Details

analyze8.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample1.8s (55.4%)

Results

561.0ms	1328×	body	1024	valid
552.0ms	4586×	body	128	valid
491.0ms	1571×	body	512	valid
141.0ms	771×	body	256	valid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify56.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1226×	`rules-42_binary64`
1080×	`rules-43_binary64`
780×	`fma-neg_binary64`
384×	`fma-def_binary64`
329×	`rules-40_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	74	22
2	271	22
3	1194	22
4	3582	22
5	18	22

prune2.0ms (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

9.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.4b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 63 to 51 computations (19% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
✓	0.0b	(/.f64 1 (+.f64 x 1))
✓	0.0b	(/.f64 1 (-.f64 x 1))
✓	3.3b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series15.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

6.0ms	(/.f64 1 (+.f64 x 1))
4.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
3.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
2.0ms	(/.f64 1 (-.f64 x 1))

rewrite97.0ms (2.9%)

Algorithm

2×	batch-egg-rewrite

Rules

938×	`prod-diff_binary64`
196×	`egg-rr`
123×	`add-sqr-sqrt_binary64`
121×	`log1p-expm1-u_binary64`
121×	`expm1-log1p-u_binary64`

Counts

4 → 196

Calls

4 calls:

93.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
93.0ms	(/.f64 1 (+.f64 x 1))
93.0ms	(/.f64 1 (-.f64 x 1))
93.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	49
1	281	49
2	3773	49
3	5612	49
0	0	0
1	0	0

simplify72.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

697×	`rules-40_binary64`
697×	`rules-41_binary64`
697×	`rules-42_binary64`
697×	`rules-43_binary64`
382×	`rules-20_binary64`

Counts

244 → 249

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	78	752
1	554	736
2	2412	682
3	4949	682
4	5002	682

prune177.0ms (5.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	247	2	249
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	247	3	250

Error

0.1b

Counts

250 → 3

Alt Table

Status	Error	Program
	33.3b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))))
✓	9.4b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
▶	30.6b	(neg.f64 (fma.f64 2 (+.f64 x (pow.f64 x 3)) (/.f64 2 x)))

Compiler

Compiled 5859 to 4733 computations (19.2% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 2 (+.f64 x (pow.f64 x 3)) (/.f64 2 x))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(fma.f64 2 (+.f64 x (pow.f64 x 3)) (/.f64 2 x))

rewrite50.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

773×	`log1p-expm1-u_binary64`
773×	`expm1-log1p-u_binary64`
349×	`prod-diff_binary64`
80×	`add-sqr-sqrt_binary64`
75×	`add-cbrt-cube_binary64`

Counts

1 → 34

Calls

1 calls:

49.0ms

(fma.f64 2 (+.f64 x (pow.f64 x 3)) (/.f64 2 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	191	14
2	2250	14
3	5577	14
0	0	0
1	0	0

simplify64.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

445×	`rules-40_binary64`
445×	`rules-42_binary64`
443×	`rules-41_binary64`
443×	`rules-43_binary64`
389×	`rules-14-rev_binary64`

Counts

46 → 39

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	48
1	95	48
2	361	48
3	1682	48
4	4182	48
5	202	48

prune25.0ms (0.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	39	0	39
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	39	3	42

Error

0.1b

Counts

42 → 3

Alt Table

Status	Error	Program
▶	33.3b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))))
✓	9.4b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
✓	30.6b	(neg.f64 (fma.f64 2 (+.f64 x (pow.f64 x 3)) (/.f64 2 x)))

Compiler

Compiled 724 to 566 computations (21.8% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7)))
✓	0.1b	(/.f64 2 (pow.f64 x 3))
✓	0.2b	(/.f64 2 (pow.f64 x 5))
✓	0.2b	(/.f64 2 (pow.f64 x 7))

series16.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

5.0ms	(+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7)))
5.0ms	(/.f64 2 (pow.f64 x 5))
4.0ms	(/.f64 2 (pow.f64 x 7))
3.0ms	(/.f64 2 (pow.f64 x 3))

rewrite70.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

487×	`prod-diff_binary64`
228×	`expm1-udef_binary64`
228×	`log1p-udef_binary64`
129×	`add-sqr-sqrt_binary64`
127×	`log1p-expm1-u_binary64`

Counts

4 → 123

Calls

4 calls:

68.0ms	(+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7)))
68.0ms	(/.f64 2 (pow.f64 x 3))
68.0ms	(/.f64 2 (pow.f64 x 5))
68.0ms	(/.f64 2 (pow.f64 x 7))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	37
1	311	37
2	3543	37
3	5022	37
0	0	0
1	0	0

simplify55.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1178×	`rules-42_binary64`
1018×	`rules-43_binary64`
507×	`fma-neg_binary64`
340×	`fma-def_binary64`
323×	`rules-40_binary64`

Counts

135 → 126

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	84
1	85	84
2	260	84
3	1148	84
4	3487	84
5	25	84

prune107.0ms (3.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	124	2	126
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	124	5	129

Error

0.0b

Counts

129 → 5

Alt Table

Status	Error	Program
✓	33.3b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))))
✓	9.4b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
✓	30.6b	(neg.f64 (fma.f64 2 (+.f64 x (pow.f64 x 3)) (/.f64 2 x)))
	38.1b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (pow.f64 (sqrt.f64 (/.f64 2 (pow.f64 x 3))) 2) (/.f64 2 (pow.f64 x 7))))
▶	33.5b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (pow.f64 (/.f64 (cbrt.f64 2) x) 3) (/.f64 2 (pow.f64 x 7))))

Compiler

Compiled 3013 to 2545 computations (15.5% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f64 2 (pow.f64 x 5))
	0.2b	(/.f64 2 (pow.f64 x 7))
✓	0.3b	(pow.f64 (/.f64 (cbrt.f64 2) x) 3)
✓	1.0b	(cbrt.f64 2)

series13.0ms (0.4%)

Counts

2 → 12

Calls

2 calls:

13.0ms	(pow.f64 (/.f64 (cbrt.f64 2) x) 3)
0.0ms	(cbrt.f64 2)

rewrite90.0ms (2.7%)

Algorithm

2×	batch-egg-rewrite

Rules

559×	`log1p-expm1-u_binary64`
559×	`expm1-log1p-u_binary64`
381×	`fma-neg_binary64`
192×	`fma-def_binary64`
153×	`prod-diff_binary64`

Counts

2 → 108

Calls

2 calls:

88.0ms	(pow.f64 (/.f64 (cbrt.f64 2) x) 3)
88.0ms	(cbrt.f64 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	161	10
2	1693	10
3	4958	10
4	4901	10
0	0	0
1	0	0

simplify16.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

78×	`fma-neg_binary64`
76×	`rules-42_binary64`
71×	`rules-41_binary64`
70×	`rules-40_binary64`
68×	`rules-43_binary64`

Counts

120 → 109

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	6	84
1	35	84
2	92	84
3	247	12
4	154	12
5	9	12

prune166.0ms (5.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	156	3	159
Fresh	0	1	1
Picked	1	0	1
Done	0	3	3
Total	157	7	164

Error

0.0b

Counts

164 → 7

Alt Table

Status	Error	Program
	33.5b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (cbrt.f64 2) x)) 2) 3) (/.f64 (cbrt.f64 2) x)) (/.f64 2 (pow.f64 x 7))))
	33.4b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (.f64 (cbrt.f64 (/.f64 (cbrt.f64 2) x)) (.f64 (pow.f64 (/.f64 (cbrt.f64 2) x) 2) (pow.f64 (cbrt.f64 (/.f64 (cbrt.f64 2) x)) 2))) (/.f64 2 (pow.f64 x 7))))
	33.3b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (pow.f64 (/.f64 (pow.f64 2 1/3) x) 3) (/.f64 2 (pow.f64 x 7))))
✓	33.3b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))))
✓	9.4b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
✓	30.6b	(neg.f64 (fma.f64 2 (+.f64 x (pow.f64 x 3)) (/.f64 2 x)))
	38.1b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (pow.f64 (sqrt.f64 (/.f64 2 (pow.f64 x 3))) 2) (/.f64 2 (pow.f64 x 7))))

Compiler

Compiled 4325 to 3685 computations (14.8% saved)

regimes120.0ms (3.6%)

Accuracy

Total 0.4b remaining (89.9%)

Threshold costs 0.4b (89.9%)

Counts

36 → 3

Compiler

Compiled 1344 to 1114 computations (17.1% saved)

bsearch39.0ms (1.2%)

Steps

Iters	Range		Point
9	0.000714967568793734	709.3410132448988	0.9945083062221113
9	-20325.725809968826	-0.0005630524608686685	-1.0063945433797883

Compiler

Compiled 2 to 1 computations (50% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	81
1	31	81

end165.0ms (5%)

Compiler: Compiled 259 to 213 computations (17.8% saved)

Details

analyze8.0ms (0.3%)

sample1.8s (55.4%)

simplify56.0ms (1.7%)

prune2.0ms (0.1%)

localize8.0ms (0.2%)

series15.0ms (0.4%)

rewrite97.0ms (2.9%)

simplify72.0ms (2.2%)

prune177.0ms (5.4%)

localize6.0ms (0.2%)

series3.0ms (0.1%)

rewrite50.0ms (1.5%)

simplify64.0ms (1.9%)

prune25.0ms (0.8%)

localize10.0ms (0.3%)

series16.0ms (0.5%)

rewrite70.0ms (2.1%)

simplify55.0ms (1.7%)

prune107.0ms (3.3%)

localize14.0ms (0.4%)

series13.0ms (0.4%)

rewrite90.0ms (2.7%)

simplify16.0ms (0.5%)

prune166.0ms (5.1%)

regimes120.0ms (3.6%)

bsearch39.0ms (1.2%)

simplify2.0ms (0.1%)

end165.0ms (5%)

Profiling