Details

analyze14.0ms (0.6%)

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
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
93.7%	6.2%	0.1%	7
96.8%	3.1%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

Compiler

Compiled 22 to 13 computations (40.9% saved)

sample978.0ms (40%)

Results

921.0ms

8256×

body

128

valid

Compiler

Compiled 65 to 38 computations (41.5% saved)

simplify31.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-def_binary64`
456×	`cancel-sign-sub-inv_binary64`
430×	`times-frac_binary64`
358×	`div-sub_binary64`
252×	`distribute-frac-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	24	24
2	56	24
3	114	24
4	240	24
5	457	24
6	723	24
7	987	24
8	1607	24
9	3745	24

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

30.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	30.8b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

Compiler

Compiled 80 to 45 computations (43.8% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
✓	2.6b	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
✓	30.1b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

series32.0ms (1.3%)

Counts

3 → 72

Calls

3 calls:

15.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))
9.0ms	(+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
7.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))

rewrite83.0ms (3.4%)

Algorithm

1×	batch-egg-rewrite

Rules

450×	`fma-def_binary64`
279×	`egg-rr`
230×	`fma-neg_binary64`
208×	`expm1-udef_binary64`
208×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	50
1	237	46
2	3393	46

Stop Event

1×	node limit

Counts

3 → 279

Calls

3 calls:

77.0ms	(+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
77.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
77.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

simplify44.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

499×	`associate-*l/_binary64`
439×	`associate-*r/_binary64`
378×	`fma-def_binary64`
318×	`associate-/r/_binary64`
311×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	1038
1	124	984
2	352	972
3	1389	954

Stop Event

1×	node limit

Counts

351 → 301

prune219.0ms (9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	298	3	301
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	299	3	302

Error

0.4b

Counts

302 → 3

Alt Table

Status	Error	Program
	30.8b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (fma.f64 y (.f64 y 4) (*.f64 x x)))
▶	30.1b	(fma.f64 (*.f64 (/.f64 y x) (/.f64 y x)) -8 1)
	33.0b	(fma.f64 1/2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)

Compiler

Compiled 9324 to 5324 computations (42.9% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (*.f64 (/.f64 y x) (/.f64 y x)) -8 1)
✓	0.2b	(*.f64 (/.f64 y x) (/.f64 y x))

series44.0ms (1.8%)

Counts

2 → 48

Calls

2 calls:

24.0ms	(*.f64 (/.f64 y x) (/.f64 y x))
20.0ms	(fma.f64 (*.f64 (/.f64 y x) (/.f64 y x)) -8 1)

rewrite43.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

739×	`log1p-expm1-u_binary64`
739×	`expm1-log1p-u_binary64`
136×	`log1p-udef_binary64`
79×	`add-sqr-sqrt_binary64`
74×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	164	18
2	2054	18

Stop Event

1×	node limit

Counts

2 → 59

Calls

2 calls:

42.0ms	(fma.f64 (*.f64 (/.f64 y x) (/.f64 y x)) -8 1)
42.0ms	(*.f64 (/.f64 y x) (/.f64 y x))

simplify28.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

740×	`associate-/r*_binary64`
623×	`associate-*l/_binary64`
535×	`associate-/l/_binary64`
377×	`associate-/r/_binary64`
156×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	570
1	32	570
2	74	534
3	242	534
4	1326	534

Stop Event

1×	node limit

Counts

107 → 65

prune34.0ms (1.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	63	2	65
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	64	4	68

Error

0.4b

Counts

68 → 4

Alt Table

Status	Error	Program
▶	30.1b	(+.f64 1 (*.f64 (pow.f64 (/.f64 y x) 2) -8))
	30.8b	(fma.f64 (log.f64 (exp.f64 (pow.f64 (/.f64 y x) 2))) -8 1)
	30.8b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (fma.f64 y (.f64 y 4) (*.f64 x x)))
	33.0b	(fma.f64 1/2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)

Compiler

Compiled 885 to 560 computations (36.7% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (*.f64 (pow.f64 (/.f64 y x) 2) -8))
✓	0.0b	(*.f64 (pow.f64 (/.f64 y x) 2) -8)
✓	0.2b	(pow.f64 (/.f64 y x) 2)

series63.0ms (2.6%)

Counts

3 → 72

Calls

3 calls:

28.0ms	(*.f64 (pow.f64 (/.f64 y x) 2) -8)
24.0ms	(+.f64 1 (*.f64 (pow.f64 (/.f64 y x) 2) -8))
10.0ms	(pow.f64 (/.f64 y x) 2)

rewrite54.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

913×	`log1p-expm1-u_binary64`
913×	`expm1-log1p-u_binary64`
260×	`prod-diff_binary64`
97×	`add-sqr-sqrt_binary64`
93×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	212	28
2	2512	28

Stop Event

1×	node limit

Counts

3 → 83

Calls

3 calls:

52.0ms	(+.f64 1 (*.f64 (pow.f64 (/.f64 y x) 2) -8))
52.0ms	(*.f64 (pow.f64 (/.f64 y x) 2) -8)
52.0ms	(pow.f64 (/.f64 y x) 2)

simplify41.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

740×	`associate-/r*_binary64`
625×	`associate-*l/_binary64`
537×	`associate-/l/_binary64`
383×	`associate-/r/_binary64`
156×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	882
1	32	882
2	74	846
3	242	846
4	1333	846

Stop Event

1×	node limit

Counts

155 → 90

prune49.0ms (2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	90	4	94

Error

0.4b

Counts

94 → 4

Alt Table

Status	Error	Program
✓	30.1b	(+.f64 1 (*.f64 (pow.f64 (/.f64 y x) 2) -8))
	30.8b	(fma.f64 (log.f64 (exp.f64 (pow.f64 (/.f64 y x) 2))) -8 1)
▶	30.8b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (fma.f64 y (.f64 y 4) (*.f64 x x)))
	33.0b	(fma.f64 1/2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)

Compiler

Compiled 1346 to 887 computations (34.1% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y (.f64 y 4) (.f64 x x))
	2.6b	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
✓	30.1b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (fma.f64 y (.f64 y 4) (*.f64 x x)))

series22.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

15.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (fma.f64 y (.f64 y 4) (*.f64 x x)))
6.0ms	(fma.f64 y (.f64 y 4) (.f64 x x))

rewrite56.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

408×	`fma-def_binary64`
215×	`fma-neg_binary64`
202×	`expm1-udef_binary64`
202×	`log1p-udef_binary64`
175×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	37
1	233	35
2	3268	35

Stop Event

1×	node limit

Counts

2 → 78

Calls

2 calls:

54.0ms	(fma.f64 y (.f64 y 4) (.f64 x x))
54.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (fma.f64 y (.f64 y 4) (*.f64 x x)))

simplify34.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

500×	`associate-*l/_binary64`
457×	`associate-*r/_binary64`
357×	`fma-def_binary64`
319×	`associate-/r/_binary64`
296×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	771
1	116	753
2	329	741
3	1320	723

Stop Event

1×	node limit

Counts

126 → 98

prune176.0ms (7.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	265	0	265
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	265	4	269

Error

0.4b

Counts

269 → 4

Alt Table

Status	Error	Program
✓	30.1b	(+.f64 1 (*.f64 (pow.f64 (/.f64 y x) 2) -8))
	30.8b	(fma.f64 (log.f64 (exp.f64 (pow.f64 (/.f64 y x) 2))) -8 1)
✓	30.8b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (fma.f64 y (.f64 y 4) (*.f64 x x)))
	33.0b	(fma.f64 1/2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)

Compiler

Compiled 8026 to 4532 computations (43.5% saved)

regimes210.0ms (8.6%)

Accuracy

Total 11.9b remaining (98.6%)

Threshold costs 0b (0%)

Counts

19 → 5

Compiler

Compiled 1598 to 1034 computations (35.3% saved)

bsearch74.0ms (3%)

Steps

Iters	Range		Point
8	8.82690001033859e+99	1.4256352666301827e+104	1.2495046734520845e+104
10	4.5094345297390044e-116	2.818380447718831e-102	5.885754200942679e-107
8	-7.642869988049694e-143	-3.724985620701549e-147	-3.2812740382304326e-143
9	-1.9881961203309224e+152	-3.9036015836999328e+146	-3.940563540672608e+146

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	108
1	39	108

Stop Event

1×

saturated

end85.0ms (3.5%)

Compiler: Compiled 211 to 127 computations (39.8% saved)

Details

analyze14.0ms (0.6%)

sample978.0ms (40%)

simplify31.0ms (1.3%)

prune3.0ms (0.1%)

localize7.0ms (0.3%)

series32.0ms (1.3%)

rewrite83.0ms (3.4%)

simplify44.0ms (1.8%)

prune219.0ms (9%)

localize6.0ms (0.2%)

series44.0ms (1.8%)

rewrite43.0ms (1.8%)

simplify28.0ms (1.1%)

prune34.0ms (1.4%)

localize5.0ms (0.2%)

series63.0ms (2.6%)

rewrite54.0ms (2.2%)

simplify41.0ms (1.7%)

prune49.0ms (2%)

localize8.0ms (0.3%)

series22.0ms (0.9%)

rewrite56.0ms (2.3%)

simplify34.0ms (1.4%)

prune176.0ms (7.2%)

regimes210.0ms (8.6%)

bsearch74.0ms (3%)

simplify4.0ms (0.2%)

end85.0ms (3.5%)

Profiling