Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample784.0ms (26.8%)

Results

747.0ms

8256×

body

128

valid

Compiler

Compiled 38 to 28 computations (26.3% saved)

simplify16.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

164×	`fma-neg_binary64`
99×	`rules-40_binary64`
99×	`rules-41_binary64`
99×	`rules-42_binary64`
99×	`rules-43_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	41	10
2	106	10
3	374	10
4	18	10

prune2.0ms (0.1%)

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

7.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	7.9b	(/.f64 10 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 24 to 18 computations (25% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 10 (-.f64 1 (*.f64 x x)))
✓	7.9b	(-.f64 1 (*.f64 x x))

series8.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(/.f64 10 (-.f64 1 (*.f64 x x)))
2.0ms	(-.f64 1 (*.f64 x x))

rewrite115.0ms (3.9%)

Algorithm

2×	batch-egg-rewrite

Rules

631×	`log1p-expm1-u_binary64`
631×	`expm1-log1p-u_binary64`
471×	`fma-neg_binary64`
240×	`prod-diff_binary64`
224×	`fma-udef_binary64`

Counts

2 → 76

Calls

2 calls:

113.0ms	(/.f64 10 (-.f64 1 (*.f64 x x)))
113.0ms	(-.f64 1 (*.f64 x x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	164	17
2	1840	17
3	4975	17
4	4899	17
5	5220	17
0	0	0
1	0	0

simplify35.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

487×	`rules-13_binary64`
454×	`fma-def_binary64`
421×	`fma-neg_binary64`
367×	`rules-14-rev_binary64`
330×	`rules-40_binary64`

Counts

100 → 96

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	42	305
1	295	296
2	1158	293
3	5074	293

prune44.0ms (1.5%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	1	97

Error

0.2b

Counts

97 → 1

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 10 (+.f64 (-.f64 1 (.f64 x x)) (fma.f64 (neg.f64 x) x (.f64 x x))))

Compiler

Compiled 1366 to 904 computations (33.8% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 10 (+.f64 (-.f64 1 (.f64 x x)) (fma.f64 (neg.f64 x) x (.f64 x x))))
	7.9b	(-.f64 1 (*.f64 x x))
✓	61.9b	(fma.f64 (neg.f64 x) x (*.f64 x x))

series11.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

7.0ms	(fma.f64 (neg.f64 x) x (*.f64 x x))
4.0ms	(/.f64 10 (+.f64 (-.f64 1 (.f64 x x)) (fma.f64 (neg.f64 x) x (.f64 x x))))

rewrite64.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

810×	`fma-neg_binary64`
689×	`prod-diff_binary64`
181×	`expm1-udef_binary64`
181×	`log1p-udef_binary64`
104×	`add-sqr-sqrt_binary64`

Counts

2 → 62

Calls

2 calls:

63.0ms	(/.f64 10 (+.f64 (-.f64 1 (.f64 x x)) (fma.f64 (neg.f64 x) x (.f64 x x))))
63.0ms	(fma.f64 (neg.f64 x) x (*.f64 x x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	32
1	240	32
2	2923	20
3	4892	20
0	0	0
1	0	0

simplify36.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

482×	`rules-13_binary64`
454×	`fma-def_binary64`
412×	`fma-neg_binary64`
367×	`rules-14-rev_binary64`
323×	`rules-40_binary64`

Counts

86 → 78

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	239
1	283	230
2	1120	227
3	5010	227

prune76.0ms (2.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	125	5	130
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	125	6	131

Error

0.1b

Counts

131 → 6

Alt Table

Status	Error	Program
▶	0.4b	(/.f64 10 (+.f64 (/.f64 (pow.f64 (-.f64 1 (.f64 x x)) 3) (+.f64 (pow.f64 (-.f64 1 (.f64 x x)) 2) (-.f64 0 (.f64 (-.f64 1 (.f64 x x)) 0)))) (fma.f64 (neg.f64 x) x (*.f64 x x))))
✓	0.2b	(/.f64 10 (+.f64 (-.f64 1 (.f64 x x)) (fma.f64 (neg.f64 x) x (.f64 x x))))
	0.7b	(/.f64 10 (+.f64 (cbrt.f64 (pow.f64 (-.f64 1 (.f64 x x)) 3)) (fma.f64 (neg.f64 x) x (.f64 x x))))
	1.3b	(/.f64 10 (+.f64 (.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 x x))) 2) (cbrt.f64 (-.f64 1 (.f64 x x)))) (fma.f64 (neg.f64 x) x (.f64 x x))))
	0.5b	(.f64 (+.f64 (pow.f64 (-.f64 1 (.f64 x x)) 2) (-.f64 (pow.f64 (fma.f64 (neg.f64 x) x (.f64 x x)) 2) (.f64 (fma.f64 (neg.f64 x) x (.f64 x x)) (-.f64 1 (.f64 x x))))) (/.f64 10 (+.f64 (pow.f64 (fma.f64 (neg.f64 x) x (.f64 x x)) 3) (pow.f64 (-.f64 1 (.f64 x x)) 3))))
	25.4b	(/.f64 10 (+.f64 (pow.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 2) (fma.f64 (neg.f64 x) x (.f64 x x))))

Compiler

Compiled 2831 to 1427 computations (49.6% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (-.f64 1 (*.f64 x x)) 2)
✓	0.7b	(pow.f64 (-.f64 1 (*.f64 x x)) 3)
	7.9b	(-.f64 1 (*.f64 x x))
	61.9b	(fma.f64 (neg.f64 x) x (*.f64 x x))

series9.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

6.0ms	(pow.f64 (-.f64 1 (*.f64 x x)) 2)
3.0ms	(pow.f64 (-.f64 1 (*.f64 x x)) 3)

rewrite71.0ms (2.4%)

Algorithm

2×	batch-egg-rewrite

Rules

700×	`log1p-expm1-u_binary64`
700×	`expm1-log1p-u_binary64`
279×	`prod-diff_binary64`
142×	`egg-rr`
78×	`add-sqr-sqrt_binary64`

Counts

2 → 142

Calls

2 calls:

68.0ms	(pow.f64 (-.f64 1 (*.f64 x x)) 2)
68.0ms	(pow.f64 (-.f64 1 (*.f64 x x)) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	211	20
2	2066	20
3	5009	20
0	0	0
1	0	0

simplify71.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

745×	`rules-40_binary64`
745×	`rules-41_binary64`
745×	`rules-42_binary64`
745×	`rules-43_binary64`
705×	`rules-21_binary64`

Counts

166 → 161

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	26	322
1	173	311
2	585	297
3	2807	297
4	4507	297
5	4992	297

prune463.0ms (15.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	348	3	351
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	349	8	357

Error

0.1b

Counts

357 → 8

Alt Table

Status	Error	Program
	0.7b	(/.f64 10 (+.f64 (cbrt.f64 (pow.f64 (-.f64 1 (.f64 x x)) 3)) (fma.f64 (neg.f64 x) x (.f64 x x))))
	0.8b	(/.f64 10 (+.f64 (/.f64 (pow.f64 (-.f64 1 (.f64 x x)) 3) (+.f64 (cbrt.f64 (pow.f64 (-.f64 1 (.f64 x x)) 6)) (-.f64 0 (.f64 (-.f64 1 (.f64 x x)) 0)))) (fma.f64 (neg.f64 x) x (*.f64 x x))))
	0.5b	(/.f64 10 (+.f64 (/.f64 (pow.f64 (-.f64 1 (.f64 x x)) 3) (+.f64 (/.f64 (-.f64 1 (.f64 x x)) (/.f64 1 (-.f64 1 (.f64 x x)))) (-.f64 0 (.f64 (-.f64 1 (.f64 x x)) 0)))) (fma.f64 (neg.f64 x) x (.f64 x x))))
▶	0.3b	(/.f64 10 (+.f64 (/.f64 (.f64 (-.f64 1 (.f64 x x)) (pow.f64 (-.f64 1 (.f64 x x)) 2)) (+.f64 (pow.f64 (-.f64 1 (.f64 x x)) 2) (-.f64 0 (.f64 (-.f64 1 (.f64 x x)) 0)))) (fma.f64 (neg.f64 x) x (*.f64 x x))))
	1.3b	(/.f64 10 (+.f64 (.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 x x))) 2) (cbrt.f64 (-.f64 1 (.f64 x x)))) (fma.f64 (neg.f64 x) x (.f64 x x))))
✓	0.2b	(/.f64 10 (+.f64 (-.f64 1 (.f64 x x)) (fma.f64 (neg.f64 x) x (.f64 x x))))
	0.5b	(.f64 (+.f64 (pow.f64 (-.f64 1 (.f64 x x)) 2) (-.f64 (pow.f64 (fma.f64 (neg.f64 x) x (.f64 x x)) 2) (.f64 (fma.f64 (neg.f64 x) x (.f64 x x)) (-.f64 1 (.f64 x x))))) (/.f64 10 (+.f64 (pow.f64 (fma.f64 (neg.f64 x) x (.f64 x x)) 3) (pow.f64 (-.f64 1 (.f64 x x)) 3))))
	25.4b	(/.f64 10 (+.f64 (pow.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 2) (fma.f64 (neg.f64 x) x (.f64 x x))))

Compiler

Compiled 17021 to 9575 computations (43.7% saved)

localize16.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (.f64 (-.f64 1 (.f64 x x)) (pow.f64 (-.f64 1 (.f64 x x)) 2)) (+.f64 (pow.f64 (-.f64 1 (.f64 x x)) 2) (-.f64 0 (.f64 (-.f64 1 (.f64 x x)) 0))))
	0.5b	(pow.f64 (-.f64 1 (*.f64 x x)) 2)
	7.9b	(-.f64 1 (*.f64 x x))
	61.9b	(fma.f64 (neg.f64 x) x (*.f64 x x))

series5.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

5.0ms

(/.f64 (*.f64 (-.f64 1 (*.f64 x x)) (pow.f64 (-.f64 1 (*.f64 x x)) 2)) (+.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 2) (-.f64 0 (*.f64 (-.f64 1 (*.f64 x x)) 0))))

rewrite53.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

726×	`log1p-expm1-u_binary64`
726×	`expm1-log1p-u_binary64`
334×	`prod-diff_binary64`
87×	`add-cbrt-cube_binary64`
87×	`add-log-exp_binary64`

Counts

1 → 49

Calls

1 calls:

52.0ms

(/.f64 (*.f64 (-.f64 1 (*.f64 x x)) (pow.f64 (-.f64 1 (*.f64 x x)) 2)) (+.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 2) (-.f64 0 (*.f64 (-.f64 1 (*.f64 x x)) 0))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	31
1	241	7
2	2072	7
3	5205	7
0	0	0
1	0	0

simplify14.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

80×	`fma-neg_binary64`
62×	`rules-11_binary64`
55×	`rules-40_binary64`
55×	`rules-41_binary64`
55×	`rules-42_binary64`

Counts

61 → 52

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	78
1	44	78
2	95	78
3	248	78
4	199	78

prune520.0ms (17.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	418	2	420
Fresh	2	4	6
Picked	0	1	1
Done	1	0	1
Total	421	7	428

Error

0.1b

Counts

428 → 7

Alt Table

Status	Error	Program
	1.3b	(/.f64 10 (+.f64 (.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 x x))) 2) (cbrt.f64 (-.f64 1 (.f64 x x)))) (fma.f64 (neg.f64 x) x (.f64 x x))))
	0.5b	(/.f64 10 (+.f64 (.f64 (pow.f64 (-.f64 1 (.f64 x x)) 4) (/.f64 (pow.f64 (-.f64 1 (.f64 x x)) 3) (pow.f64 (-.f64 1 (.f64 x x)) 6))) (fma.f64 (neg.f64 x) x (*.f64 x x))))
	0.5b	(.f64 (+.f64 (pow.f64 (-.f64 1 (.f64 x x)) 2) (-.f64 (pow.f64 (fma.f64 (neg.f64 x) x (.f64 x x)) 2) (.f64 (fma.f64 (neg.f64 x) x (.f64 x x)) (-.f64 1 (.f64 x x))))) (/.f64 10 (+.f64 (pow.f64 (fma.f64 (neg.f64 x) x (.f64 x x)) 3) (pow.f64 (-.f64 1 (.f64 x x)) 3))))
	0.3b	(/.f64 10 (+.f64 (.f64 (pow.f64 (-.f64 1 (.f64 x x)) 2) (/.f64 (-.f64 1 (.f64 x x)) (pow.f64 (-.f64 1 (.f64 x x)) 2))) (fma.f64 (neg.f64 x) x (*.f64 x x))))
	0.7b	(/.f64 10 (+.f64 (cbrt.f64 (pow.f64 (-.f64 1 (.f64 x x)) 3)) (fma.f64 (neg.f64 x) x (.f64 x x))))
	0.8b	(/.f64 10 (+.f64 (/.f64 (pow.f64 (-.f64 1 (.f64 x x)) 3) (+.f64 (cbrt.f64 (pow.f64 (-.f64 1 (.f64 x x)) 6)) (-.f64 0 (.f64 (-.f64 1 (.f64 x x)) 0)))) (fma.f64 (neg.f64 x) x (*.f64 x x))))
✓	0.3b	(/.f64 10 (+.f64 (/.f64 (.f64 (-.f64 1 (.f64 x x)) (pow.f64 (-.f64 1 (.f64 x x)) 2)) (+.f64 (pow.f64 (-.f64 1 (.f64 x x)) 2) (-.f64 0 (.f64 (-.f64 1 (.f64 x x)) 0)))) (fma.f64 (neg.f64 x) x (*.f64 x x))))

Compiler

Compiled 20154 to 10919 computations (45.8% saved)

regimes329.0ms (11.2%)

Accuracy

Total 0.2b remaining (69.1%)

Threshold costs 0.2b (69.1%)

Counts

61 → 1

Compiler

Compiled 8504 to 5390 computations (36.6% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	14	26
2	13	26

end158.0ms (5.4%)

Compiler: Compiled 278 to 165 computations (40.6% saved)

Details

analyze3.0ms (0.1%)

sample784.0ms (26.8%)

simplify16.0ms (0.5%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

series8.0ms (0.3%)

rewrite115.0ms (3.9%)

simplify35.0ms (1.2%)

prune44.0ms (1.5%)

localize8.0ms (0.3%)

series11.0ms (0.4%)

rewrite64.0ms (2.2%)

simplify36.0ms (1.2%)

prune76.0ms (2.6%)

localize14.0ms (0.5%)

series9.0ms (0.3%)

rewrite71.0ms (2.4%)

simplify71.0ms (2.4%)

prune463.0ms (15.8%)

localize16.0ms (0.6%)

series5.0ms (0.2%)

rewrite53.0ms (1.8%)

simplify14.0ms (0.5%)

prune520.0ms (17.7%)

regimes329.0ms (11.2%)

simplify1.0ms (0%)

end158.0ms (5.4%)

Profiling