Details

analyze550.0ms (19.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
14%	85.8%	0.1%	7
22.6%	77.2%	0.1%	8
23.8%	74.5%	1.7%	9
40%	56.4%	3.7%	10
46.9%	48.7%	4.4%	11
48%	45.8%	6.2%	12
58.1%	32.2%	9.7%	13
62.1%	27.2%	10.6%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample1.1s (38.7%)

Results

851.0ms	8256×	body	128	valid
111.0ms	1064×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify54.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

823×	`div-sub_binary64`
529×	`fma-neg_binary64`
475×	`distribute-rgt-in_binary64`
409×	`fma-def_binary64`
380×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	25	11
2	50	11
3	156	11
4	331	11
5	666	11
6	1744	11
7	3988	11
8	4953	11

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

8.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	8.2b	(/.f64 (fma.f64 x (-.f64 y z) x) z)

Compiler

Compiled 42 to 22 computations (47.6% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (-.f64 y z) x)
✓	7.6b	(/.f64 (fma.f64 x (-.f64 y z) x) z)

series25.0ms (0.9%)

Counts

2 → 72

Calls

2 calls:

15.0ms	(/.f64 (fma.f64 x (-.f64 y z) x) z)
9.0ms	(fma.f64 x (-.f64 y z) x)

rewrite4.0ms (0.1%)

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:

2.0ms	(/.f64 (fma.f64 x (-.f64 y z) x) z)
0.0ms	(fma.f64 x (-.f64 y z) x)

simplify71.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

672×	`associate-/l*_binary64`
629×	`fma-def_binary64`
448×	`associate-/l/_binary64`
308×	`associate-/r*_binary64`
291×	`associate-/r/_binary64`

Counts

111 → 73

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	82	1522
1	160	1371
2	374	1332
3	1227	1332
4	4358	1332
5	5042	1332

prune50.0ms (1.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	65	8	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	8	74

Error

Counts

74 → 8

Alt Table

Status	Error	Program
	9.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (-.f64 y z) x)) (cbrt.f64 (fma.f64 x (-.f64 y z) x))) (/.f64 (cbrt.f64 (fma.f64 x (-.f64 y z) x)) z))
▶	2.2b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
	39.9b	(cbrt.f64 (pow.f64 (-.f64 (/.f64 (fma.f64 y x x) z) x) 3))
	35.2b	(/.f64 (/.f64 (fma.f64 x (-.f64 y z) x) (sqrt.f64 z)) (sqrt.f64 z))
	8.3b	(*.f64 (fma.f64 x (-.f64 y z) x) (/.f64 1 z))
	8.3b	(/.f64 1 (/.f64 z (fma.f64 x (-.f64 y z) x)))
	9.2b	(.f64 (/.f64 1 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (fma.f64 x (-.f64 y z) x) (cbrt.f64 z)))
	34.3b	(*.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) (/.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) z))

Compiler

Compiled 1227 to 331 computations (73% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.4b	(fma.f64 (/.f64 x z) y (/.f64 x z))

series18.0ms (0.7%)

Counts

1 → 36

Calls

1 calls:

18.0ms

(fma.f64 (/.f64 x z) y (/.f64 x z))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (/.f64 x z) y (/.f64 x z))

simplify78.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

662×	`associate-*l/_binary64`
661×	`times-frac_binary64`
661×	`fma-def_binary64`
537×	`associate-*r/_binary64`
435×	`distribute-rgt-in_binary64`

Counts

46 → 25

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	26	610
1	40	577
2	78	557
3	204	392
4	784	392
5	3618	392
6	4565	392
7	4941	392
8	4972	392

prune23.0ms (0.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	24	1	25
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	25	8	33

Error

Counts

33 → 8

Alt Table

Status	Error	Program
	9.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (-.f64 y z) x)) (cbrt.f64 (fma.f64 x (-.f64 y z) x))) (/.f64 (cbrt.f64 (fma.f64 x (-.f64 y z) x)) z))
✓	2.2b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
	35.2b	(/.f64 (/.f64 (fma.f64 x (-.f64 y z) x) (sqrt.f64 z)) (sqrt.f64 z))
	8.3b	(*.f64 (fma.f64 x (-.f64 y z) x) (/.f64 1 z))
	8.3b	(/.f64 1 (/.f64 z (fma.f64 x (-.f64 y z) x)))
	9.2b	(.f64 (/.f64 1 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (fma.f64 x (-.f64 y z) x) (cbrt.f64 z)))
	34.3b	(*.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) (/.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) z))
▶	5.4b	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)

Compiler

Compiled 588 to 210 computations (64.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 y z) (/.f64 1 z))
✓	5.1b	(*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x)

series23.0ms (0.8%)

Counts

2 → 39

Calls

2 calls:

17.0ms	(*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x)
6.0ms	(+.f64 (/.f64 y z) (/.f64 1 z))

rewrite26.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`*-un-lft-identity_binary64`
23×	`times-frac_binary64`
17×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
13×	`fma-def_binary64`

Counts

2 → 68

Calls

2 calls:

13.0ms	(*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x)
9.0ms	(+.f64 (/.f64 y z) (/.f64 1 z))

simplify48.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

976×	`fma-def_binary64`
819×	`distribute-rgt-in_binary64`
779×	`distribute-lft-in_binary64`
400×	`times-frac_binary64`
246×	`associate-l_binary64`

Counts

107 → 106

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	86	1217
1	198	1132
2	556	932
3	1586	921
4	5383	921

prune74.0ms (2.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	107	7	114

Error

Counts

114 → 7

Alt Table

Status	Error	Program
	35.2b	(/.f64 (/.f64 (fma.f64 x (-.f64 y z) x) (sqrt.f64 z)) (sqrt.f64 z))
	8.3b	(*.f64 (fma.f64 x (-.f64 y z) x) (/.f64 1 z))
	8.3b	(/.f64 1 (/.f64 z (fma.f64 x (-.f64 y z) x)))
	9.2b	(.f64 (/.f64 1 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (fma.f64 x (-.f64 y z) x) (cbrt.f64 z)))
	34.3b	(*.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) (/.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) z))
▶	5.4b	(-.f64 (*.f64 (/.f64 (+.f64 1 y) z) x) x)
✓	2.2b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)

Compiler

Compiled 1966 to 954 computations (51.5% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 1 y) z)
✓	5.1b	(*.f64 (/.f64 (+.f64 1 y) z) x)

series19.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

13.0ms	(*.f64 (/.f64 (+.f64 1 y) z) x)
5.0ms	(/.f64 (+.f64 1 y) z)

rewrite16.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`*-un-lft-identity_binary64`
25×	`times-frac_binary64`
25×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
16×	`associate-l_binary64`

Counts

2 → 72

Calls

2 calls:

6.0ms	(/.f64 (+.f64 1 y) z)
6.0ms	(*.f64 (/.f64 (+.f64 1 y) z) x)

simplify102.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

690×	`distribute-rgt-in_binary64`
656×	`distribute-lft-in_binary64`
507×	`fma-def_binary64`
454×	`associate-/r/_binary64`
232×	`associate-l_binary64`

Counts

120 → 122

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	109	1532
1	252	1447
2	610	1262
3	1884	1226
4	4653	1226
5	4820	1226
6	5219	1226

prune79.0ms (2.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	122	7	129

Error

Counts

129 → 7

Alt Table

Status	Error	Program
	35.2b	(/.f64 (/.f64 (fma.f64 x (-.f64 y z) x) (sqrt.f64 z)) (sqrt.f64 z))
	8.3b	(*.f64 (fma.f64 x (-.f64 y z) x) (/.f64 1 z))
	8.3b	(/.f64 1 (/.f64 z (fma.f64 x (-.f64 y z) x)))
	9.2b	(.f64 (/.f64 1 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (fma.f64 x (-.f64 y z) x) (cbrt.f64 z)))
	34.3b	(*.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) (/.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) z))
✓	5.4b	(-.f64 (*.f64 (/.f64 (+.f64 1 y) z) x) x)
✓	2.2b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)

Compiler

Compiled 2027 to 1144 computations (43.6% saved)

regimes306.0ms (11%)

Accuracy

Total 0.2b remaining (97%)

Threshold costs 0.2b (97%)

Counts

60 → 3

Compiler

Compiled 3572 to 1934 computations (45.9% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
5×	`*-commutative_binary64`
5×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	78
1	38	78
2	46	78
3	50	78
4	52	78
5	51	78

end99.0ms (3.6%)

Compiler: Compiled 218 to 123 computations (43.6% saved)

Details

analyze550.0ms (19.8%)

sample1.1s (38.7%)

simplify54.0ms (1.9%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series25.0ms (0.9%)

rewrite4.0ms (0.1%)

simplify71.0ms (2.6%)

prune50.0ms (1.8%)

localize5.0ms (0.2%)

series18.0ms (0.7%)

rewrite1.0ms (0%)

simplify78.0ms (2.8%)

prune23.0ms (0.8%)

localize6.0ms (0.2%)

series23.0ms (0.8%)

rewrite26.0ms (0.9%)

simplify48.0ms (1.7%)

prune74.0ms (2.7%)

localize6.0ms (0.2%)

series19.0ms (0.7%)

rewrite16.0ms (0.6%)

simplify102.0ms (3.7%)

prune79.0ms (2.8%)

regimes306.0ms (11%)

bsearch3.0ms (0.1%)

simplify4.0ms (0.1%)

end99.0ms (3.6%)

Profiling