Details

analyze379.0ms (7.2%)

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
0%	74.9%	25.1%	6
6.2%	68.6%	25.1%	7
9.4%	65.5%	25.1%	8
14%	35.9%	50.1%	9
21.1%	28.9%	50.1%	10
24.6%	25.4%	50.1%	11
28.7%	21.3%	50.1%	12
33.4%	16.5%	50.1%	13
35.8%	14.1%	50.1%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.2s (22.9%)

Results

1.1s	8252×	body	128	valid
5.0ms	40×	body	128	invalid
1.0ms	3×	body	1024	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify127.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

782×	`fma-neg_binary64`
610×	`unsub-neg_binary64`
567×	`distribute-rgt-in_binary64`
442×	`sub-neg_binary64`
412×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	25	18
2	75	16
3	253	16
4	654	16
5	1767	16
6	2167	16
7	2284	16
8	2375	16
9	2374	16
10	2391	16
11	2701	16
12	3417	16
13	4877	16
14	4713	16
15	4967	16

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))

Compiler

Compiled 54 to 33 computations (38.9% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))
✓	0.1b	(fma.f64 (+.f64 y 1/2) (log.f64 y) z)

series115.0ms (2.2%)

Counts

2 → 60

Calls

2 calls:

72.0ms	(-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))
43.0ms	(fma.f64 (+.f64 y 1/2) (log.f64 y) z)

rewrite71.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

504×	`fma-def_binary64`
273×	`fma-neg_binary64`
219×	`expm1-udef_binary64`
219×	`log1p-udef_binary64`
182×	`log-pow_binary64`

Counts

2 → 142

Calls

2 calls:

67.0ms	(-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))
67.0ms	(fma.f64 (+.f64 y 1/2) (log.f64 y) z)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	229	26
2	3129	26
3	5028	26

simplify94.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

823×	`fma-def_binary64`
628×	`distribute-neg-in_binary64`
598×	`associate--l+_binary64`
440×	`neg-mul-1_binary64`
395×	`associate-+l-_binary64`

Counts

202 → 171

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	57	814
1	169	714
2	523	706
3	1515	704
4	4006	704
5	4217	704
6	4936	704
7	5103	704

prune153.0ms (2.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	164	7	171
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	165	7	172

Error

0.0b

Counts

172 → 7

Alt Table

Status	Error	Program
	33.7b	(/.f64 1 (/.f64 (+.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)) (-.f64 (*.f64 y y) (pow.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x) 2))))
	1.0b	(-.f64 y (-.f64 (*.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (pow.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) 2)) x))
	29.3b	(-.f64 y (-.f64 (pow.f64 (sqrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) 2) x))
▶	0.1b	(+.f64 (-.f64 x z) (fma.f64 (log.f64 y) (-.f64 -1/2 y) y))
	33.7b	(.f64 (-.f64 (.f64 y y) (pow.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x) 2)) (/.f64 1 (+.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))
	1.3b	(*.f64 (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) (pow.f64 (cbrt.f64 (-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))) 2))
	0.1b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))) x))

Compiler

Compiled 4204 to 2276 computations (45.9% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (log.f64 y) (-.f64 -1/2 y) y)

series7.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

7.0ms

(fma.f64 (log.f64 y) (-.f64 -1/2 y) y)

rewrite40.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

641×	`log1p-expm1-u_binary64`
641×	`expm1-log1p-u_binary64`
278×	`log-prod_binary64`
119×	`expm1-udef_binary64`
119×	`log1p-udef_binary64`

Counts

1 → 29

Calls

1 calls:

38.0ms

(fma.f64 (log.f64 y) (-.f64 -1/2 y) y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	129	10
2	1581	10
3	5120	10

simplify178.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

2271×	`fma-def_binary64`
2078×	`fma-neg_binary64`
636×	`sub-neg_binary64`
597×	`distribute-rgt-in_binary64`
576×	`unsub-neg_binary64`

Counts

41 → 37

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	136
1	91	132
2	231	132
3	566	114
4	1374	114
5	3831	114
6	4146	114
7	4145	114
8	4476	114
9	4561	114
10	4626	114
11	997	114
12	921	114
13	925	114
14	949	114
15	959	114
16	961	114
17	961	114
18	1392	114
19	2830	114
20	4826	114

prune45.0ms (0.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	36	1	37
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	37	7	44

Error

0.0b

Counts

44 → 7

Alt Table

Status	Error	Program
	33.7b	(/.f64 1 (/.f64 (+.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)) (-.f64 (*.f64 y y) (pow.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x) 2))))
	1.0b	(-.f64 y (-.f64 (*.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) (pow.f64 (cbrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) 2)) x))
	29.3b	(-.f64 y (-.f64 (pow.f64 (sqrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) 2) x))
✓	0.1b	(+.f64 (-.f64 x z) (fma.f64 (log.f64 y) (-.f64 -1/2 y) y))
	33.7b	(.f64 (-.f64 (.f64 y y) (pow.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x) 2)) (/.f64 1 (+.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))
▶	0.1b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))) x))
	0.5b	(+.f64 (-.f64 x z) (*.f64 (cbrt.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y)) (pow.f64 (cbrt.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y)) 2)))

Compiler

Compiled 946 to 532 computations (43.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y))))
✓	0.0b	(+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))
✓	0.1b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))) x))
✓	0.3b	(*.f64 y (log.f64 y))

series527.0ms (10%)

Counts

4 → 74

Calls

4 calls:

291.0ms	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))) x))
151.0ms	(*.f64 y (log.f64 y))
71.0ms	(+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y))))
13.0ms	(+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))

rewrite85.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

269×	`expm1-udef_binary64`
269×	`log1p-udef_binary64`
148×	`add-sqr-sqrt_binary64`
146×	`log1p-expm1-u_binary64`
146×	`expm1-log1p-u_binary64`

Counts

4 → 136

Calls

4 calls:

82.0ms	(+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y))))
82.0ms	(+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))
82.0ms	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))) x))
82.0ms	(*.f64 y (log.f64 y))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	45
1	286	41
2	4175	41
3	4954	41

simplify148.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

577×	`neg-sub0_binary64`
464×	`associate-+l-_binary64`
446×	`unsub-neg_binary64`
406×	`distribute-neg-in_binary64`
398×	`neg-mul-1_binary64`

Counts

210 → 168

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	966
1	188	865
2	583	796
3	1558	794
4	3474	794
5	3921	794
6	4511	794
7	4574	794
8	4807	794
9	4948	794
10	4966	794

prune212.0ms (4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	167	1	168
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	168	7	175

Error

0.0b

Counts

175 → 7

Alt Table

Status	Error	Program
	33.7b	(.f64 (-.f64 (.f64 y y) (pow.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x) 2)) (/.f64 1 (+.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))
▶	0.4b	(-.f64 y (-.f64 (+.f64 z (+.f64 (pow.f64 (cbrt.f64 (.f64 y (log.f64 y))) 3) (.f64 1/2 (log.f64 y)))) x))
	29.3b	(-.f64 y (-.f64 (pow.f64 (sqrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) 2) x))
✓	0.1b	(+.f64 (-.f64 x z) (fma.f64 (log.f64 y) (-.f64 -1/2 y) y))
	33.7b	(/.f64 1 (/.f64 (+.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x)) (-.f64 (*.f64 y y) (pow.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x) 2))))
✓	0.1b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))) x))
	0.5b	(+.f64 (-.f64 x z) (*.f64 (cbrt.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y)) (pow.f64 (cbrt.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y)) 2)))

Compiler

Compiled 3632 to 1915 computations (47.3% saved)

localize53.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(-.f64 y (-.f64 (+.f64 z (+.f64 (pow.f64 (cbrt.f64 (.f64 y (log.f64 y))) 3) (.f64 1/2 (log.f64 y)))) x))
	0.3b	(*.f64 y (log.f64 y))
✓	0.6b	(cbrt.f64 (*.f64 y (log.f64 y)))
✓	0.7b	(pow.f64 (cbrt.f64 (*.f64 y (log.f64 y))) 3)

series698.0ms (13.2%)

Counts

3 → 60

Calls

3 calls:

295.0ms	(cbrt.f64 (*.f64 y (log.f64 y)))
259.0ms	(pow.f64 (cbrt.f64 (*.f64 y (log.f64 y))) 3)
143.0ms	(-.f64 y (-.f64 (+.f64 z (+.f64 (pow.f64 (cbrt.f64 (.f64 y (log.f64 y))) 3) (.f64 1/2 (log.f64 y)))) x))

rewrite79.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

296×	`log1p-udef_binary64`
165×	`add-sqr-sqrt_binary64`
165×	`log1p-expm1-u_binary64`
165×	`expm1-log1p-u_binary64`
155×	`add-log-exp_binary64`

Counts

3 → 99

Calls

3 calls:

77.0ms	(-.f64 y (-.f64 (+.f64 z (+.f64 (pow.f64 (cbrt.f64 (.f64 y (log.f64 y))) 3) (.f64 1/2 (log.f64 y)))) x))
77.0ms	(cbrt.f64 (*.f64 y (log.f64 y)))
77.0ms	(pow.f64 (cbrt.f64 (*.f64 y (log.f64 y))) 3)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	37
1	331	32
2	4560	32
3	4946	32

simplify101.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

781×	`fma-def_binary64`
558×	`associate--l+_binary64`
538×	`sub-neg_binary64`
310×	`unsub-neg_binary64`
237×	`fma-neg_binary64`

Counts

159 → 123

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	71	954
1	202	892
2	524	868
3	1613	662
4	4174	662
5	4931	662
6	4979	662
7	4897	662

prune138.0ms (2.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	137	2	139
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	138	8	146

Error

0.0b

Counts

146 → 8

Alt Table

Status	Error	Program
	33.7b	(.f64 (-.f64 (.f64 y y) (pow.f64 (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x) 2)) (/.f64 1 (+.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))))
✓	0.4b	(-.f64 y (-.f64 (+.f64 z (+.f64 (pow.f64 (cbrt.f64 (.f64 y (log.f64 y))) 3) (.f64 1/2 (log.f64 y)))) x))
	29.3b	(-.f64 y (-.f64 (pow.f64 (sqrt.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z)) 2) x))
✓	0.1b	(+.f64 (-.f64 x z) (fma.f64 (log.f64 y) (-.f64 -1/2 y) y))
	16.1b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) (log.f64 y))) (.f64 1/2 (log.f64 y)))) x))
	0.4b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 (cbrt.f64 y) (.f64 (cbrt.f64 (log.f64 y)) (pow.f64 (cbrt.f64 (.f64 y (log.f64 y))) 2))) (.f64 1/2 (log.f64 y)))) x))
✓	0.1b	(-.f64 y (-.f64 (+.f64 z (+.f64 (.f64 y (log.f64 y)) (.f64 1/2 (log.f64 y)))) x))
	0.5b	(+.f64 (-.f64 x z) (*.f64 (cbrt.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y)) (pow.f64 (cbrt.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y)) 2)))

Compiler

Compiled 3207 to 1640 computations (48.9% saved)

regimes674.0ms (12.7%)

Accuracy

Total 0.1b remaining (69.5%)

Threshold costs 0.1b (69.5%)

Counts

129 → 1

Compiler

Compiled 10802 to 7243 computations (32.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	15	16
2	23	16
3	27	16
4	29	16
5	29	16

end126.0ms (2.4%)

Compiler: Compiled 208 to 134 computations (35.6% saved)

Details

analyze379.0ms (7.2%)

sample1.2s (22.9%)

simplify127.0ms (2.4%)

prune3.0ms (0.1%)

localize8.0ms (0.1%)

series115.0ms (2.2%)

rewrite71.0ms (1.3%)

simplify94.0ms (1.8%)

prune153.0ms (2.9%)

localize8.0ms (0.2%)

series7.0ms (0.1%)

rewrite40.0ms (0.7%)

simplify178.0ms (3.4%)

prune45.0ms (0.9%)

localize9.0ms (0.2%)

series527.0ms (10%)

rewrite85.0ms (1.6%)

simplify148.0ms (2.8%)

prune212.0ms (4%)

localize53.0ms (1%)

series698.0ms (13.2%)

rewrite79.0ms (1.5%)

simplify101.0ms (1.9%)

prune138.0ms (2.6%)

regimes674.0ms (12.7%)

simplify3.0ms (0.1%)

end126.0ms (2.4%)

Profiling