Details

analyze78.0ms (2.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12
50.4%	0%	49.6%	13
50.4%	0%	49.6%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample63.0ms (2.1%)

Algorithm

1×

intervals

Results

41.0ms	142×	body	1024	valid
9.0ms	55×	body	512	valid
3.0ms	10×	body	2048	valid
3.0ms	27×	body	256	valid
1.0ms	22×	body	128	valid

Compiler

Compiled 20 to 16 computations (20% saved)

simplify61.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

618×	`fma-neg_binary64`
579×	`fma-def_binary64`
510×	`associate-/l*_binary64`
467×	`div-sub_binary64`
425×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	19	13
2	33	13
3	57	13
4	112	13
5	224	13
6	514	13
7	1303	13
8	3047	12
9	4469	12
10	4859	12

prune3.0ms (0.1%)

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

58.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	58.9b	(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))

Compiler

Compiled 35 to 23 computations (34.3% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 -1/2 (exp.f64 x))
✓	6.6b	(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 39

Calls

2 calls:

3.0ms	(/.f64 -1/2 (exp.f64 x))
0.0ms	(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))

series28.0ms (1%)

Counts

2 → 16

Calls

2 calls:

17.0ms	(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
12.0ms	(/.f64 -1/2 (exp.f64 x))

simplify106.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

622×	`associate-l_binary64`
537×	`fma-neg_binary64`
481×	`associate-r_binary64`
467×	`fma-def_binary64`
387×	`cancel-sign-sub-inv_binary64`

Counts

55 → 79

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	95	729
1	196	668
2	411	666
3	1095	660
4	3465	659
5	4949	659
6	4974	659
7	4885	659

prune29.0ms (1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	78	2	80

Error

0.0b

Counts

80 → 2

Alt Table

Status	Error	Program
✓	58.9b	(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
▶	0.5b	(fma.f64 1/120 (pow.f64 x 5) (fma.f64 1/6 (pow.f64 x 3) x))

Compiler

Compiled 821 to 506 computations (38.4% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/120 (pow.f64 x 5) (fma.f64 1/6 (pow.f64 x 3) x))
✓	0.0b	(fma.f64 1/6 (pow.f64 x 3) x)

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`
2×	`add-exp-log_binary64`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma.f64 1/6 (pow.f64 x 3) x)
0.0ms	(fma.f64 1/120 (pow.f64 x 5) (fma.f64 1/6 (pow.f64 x 3) x))

series24.0ms (0.8%)

Counts

2 → 24

Calls

2 calls:

12.0ms	(fma.f64 1/6 (pow.f64 x 3) x)
12.0ms	(fma.f64 1/120 (pow.f64 x 5) (fma.f64 1/6 (pow.f64 x 3) x))

simplify106.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

622×	`distribute-rgt-in_binary64`
618×	`distribute-lft-in_binary64`
484×	`associate-l_binary64`
426×	`associate-r_binary64`
400×	`unswap-sqr_binary64`

Counts

44 → 64

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	34	566
1	54	518
2	146	518
3	554	518
4	3054	518
5	3713	518
6	4901	518
7	4974	518
8	4863	518

prune22.0ms (0.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	63	3	66

Error

Counts

66 → 3

Alt Table

Status	Error	Program
▶	2.0b	(fma.f64 1/120 (pow.f64 x 5) (.f64 (.f64 (cbrt.f64 (fma.f64 1/6 (pow.f64 x 3) x)) (cbrt.f64 (fma.f64 1/6 (pow.f64 x 3) x))) (cbrt.f64 (fma.f64 1/6 (pow.f64 x 3) x))))
✓	58.9b	(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
✓	0.5b	(fma.f64 1/120 (pow.f64 x 5) (fma.f64 1/6 (pow.f64 x 3) x))

Compiler

Compiled 553 to 419 computations (24.2% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(*.f64 (cbrt.f64 (fma.f64 1/6 (pow.f64 x 3) x)) (cbrt.f64 (fma.f64 1/6 (pow.f64 x 3) x)))
	0.6b	(cbrt.f64 (fma.f64 1/6 (pow.f64 x 3) x))
	0.6b	(cbrt.f64 (fma.f64 1/6 (pow.f64 x 3) x))
✓	0.6b	(cbrt.f64 (fma.f64 1/6 (pow.f64 x 3) x))

rewrite10.0ms (0.3%)

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 1/6 (pow.f64 x 3) x)) (cbrt.f64 (fma.f64 1/6 (pow.f64 x 3) x)))
1.0ms	(cbrt.f64 (fma.f64 1/6 (pow.f64 x 3) x))

series25.0ms (0.8%)

Counts

2 → 24

Calls

2 calls:

13.0ms	(*.f64 (cbrt.f64 (fma.f64 1/6 (pow.f64 x 3) x)) (cbrt.f64 (fma.f64 1/6 (pow.f64 x 3) x)))
12.0ms	(cbrt.f64 (fma.f64 1/6 (pow.f64 x 3) x))

simplify95.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

430×	`cancel-sign-sub-inv_binary64`
329×	`fma-neg_binary64`
325×	`fma-def_binary64`
246×	`associate-l_binary64`
246×	`times-frac_binary64`

Counts

79 → 140

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	168	2402
1	426	2238
2	1028	1818
3	3371	1666
4	4987	1666

prune212.0ms (7.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	260	0	260
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	260	3	263

Error

Counts

263 → 3

Alt Table

Status	Error	Program
✓	2.0b	(fma.f64 1/120 (pow.f64 x 5) (.f64 (.f64 (cbrt.f64 (fma.f64 1/6 (pow.f64 x 3) x)) (cbrt.f64 (fma.f64 1/6 (pow.f64 x 3) x))) (cbrt.f64 (fma.f64 1/6 (pow.f64 x 3) x))))
✓	58.9b	(fma.f64 1/2 (exp.f64 x) (/.f64 -1/2 (exp.f64 x)))
✓	0.5b	(fma.f64 1/120 (pow.f64 x 5) (fma.f64 1/6 (pow.f64 x 3) x))

Compiler

Compiled 7850 to 6175 computations (21.3% saved)

regimes40.0ms (1.3%)

Accuracy

Total 0.6b remaining (97.2%)

Threshold costs 0.6b (97.2%)

Compiler

Compiled 648 to 494 computations (23.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	10	15

end1.0ms (0%)

Compiler: Compiled 12 to 9 computations (25% saved)

sample2.0s (68.4%)

Algorithm

1×

intervals

Results

1.2s	3970×	body	1024	valid
315.0ms	1996×	body	512	valid
126.0ms	408×	body	2048	valid
103.0ms	952×	body	256	valid
35.0ms	674×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 73 to 55 computations (24.7% saved)

Details

analyze78.0ms (2.6%)

sample63.0ms (2.1%)

simplify61.0ms (2.1%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

rewrite5.0ms (0.2%)

series28.0ms (1%)

simplify106.0ms (3.6%)

prune29.0ms (1%)

localize7.0ms (0.2%)

rewrite3.0ms (0.1%)

series24.0ms (0.8%)

simplify106.0ms (3.6%)

prune22.0ms (0.8%)

localize11.0ms (0.4%)

rewrite10.0ms (0.3%)

series25.0ms (0.8%)

simplify95.0ms (3.2%)

prune212.0ms (7.2%)

regimes40.0ms (1.3%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample2.0s (68.4%)

Profiling