Details

analyze74.0ms (3.6%)

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
25%	74.9%	0.1%	5
50%	50%	0.1%	6
62.4%	31.2%	6.3%	7
71.8%	21.9%	6.3%	8
76.5%	14%	9.5%	9
80.4%	10.1%	9.5%	10
82.3%	6.6%	11%	11
84.1%	4.9%	11%	12
85%	3.2%	11.8%	13
85.8%	2.4%	11.8%	14

Compiler

Compiled 12 to 10 computations (16.7% saved)

sample932.0ms (45.6%)

Results

895.0ms	8256×	body	128	valid
6.0ms	64×	body	128	invalid

Compiler

Compiled 35 to 29 computations (17.1% saved)

simplify8.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

18×	`fma-def_binary64`
13×	`distribute-lft-in_binary64`
13×	`distribute-rgt-in_binary64`
10×	`*-commutative_binary64`
9×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	10
1	18	10
2	32	8
3	56	8
4	68	8
5	74	8
6	66	8

prune3.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.2b	(*.f64 (fma.f64 x 3 -12/29) y)
	0.2b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)

Compiler

Compiled 55 to 43 computations (21.8% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x 3 -12/29)
✓	0.2b	(*.f64 (fma.f64 x 3 -12/29) y)

series8.0ms (0.4%)

Counts

2 → 36

Calls

2 calls:

6.0ms	(*.f64 (fma.f64 x 3 -12/29) y)
1.0ms	(fma.f64 x 3 -12/29)

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

3.0ms	(*.f64 (fma.f64 x 3 -12/29) y)
0.0ms	(fma.f64 x 3 -12/29)

simplify45.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

939×	`fma-def_binary64`
595×	`distribute-rgt-in_binary64`
593×	`distribute-lft-in_binary64`
497×	`associate-+r+_binary64`
408×	`associate-+l+_binary64`

Counts

66 → 60

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	50	691
1	91	531
2	246	531
3	644	531
4	2128	531
5	5282	531

prune48.0ms (2.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	53	7	60
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	55	7	62

Error

0.0b

Counts

62 → 7

Alt Table

Status	Error	Program
	27.2b	(*.f64 (log1p.f64 (expm1.f64 (fma.f64 x 3 -12/29))) y)
	0.2b	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
	0.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 x 3 -12/29)) (cbrt.f64 (fma.f64 x 3 -12/29))) (*.f64 (cbrt.f64 (fma.f64 x 3 -12/29)) y))
	30.8b	(.f64 (sqrt.f64 (.f64 (fma.f64 x 3 -12/29) y)) (sqrt.f64 (*.f64 (fma.f64 x 3 -12/29) y)))
	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 (fma.f64 x 3 -12/29) y)) (cbrt.f64 (.f64 (fma.f64 x 3 -12/29) y))) (cbrt.f64 (*.f64 (fma.f64 x 3 -12/29) y)))
	17.2b	(*.f64 (cbrt.f64 (pow.f64 (fma.f64 3 x -12/29) 3)) y)
▶	0.2b	(.f64 (-.f64 (.f64 3 x) 12/29) y)

Compiler

Compiled 841 to 618 computations (26.5% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 3 x) 12/29)
✓	0.2b	(.f64 (-.f64 (.f64 3 x) 12/29) y)

series7.0ms (0.4%)

Counts

2 → 15

Calls

2 calls:

6.0ms	(.f64 (-.f64 (.f64 3 x) 12/29) y)
2.0ms	(-.f64 (*.f64 3 x) 12/29)

rewrite10.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 42

Calls

2 calls:

6.0ms	(.f64 (-.f64 (.f64 3 x) 12/29) y)
3.0ms	(-.f64 (*.f64 3 x) 12/29)

simplify55.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

600×	`distribute-rgt-in_binary64`
596×	`distribute-lft-in_binary64`
498×	`associate-+r+_binary64`
410×	`associate-+l+_binary64`
366×	`fma-def_binary64`

Counts

57 → 75

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	87	586
1	179	473
2	422	471
3	983	468
4	2586	468
5	5023	468

prune60.0ms (2.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	73	2	75
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	76	6	82

Error

0.0b

Counts

82 → 6

Alt Table

Status	Error	Program
	0.2b	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
	11.5b	(/.f64 (.f64 y (fma.f64 x (.f64 x 9) -144/841)) (+.f64 (*.f64 3 x) 12/29))
	0.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 x 3 -12/29)) (cbrt.f64 (fma.f64 x 3 -12/29))) (*.f64 (cbrt.f64 (fma.f64 x 3 -12/29)) y))
	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 (fma.f64 x 3 -12/29) y)) (cbrt.f64 (.f64 (fma.f64 x 3 -12/29) y))) (cbrt.f64 (*.f64 (fma.f64 x 3 -12/29) y)))
▶	0.2b	(*.f64 (fma.f64 3 x (neg.f64 12/29)) y)
✓	0.2b	(.f64 (-.f64 (.f64 3 x) 12/29) y)

Compiler

Compiled 1138 to 872 computations (23.4% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 3 x (neg.f64 12/29))
✓	0.2b	(*.f64 (fma.f64 3 x (neg.f64 12/29)) y)

series8.0ms (0.4%)

Counts

2 → 36

Calls

2 calls:

6.0ms	(*.f64 (fma.f64 3 x (neg.f64 12/29)) y)
2.0ms	(fma.f64 3 x (neg.f64 12/29))

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

3.0ms	(*.f64 (fma.f64 3 x (neg.f64 12/29)) y)
0.0ms	(fma.f64 3 x (neg.f64 12/29))

simplify50.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

939×	`fma-def_binary64`
595×	`distribute-rgt-in_binary64`
593×	`distribute-lft-in_binary64`
497×	`associate-+r+_binary64`
408×	`associate-+l+_binary64`

Counts

66 → 59

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	50	691
1	89	531
2	246	531
3	644	531
4	2128	531
5	5282	531

prune36.0ms (1.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	59	0	59
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	59	6	65

Error

0.0b

Counts

65 → 6

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
	11.5b	(/.f64 (.f64 y (fma.f64 x (.f64 x 9) -144/841)) (+.f64 (*.f64 3 x) 12/29))
	0.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 x 3 -12/29)) (cbrt.f64 (fma.f64 x 3 -12/29))) (*.f64 (cbrt.f64 (fma.f64 x 3 -12/29)) y))
	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 (fma.f64 x 3 -12/29) y)) (cbrt.f64 (.f64 (fma.f64 x 3 -12/29) y))) (cbrt.f64 (*.f64 (fma.f64 x 3 -12/29) y)))
✓	0.2b	(*.f64 (fma.f64 3 x (neg.f64 12/29)) y)
✓	0.2b	(.f64 (-.f64 (.f64 3 x) 12/29) y)

Compiler

Compiled 837 to 624 computations (25.4% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
✓	0.1b	(*.f64 12/29 y)
✓	0.3b	(.f64 3 (.f64 y x))

series13.0ms (0.6%)

Counts

3 → 15

Calls

3 calls:

7.0ms	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
4.0ms	(.f64 3 (.f64 y x))
1.0ms	(*.f64 12/29 y)

rewrite12.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
10×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`

Counts

3 → 56

Calls

3 calls:

4.0ms	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
4.0ms	(.f64 3 (.f64 y x))
3.0ms	(*.f64 12/29 y)

simplify77.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

605×	`times-frac_binary64`
509×	`associate-l_binary64`
472×	`fma-neg_binary64`
366×	`associate-r_binary64`
288×	`distribute-rgt-in_binary64`

Counts

71 → 85

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	105	701
1	230	632
2	626	623
3	1846	614
4	3688	612
5	4571	612
6	5558	612

prune68.0ms (3.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	84	7	91

Error

Counts

91 → 7

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
	11.5b	(/.f64 (.f64 y (fma.f64 x (.f64 x 9) -144/841)) (+.f64 (*.f64 3 x) 12/29))
	0.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 x 3 -12/29)) (cbrt.f64 (fma.f64 x 3 -12/29))) (*.f64 (cbrt.f64 (fma.f64 x 3 -12/29)) y))
	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 (fma.f64 x 3 -12/29) y)) (cbrt.f64 (.f64 (fma.f64 x 3 -12/29) y))) (cbrt.f64 (*.f64 (fma.f64 x 3 -12/29) y)))
✓	0.2b	(*.f64 (fma.f64 3 x (neg.f64 12/29)) y)
	36.9b	(/.f64 (.f64 (.f64 y y) (fma.f64 9 (.f64 x x) -144/841)) (.f64 y (+.f64 (*.f64 3 x) 12/29)))
✓	0.2b	(.f64 (-.f64 (.f64 3 x) 12/29) y)

Compiler

Compiled 1265 to 824 computations (34.9% saved)

regimes394.0ms (19.3%)

Accuracy

Total 0.1b remaining (87.9%)

Threshold costs 0.1b (87.9%)

Counts

83 → 1

Compiler

Compiled 5950 to 4536 computations (23.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	8
1	13	8
2	12	8

end105.0ms (5.1%)

Compiler: Compiled 127 to 96 computations (24.4% saved)

Details

analyze74.0ms (3.6%)

sample932.0ms (45.6%)

simplify8.0ms (0.4%)

prune3.0ms (0.2%)

localize4.0ms (0.2%)

series8.0ms (0.4%)

rewrite4.0ms (0.2%)

simplify45.0ms (2.2%)

prune48.0ms (2.4%)

localize5.0ms (0.3%)

series7.0ms (0.4%)

rewrite10.0ms (0.5%)

simplify55.0ms (2.7%)

prune60.0ms (2.9%)

localize5.0ms (0.2%)

series8.0ms (0.4%)

rewrite4.0ms (0.2%)

simplify50.0ms (2.5%)

prune36.0ms (1.8%)

localize7.0ms (0.3%)

series13.0ms (0.6%)

rewrite12.0ms (0.6%)

simplify77.0ms (3.8%)

prune68.0ms (3.3%)

regimes394.0ms (19.3%)

simplify2.0ms (0.1%)

end105.0ms (5.1%)

Profiling