Details

analyze85.0ms (3.7%)

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)

sample962.0ms (41.7%)

Results

923.0ms	8256×	body	128	valid
7.0ms	74×	body	128	invalid

Compiler

Compiled 35 to 29 computations (17.1% saved)

simplify7.0ms (0.3%)

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 (0.1%)

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

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

rewrite7.0ms (0.3%)

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:

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

simplify55.0ms (2.4%)

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

prune54.0ms (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
	31.0b	(.f64 (.f64 (fma.f64 x 3 -12/29) (sqrt.f64 y)) (sqrt.f64 y))
	28.9b	(*.f64 (log1p.f64 (expm1.f64 (fma.f64 x 3 -12/29))) y)
▶	0.2b	(.f64 (-.f64 (.f64 3 x) 12/29) y)
	0.2b	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
	47.9b	(.f64 (sqrt.f64 (fma.f64 x 3 -12/29)) (.f64 (sqrt.f64 (fma.f64 x 3 -12/29)) y))
	19.9b	(.f64 (cbrt.f64 (.f64 (*.f64 (fma.f64 x 3 -12/29) (fma.f64 x 3 -12/29)) (fma.f64 x 3 -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))

Compiler

Compiled 827 to 606 computations (26.7% saved)

localize6.0ms (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)

series11.0ms (0.5%)

Counts

2 → 15

Calls

2 calls:

9.0ms	(.f64 (-.f64 (.f64 3 x) 12/29) y)
2.0ms	(-.f64 (*.f64 3 x) 12/29)

rewrite10.0ms (0.4%)

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)

simplify51.0ms (2.2%)

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

prune62.0ms (2.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	73	2	75
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	75	7	82

Error

0.0b

Counts

82 → 7

Alt Table

Status	Error	Program
	15.5b	(/.f64 (.f64 (-.f64 (.f64 (.f64 3 x) (.f64 3 x)) (.f64 12/29 12/29)) y) (+.f64 (.f64 3 x) 12/29))
✓	0.2b	(.f64 (-.f64 (.f64 3 x) 12/29) y)
	31.0b	(.f64 (.f64 (fma.f64 x 3 -12/29) (sqrt.f64 y)) (sqrt.f64 y))
	19.9b	(*.f64 (/.f64 (fma.f64 27 (pow.f64 x 3) -1728/24389) (fma.f64 x (fma.f64 x 9 36/29) 144/841)) y)
▶	0.2b	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
	47.9b	(.f64 (sqrt.f64 (fma.f64 x 3 -12/29)) (.f64 (sqrt.f64 (fma.f64 x 3 -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))

Compiler

Compiled 1170 to 898 computations (23.2% saved)

localize11.0ms (0.5%)

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))

series19.0ms (0.8%)

Counts

3 → 15

Calls

3 calls:

10.0ms	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
7.0ms	(.f64 3 (.f64 y x))
2.0ms	(*.f64 12/29 y)

rewrite12.0ms (0.5%)

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))
3.0ms	(.f64 3 (.f64 y x))
2.0ms	(*.f64 12/29 y)

simplify90.0ms (3.9%)

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

prune86.0ms (3.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	82	3	85
Fresh	4	1	5
Picked	1	0	1
Done	0	1	1
Total	87	5	92

Error

Counts

92 → 5

Alt Table

Status	Error	Program
	15.5b	(/.f64 (.f64 (-.f64 (.f64 (.f64 3 x) (.f64 3 x)) (.f64 12/29 12/29)) y) (+.f64 (.f64 3 x) 12/29))
✓	0.2b	(.f64 (-.f64 (.f64 3 x) 12/29) y)
	0.3b	(-.f64 (.f64 3 (.f64 y x)) (.f64 (.f64 (cbrt.f64 12/29) (cbrt.f64 12/29)) (*.f64 (cbrt.f64 12/29) y)))
▶	0.2b	(-.f64 (.f64 (.f64 3 y) x) (*.f64 12/29 y))
	0.4b	(-.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (.f64 y x))) (.f64 12/29 y))

Compiler

Compiled 1293 to 851 computations (34.2% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 (.f64 3 y) x) (*.f64 12/29 y))
	0.1b	(*.f64 12/29 y)
✓	0.2b	(.f64 (.f64 3 y) x)

series11.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

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

rewrite9.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
4×	`add-log-exp_binary64`
3×	`associate-r_binary64`

Counts

2 → 36

Calls

2 calls:

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

simplify83.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

684×	`fma-def_binary64`
568×	`fma-neg_binary64`
419×	`distribute-rgt-neg-in_binary64`
285×	`*-commutative_binary64`
215×	`cancel-sign-sub-inv_binary64`

Counts

84 → 61

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	84	813
1	207	746
2	678	736
3	1414	725
4	2819	723
5	4514	723
6	4843	723

prune63.0ms (2.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	83	5	88

Error

Counts

88 → 5

Alt Table

Status	Error	Program
	15.5b	(/.f64 (.f64 (-.f64 (.f64 (.f64 3 x) (.f64 3 x)) (.f64 12/29 12/29)) y) (+.f64 (.f64 3 x) 12/29))
✓	0.2b	(.f64 (-.f64 (.f64 3 x) 12/29) y)
	0.3b	(-.f64 (.f64 3 (.f64 y x)) (.f64 (.f64 (cbrt.f64 12/29) (cbrt.f64 12/29)) (*.f64 (cbrt.f64 12/29) y)))
✓	0.2b	(-.f64 (.f64 (.f64 3 y) x) (*.f64 12/29 y))
	0.4b	(-.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (.f64 y x))) (.f64 12/29 y))

Compiler

Compiled 1207 to 846 computations (29.9% saved)

regimes500.0ms (21.7%)

Accuracy

Total 0.2b remaining (92.9%)

Threshold costs 0.2b (92.9%)

Counts

96 → 1

Compiler

Compiled 6595 to 5056 computations (23.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	10	11
2	10	11

end92.0ms (4%)

Compiler: Compiled 94 to 73 computations (22.3% saved)

Details

analyze85.0ms (3.7%)

sample962.0ms (41.7%)

simplify7.0ms (0.3%)

prune3.0ms (0.1%)

localize4.0ms (0.2%)

series8.0ms (0.4%)

rewrite7.0ms (0.3%)

simplify55.0ms (2.4%)

prune54.0ms (2.4%)

localize6.0ms (0.3%)

series11.0ms (0.5%)

rewrite10.0ms (0.4%)

simplify51.0ms (2.2%)

prune62.0ms (2.7%)

localize11.0ms (0.5%)

series19.0ms (0.8%)

rewrite12.0ms (0.5%)

simplify90.0ms (3.9%)

prune86.0ms (3.7%)

localize5.0ms (0.2%)

series11.0ms (0.5%)

rewrite9.0ms (0.4%)

simplify83.0ms (3.6%)

prune63.0ms (2.8%)

regimes500.0ms (21.7%)

simplify2.0ms (0.1%)

end92.0ms (4%)

Profiling