 (.f64 eps a)) (.f64 (cbrt.f64 (expm1.f64 (.f64 eps b))) (cbrt.f64 (expm1.f64 (.f64 eps b))))) (cbrt.f64 (expm1.f64 (*.f64 eps b)))))

Compiler

Compiled 47378 to 28785 computations (39.2% saved)

localize6.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	11.8b	(/.f64 (+.f64 a b) (*.f64 a b))

series7.0ms (0%)

Counts

1 → 24

Calls

1 calls:

7.0ms

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

rewrite6.0ms (0%)

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:

5.0ms

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

simplify88.0ms (0.6%)

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

prune32.0ms (0.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	32	1	33
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	33	9	42

Error

0.0b

Counts

42 → 9

Alt Table

Status	Error	Program
	27.5b	(/.f64 (.f64 (/.f64 eps (expm1.f64 (.f64 a eps))) (expm1.f64 (.f64 (+.f64 a b) eps))) (expm1.f64 (.f64 eps b)))
	10.6b	(/.f64 (/.f64 (+.f64 a b) a) b)
	27.5b	(.f64 (/.f64 eps (expm1.f64 (.f64 eps a))) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps b))))
✓	7.1b	(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))))
✓	8.3b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (.f64 (.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))) (cbrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))) (cbrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))))
	49.3b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (fma.f64 b eps (.f64 1/2 (.f64 (.f64 eps eps) (.f64 b b))))))
✓	12.2b	(/.f64 (+.f64 a b) (*.f64 a b))
	38.8b	(/.f64 eps (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (expm1.f64 (.f64 eps (+.f64 a b)))))
	40.1b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (.f64 (expm1.f64 (.f64 eps a)) (.f64 (cbrt.f64 (expm1.f64 (.f64 eps b))) (cbrt.f64 (expm1.f64 (.f64 eps b))))) (cbrt.f64 (expm1.f64 (*.f64 eps b)))))

Compiler

Compiled 653 to 256 computations (60.8% saved)

regimes558.0ms (3.8%)

Accuracy

Total 0.2b remaining (89.5%)

Threshold costs 0.2b (89.5%)

Counts

98 → 3

Compiler

Compiled 9302 to 5632 computations (39.5% saved)

bsearch6.0ms (0%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	137
1	53	137
2	56	137
3	54	137

end323.0ms (2.2%)

Compiler: Compiled 595 to 345 computations (42% saved)

Details

analyze2.7s (18.1%)

sample8.6s (58.1%)

simplify22.0ms (0.1%)

prune4.0ms (0%)

localize14.0ms (0.1%)

series338.0ms (2.3%)

rewrite15.0ms (0.1%)

simplify131.0ms (0.9%)

prune173.0ms (1.2%)

localize13.0ms (0.1%)

series60.0ms (0.4%)

rewrite18.0ms (0.1%)

simplify103.0ms (0.7%)

prune116.0ms (0.8%)

localize15.0ms (0.1%)

series307.0ms (2.1%)

rewrite32.0ms (0.2%)

simplify186.0ms (1.3%)

prune951.0ms (6.4%)

localize6.0ms (0%)

series7.0ms (0%)

rewrite6.0ms (0%)

simplify88.0ms (0.6%)

prune32.0ms (0.2%)

regimes558.0ms (3.8%)

bsearch6.0ms (0%)

simplify4.0ms (0%)

end323.0ms (2.2%)

Profiling