Details

analyze1.5s (19%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
12.5%	87.3%	0.2%	7
15.6%	84.2%	0.2%	8
28.1%	71.7%	0.2%	9
37.4%	62.4%	0.2%	10
43.7%	56.1%	0.2%	11
53%	46.8%	0.2%	12
64.1%	35.6%	0.3%	13
66.7%	32.8%	0.5%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample62.0ms (0.8%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
2.0ms	21×	body	128	invalid

Compiler

Compiled 35 to 25 computations (28.6% saved)

simplify144.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1226×	`div-sub_binary64`
778×	`fma-def_binary64`
701×	`unsub-neg_binary64`
456×	`sub-neg_binary64`
437×	`fma-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	22	16
2	50	16
3	121	16
4	299	16
5	674	16
6	1361	16
7	2742	16
8	3706	16
9	3871	16
10	4083	16
11	4304	16
12	4387	16
13	5424	16

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

1.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	1.1b	(-.f64 1 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

Compiler

Compiled 45 to 30 computations (33.3% saved)

localize15.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 y z) (-.f64 y t))
✓	6.2b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

rewrite43.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

2 → 89

Calls

2 calls:

16.0ms	(*.f64 (-.f64 y z) (-.f64 y t))
14.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

series305.0ms (3.9%)

Counts

2 → 84

Calls

2 calls:

268.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))
36.0ms	(*.f64 (-.f64 y z) (-.f64 y t))

simplify220.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

744×	`times-frac_binary64`
589×	`associate-/l*_binary64`
505×	`associate-/r*_binary64`
195×	`fma-def_binary64`
134×	`*-commutative_binary64`

Counts

173 → 318

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	444	5989
1	1376	5678
2	5010	5678

prune338.0ms (4.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	313	5	318
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	314	5	319

Error

Counts

319 → 5

Alt Table

Status	Error	Program
▶	1.1b	(-.f64 1 (/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)))
	1.8b	(-.f64 1 (*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 y t))))
	7.3b	(-.f64 1 (/.f64 x (-.f64 (fma.f64 y y (.f64 t z)) (.f64 y (+.f64 z t)))))
	1.3b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
	14.2b	(-.f64 1 (.f64 (/.f64 x (.f64 (-.f64 y z) (-.f64 (.f64 y y) (.f64 t t)))) (+.f64 y t)))

Compiler

Compiled 6328 to 2609 computations (58.8% saved)

localize23.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (-.f64 y z) (-.f64 y t))
✓	0.3b	(/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x))
✓	6.2b	(/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)

rewrite52.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
28×	`add-exp-log_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`

Counts

2 → 89

Calls

2 calls:

23.0ms	(/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x))
18.0ms	(/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)

series384.0ms (4.9%)

Counts

2 → 96

Calls

2 calls:

259.0ms	(/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x))
124.0ms	(/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)

simplify253.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

786×	`times-frac_binary64`
597×	`associate-/l*_binary64`
482×	`associate-/r*_binary64`
193×	`fma-def_binary64`
158×	`associate-/r/_binary64`

Counts

185 → 343

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	401	6774
1	1379	6393
2	5094	6393

prune522.0ms (6.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	520	0	520
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	520	5	525

Error

Counts

525 → 5

Alt Table

Status	Error	Program
✓	1.1b	(-.f64 1 (/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)))
	1.8b	(-.f64 1 (*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 y t))))
	7.3b	(-.f64 1 (/.f64 x (-.f64 (fma.f64 y y (.f64 t z)) (.f64 y (+.f64 z t)))))
▶	1.3b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
	14.2b	(-.f64 1 (.f64 (/.f64 x (.f64 (-.f64 y z) (-.f64 (.f64 y y) (.f64 t t)))) (+.f64 y t)))

Compiler

Compiled 8652 to 3607 computations (58.3% saved)

localize15.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 y z))
✓	3.2b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t))

rewrite55.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

210×	`times-frac_binary64`
176×	`*-un-lft-identity_binary64`
176×	`add-sqr-sqrt_binary64`
88×	`add-cube-cbrt_binary64`
44×	`distribute-lft-out--_binary64`

Counts

2 → 189

Calls

2 calls:

22.0ms	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t))
6.0ms	(/.f64 x (-.f64 y z))

series321.0ms (4.1%)

Counts

2 → 72

Calls

2 calls:

295.0ms	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t))
25.0ms	(/.f64 x (-.f64 y z))

simplify321.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

709×	`times-frac_binary64`
587×	`associate-/l*_binary64`
544×	`associate-/r*_binary64`
305×	`associate-/l/_binary64`
166×	`fma-def_binary64`

Counts

261 → 425

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	547	9298
1	1717	9038
2	5431	9038

prune199.0ms (2.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	425	0	425
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	425	5	430

Error

Counts

430 → 5

Alt Table

Status	Error	Program
✓	1.1b	(-.f64 1 (/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)))
▶	1.8b	(-.f64 1 (*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 y t))))
	7.3b	(-.f64 1 (/.f64 x (-.f64 (fma.f64 y y (.f64 t z)) (.f64 y (+.f64 z t)))))
✓	1.3b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
	14.2b	(-.f64 1 (.f64 (/.f64 x (.f64 (-.f64 y z) (-.f64 (.f64 y y) (.f64 t t)))) (+.f64 y t)))

Compiler

Compiled 8406 to 2987 computations (64.5% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 y z))
✓	0.0b	(/.f64 x (-.f64 y t))
✓	2.6b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 y t)))

rewrite32.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`add-sqr-sqrt_binary64`
71×	`*-un-lft-identity_binary64`
67×	`times-frac_binary64`
41×	`add-cube-cbrt_binary64`
31×	`add-exp-log_binary64`

Counts

3 → 156

Calls

3 calls:

15.0ms	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 y t)))
5.0ms	(/.f64 x (-.f64 y t))
4.0ms	(/.f64 1 (-.f64 y z))

series175.0ms (2.3%)

Counts

3 → 96

Calls

3 calls:

135.0ms	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 y t)))
33.0ms	(/.f64 x (-.f64 y t))
6.0ms	(/.f64 1 (-.f64 y z))

simplify151.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

868×	`times-frac_binary64`
672×	`associate-/l*_binary64`
510×	`associate-/r*_binary64`
168×	`fma-def_binary64`
125×	`*-commutative_binary64`

Counts

252 → 437

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	478	7409
1	1534	6993
2	5206	6993

prune239.0ms (3.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	437	0	437
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	437	5	442

Error

Counts

442 → 5

Alt Table

Status	Error	Program
✓	1.1b	(-.f64 1 (/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)))
✓	1.8b	(-.f64 1 (*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 y t))))
	7.3b	(-.f64 1 (/.f64 x (-.f64 (fma.f64 y y (.f64 t z)) (.f64 y (+.f64 z t)))))
✓	1.3b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
	14.2b	(-.f64 1 (.f64 (/.f64 x (.f64 (-.f64 y z) (-.f64 (.f64 y y) (.f64 t t)))) (+.f64 y t)))

Compiler

Compiled 8113 to 3531 computations (56.5% saved)

regimes495.0ms (6.4%)

Accuracy

Total 0.8b remaining (99.2%)

Threshold costs 0.8b (99.2%)

Compiler

Compiled 10384 to 6909 computations (33.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
10×	`sub-neg_binary64`
8×	`*-commutative_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	28
1	26	28
2	43	28
3	59	28
4	69	28
5	73	28
6	74	28
7	73	28

end6.0ms (0.1%)

Compiler: Compiled 66 to 39 computations (40.9% saved)

sample1.9s (24.6%)

Algorithm

1×

intervals

Results

589.0ms	8000×	body	128	valid
35.0ms	392×	body	128	invalid

Compiler

Compiled 134 to 88 computations (34.3% saved)

Details

analyze1.5s (19%)

sample62.0ms (0.8%)

simplify144.0ms (1.8%)

prune3.0ms (0%)

localize15.0ms (0.2%)

rewrite43.0ms (0.6%)

series305.0ms (3.9%)

simplify220.0ms (2.8%)

prune338.0ms (4.3%)

localize23.0ms (0.3%)

rewrite52.0ms (0.7%)

series384.0ms (4.9%)

simplify253.0ms (3.3%)

prune522.0ms (6.7%)

localize15.0ms (0.2%)

rewrite55.0ms (0.7%)

series321.0ms (4.1%)

simplify321.0ms (4.1%)

prune199.0ms (2.6%)

localize10.0ms (0.1%)

rewrite32.0ms (0.4%)

series175.0ms (2.3%)

simplify151.0ms (1.9%)

prune239.0ms (3.1%)

regimes495.0ms (6.4%)

simplify4.0ms (0.1%)

end6.0ms (0.1%)

sample1.9s (24.6%)

Profiling