Details

analyze529.0ms (16.3%)

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
9.4%	90.5%	0.1%	6
14%	85.8%	0.1%	7
22.6%	77.2%	0.1%	8
37.8%	60.5%	1.7%	9
40%	56%	4%	10
47.3%	48.7%	4%	11
56.8%	36.2%	7%	12
58.6%	32.4%	9%	13
63.4%	27.5%	9%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample1.3s (39.6%)

Results

1.1s	8256×	body	128	valid
77.0ms	741×	body	128	invalid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify132.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

1119×	`div-sub_binary64`
816×	`fma-def_binary64`
804×	`fma-neg_binary64`
517×	`neg-mul-1_binary64`
483×	`neg-sub0_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	12	10
2	27	10
3	57	10
4	111	10
5	180	10
6	312	10
7	977	10
8	3166	10
9	3725	10
10	4150	10
11	4786	10
12	4803	10
13	4958	10
14	5387	10

prune2.0ms (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

14.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	14.9b	(/.f64 (*.f64 x (-.f64 y z)) y)

Compiler

Compiled 30 to 18 computations (40% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (-.f64 y z))
✓	14.2b	(/.f64 (*.f64 x (-.f64 y z)) y)

series22.0ms (0.7%)

Counts

2 → 72

Calls

2 calls:

15.0ms	(/.f64 (*.f64 x (-.f64 y z)) y)
7.0ms	(*.f64 x (-.f64 y z))

rewrite17.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 75

Calls

2 calls:

7.0ms	(/.f64 (*.f64 x (-.f64 y z)) y)
5.0ms	(*.f64 x (-.f64 y z))

simplify94.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

419×	`fma-neg_binary64`
321×	`div-sub_binary64`
313×	`associate-*l/_binary64`
290×	`associate-/r*_binary64`
263×	`fma-def_binary64`

Counts

147 → 108

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	157	1568
1	298	1439
2	1158	1383
3	3774	1383
4	4927	1383
5	5098	1383

prune59.0ms (1.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	102	6	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	6	109

Error

0.0b

Counts

109 → 6

Alt Table

Status	Error	Program
	6.7b	(.f64 (/.f64 x (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (-.f64 y z) (cbrt.f64 y)))
▶	2.8b	(/.f64 x (/.f64 y (-.f64 y z)))
	15.0b	(.f64 (.f64 x (-.f64 y z)) (/.f64 1 y))
	4.0b	(-.f64 x (/.f64 (*.f64 z x) y))
	3.3b	(*.f64 x (/.f64 (-.f64 y z) y))
	35.1b	(*.f64 (/.f64 x (sqrt.f64 y)) (/.f64 (-.f64 y z) (sqrt.f64 y)))

Compiler

Compiled 1781 to 519 computations (70.9% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series27.0ms (0.8%)

Counts

2 → 60

Calls

2 calls:

15.0ms	(/.f64 x (/.f64 y (-.f64 y z)))
12.0ms	(/.f64 y (-.f64 y z))

rewrite26.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
102×	`*-un-lft-identity_binary64`
102×	`add-sqr-sqrt_binary64`
70×	`add-cube-cbrt_binary64`
26×	`associate-/r*_binary64`

Counts

2 → 143

Calls

2 calls:

7.0ms	(/.f64 x (/.f64 y (-.f64 y z)))
4.0ms	(/.f64 y (-.f64 y z))

simplify127.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

862×	`fma-def_binary64`
516×	`associate-/r/_binary64`
497×	`times-frac_binary64`
463×	`associate-/l*_binary64`
459×	`associate-/l/_binary64`

Counts

203 → 210

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	248	3761
1	540	3647
2	1917	3540
3	4751	3528
4	5354	3528

prune100.0ms (3.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	206	4	210
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	210	6	216

Error

Counts

216 → 6

Alt Table

Status	Error	Program
	10.7b	(/.f64 (/.f64 x y) (/.f64 1 (-.f64 y z)))
	4.0b	(-.f64 x (/.f64 (*.f64 z x) y))
	6.7b	(.f64 (/.f64 x (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (-.f64 y z) (cbrt.f64 y)))
	31.5b	(/.f64 (sqrt.f64 x) (/.f64 (/.f64 y (-.f64 y z)) (sqrt.f64 x)))
	10.5b	(*.f64 (/.f64 x y) (-.f64 y z))
▶	3.3b	(*.f64 x (-.f64 1 (/.f64 z y)))

Compiler

Compiled 3685 to 879 computations (76.1% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.1b	(*.f64 x (-.f64 1 (/.f64 z y)))

series14.0ms (0.4%)

Counts

1 → 36

Calls

1 calls:

14.0ms

(*.f64 x (-.f64 1 (/.f64 z y)))

rewrite39.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`add-sqr-sqrt_binary64`
89×	`*-un-lft-identity_binary64`
85×	`add-cube-cbrt_binary64`
78×	`prod-diff_binary64`
74×	`times-frac_binary64`

Counts

1 → 133

Calls

1 calls:

11.0ms

(*.f64 x (-.f64 1 (/.f64 z y)))

simplify124.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

499×	`exp-prod_binary64`
444×	`fma-def_binary64`
426×	`associate-/l*_binary64`
424×	`*-commutative_binary64`
267×	`fma-neg_binary64`

Counts

169 → 154

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	240	2940
1	534	2507
2	1496	2031
3	3889	2031
4	4834	2031
5	5092	2031

prune98.0ms (3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	154	6	160

Error

Counts

160 → 6

Alt Table

Status	Error	Program
	10.7b	(/.f64 (/.f64 x y) (/.f64 1 (-.f64 y z)))
▶	4.0b	(-.f64 x (/.f64 (*.f64 z x) y))
	6.7b	(.f64 (/.f64 x (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (-.f64 y z) (cbrt.f64 y)))
	31.5b	(/.f64 (sqrt.f64 x) (/.f64 (/.f64 y (-.f64 y z)) (sqrt.f64 x)))
	10.5b	(*.f64 (/.f64 x y) (-.f64 y z))
✓	3.3b	(*.f64 x (-.f64 1 (/.f64 z y)))

Compiler

Compiled 4715 to 1667 computations (64.6% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 (*.f64 z x) y))
✓	6.1b	(/.f64 (*.f64 z x) y)

series29.0ms (0.9%)

Counts

2 → 18

Calls

2 calls:

17.0ms	(/.f64 (*.f64 z x) y)
11.0ms	(-.f64 x (/.f64 (*.f64 z x) y))

rewrite15.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
21×	`prod-diff_binary64`
20×	`add-cube-cbrt_binary64`
15×	`times-frac_binary64`

Counts

2 → 69

Calls

2 calls:

7.0ms	(-.f64 x (/.f64 (*.f64 z x) y))
3.0ms	(/.f64 (*.f64 z x) y)

simplify67.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

981×	`fma-def_binary64`
714×	`associate-/l*_binary64`
631×	`times-frac_binary64`
246×	`associate-/l/_binary64`
130×	`distribute-rgt-neg-in_binary64`

Counts

87 → 104

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	145	1424
1	334	1197
2	1130	1008
3	4401	1008
4	4909	1008

prune58.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	105	5	110

Error

Counts

110 → 5

Alt Table

Status	Error	Program
✓	3.3b	(*.f64 x (-.f64 1 (/.f64 z y)))
	4.1b	(-.f64 x (/.f64 1 (/.f64 y (*.f64 z x))))
	4.2b	(-.f64 x (*.f64 z (/.f64 x y)))
	10.7b	(/.f64 (/.f64 x y) (/.f64 1 (-.f64 y z)))
	31.5b	(/.f64 (sqrt.f64 x) (/.f64 (/.f64 y (-.f64 y z)) (sqrt.f64 x)))

Compiler

Compiled 1953 to 491 computations (74.9% saved)

regimes254.0ms (7.8%)

Accuracy

Total 1.4b remaining (98.9%)

Threshold costs 0b (0%)

Counts

55 → 3

Compiler

Compiled 3382 to 1866 computations (44.8% saved)

bsearch38.0ms (1.2%)

Steps

Iters	Range		Point
7	1.8445587745353324e+116	1.4893407459501468e+118	2.1939773630248555e+116
8	-7.457323989506932e+52	-9.858595396674092e+48	-1.715631163475474e+50

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
6×	`*-commutative_binary64`
5×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	76
1	44	76
2	56	76
3	63	76
4	66	76
5	66	76

end73.0ms (2.2%)

Compiler: Compiled 160 to 87 computations (45.6% saved)

Details

analyze529.0ms (16.3%)

sample1.3s (39.6%)

simplify132.0ms (4.1%)

prune2.0ms (0%)

localize5.0ms (0.2%)

series22.0ms (0.7%)

rewrite17.0ms (0.5%)

simplify94.0ms (2.9%)

prune59.0ms (1.8%)

localize5.0ms (0.1%)

series27.0ms (0.8%)

rewrite26.0ms (0.8%)

simplify127.0ms (3.9%)

prune100.0ms (3.1%)

localize5.0ms (0.1%)

series14.0ms (0.4%)

rewrite39.0ms (1.2%)

simplify124.0ms (3.8%)

prune98.0ms (3%)

localize5.0ms (0.1%)

series29.0ms (0.9%)

rewrite15.0ms (0.4%)

simplify67.0ms (2.1%)

prune58.0ms (1.8%)

regimes254.0ms (7.8%)

bsearch38.0ms (1.2%)

simplify4.0ms (0.1%)

end73.0ms (2.2%)

Profiling