Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	50%	25%	3
37.5%	25%	37.5%	4
43.7%	12.5%	43.8%	5
46.9%	6.2%	46.9%	6
48.4%	3.1%	48.5%	7
49.2%	1.6%	49.2%	8
49.6%	0.8%	49.6%	9
49.6%	0.4%	50%	10
49.7%	0.2%	50.1%	11
49.7%	0.1%	50.2%	12
49.7%	0%	50.2%	13
49.7%	0%	50.2%	14

Compiler

Compiled 6 to 4 computations (33.3% saved)

sample713.0ms (18.8%)

Results

685.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 17 to 11 computations (35.3% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	5	6
2	5	6

prune1.0ms (0%)

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

0.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.3b	(*.f64 x (log.f64 x))

Compiler

Compiled 15 to 9 computations (40% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 x (log.f64 x))

series31.0ms (0.8%)

Counts

1 → 12

Calls

1 calls:

31.0ms

(*.f64 x (log.f64 x))

rewrite72.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

566×	`log1p-udef_binary64`
319×	`log1p-expm1-u_binary64`
319×	`expm1-log1p-u_binary64`
286×	`add-log-exp_binary64`
285×	`add-exp-log_binary64`

Counts

1 → 21

Calls

1 calls:

71.0ms

(*.f64 x (log.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	75	6
2	859	6
3	4784	6
4	5696	6
0	0	0
1	0	0

simplify166.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

1457×	`distribute-rgt-in_binary64`
1161×	`fma-neg_binary64`
1126×	`distribute-lft-in_binary64`
786×	`fma-def_binary64`
729×	`unsub-neg_binary64`

Counts

33 → 25

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	72
1	30	72
2	56	72
3	109	72
4	259	72
5	567	72
6	1291	72
7	1028	72
8	1281	72
9	1364	72
10	1374	72
11	1532	72
12	2752	72
13	2815	72
14	2967	72
15	3049	72
16	3099	72
17	3119	72
18	3280	72
19	3204	72
20	3228	72
21	3256	72
22	3272	72
23	5377	72

prune11.0ms (0.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	21	4	25
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	21	5	26

Error

0.2b

Counts

26 → 5

Alt Table

Status	Error	Program
	3.0b	(expm1.f64 (log1p.f64 (*.f64 x (log.f64 x))))
	40.8b	(cbrt.f64 (pow.f64 (*.f64 x (log.f64 x)) 3))
	33.5b	(pow.f64 (sqrt.f64 (*.f64 x (log.f64 x))) 2)
▶	1.4b	(pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 3)
✓	0.3b	(*.f64 x (log.f64 x))

Compiler

Compiled 268 to 135 computations (49.6% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.3b	(*.f64 x (log.f64 x))
✓	0.6b	(cbrt.f64 (*.f64 x (log.f64 x)))
✓	0.8b	(pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 3)

series555.0ms (14.6%)

Counts

2 → 24

Calls

2 calls:

283.0ms	(pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 3)
271.0ms	(cbrt.f64 (*.f64 x (log.f64 x)))

rewrite47.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

493×	`log1p-expm1-u_binary64`
493×	`expm1-log1p-u_binary64`
484×	`unpow-prod-down_binary64`
269×	`log-prod_binary64`
140×	`pow2_binary64`

Counts

2 → 110

Calls

2 calls:

44.0ms	(cbrt.f64 (*.f64 x (log.f64 x)))
44.0ms	(pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	124	14
2	1321	14
3	4898	14
0	0	0
1	0	0

simplify83.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

827×	`fma-neg_binary64`
665×	`fma-def_binary64`
492×	`exp-sum_binary64`
452×	`unswap-sqr_binary64`
289×	`distribute-rgt-in_binary64`

Counts

134 → 117

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	396
1	81	396
2	151	324
3	441	168
4	1398	168
5	3772	168
6	4875	168
7	4927	168
8	4841	168

prune61.0ms (1.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	135	7	142
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	136	11	147

Error

0.1b

Counts

147 → 11

Alt Table

Status	Error	Program
	3.0b	(expm1.f64 (log1p.f64 (*.f64 x (log.f64 x))))
	33.5b	(.f64 (sqrt.f64 (log.f64 x)) (.f64 (sqrt.f64 (log.f64 x)) x))
	40.8b	(cbrt.f64 (pow.f64 (*.f64 x (log.f64 x)) 3))
▶	0.6b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 x)))
	33.5b	(pow.f64 (sqrt.f64 (*.f64 x (log.f64 x))) 2)
	1.3b	(.f64 (pow.f64 (cbrt.f64 (log.f64 x)) 2) (.f64 (cbrt.f64 (log.f64 x)) x))
	33.9b	(.f64 (pow.f64 (.f64 (cbrt.f64 (*.f64 x (log.f64 x))) (cbrt.f64 x)) 3/2) (pow.f64 (cbrt.f64 (log.f64 x)) 3/2))
	1.3b	(.f64 (.f64 x (pow.f64 (cbrt.f64 (log.f64 x)) 2)) (cbrt.f64 (log.f64 x)))
	32.3b	(.f64 (cbrt.f64 (.f64 x x)) (*.f64 (cbrt.f64 x) (log.f64 x)))
	1.7b	(pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 3)) 3)
✓	0.3b	(*.f64 x (log.f64 x))

Compiler

Compiled 2062 to 982 computations (52.4% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (sqrt.f64 x) (log.f64 x))
✓	0.3b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 x)))

series32.0ms (0.8%)

Counts

2 → 8

Calls

2 calls:

21.0ms	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 x)))
11.0ms	(*.f64 (sqrt.f64 x) (log.f64 x))

rewrite45.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

485×	`log1p-expm1-u_binary64`
485×	`expm1-log1p-u_binary64`
469×	`unpow-prod-down_binary64`
305×	`log-prod_binary64`
143×	`pow2_binary64`

Counts

2 → 34

Calls

2 calls:

45.0ms	(*.f64 (sqrt.f64 x) (log.f64 x))
45.0ms	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	14
1	115	14
2	1316	14
3	4963	14
0	0	0
1	0	0

simplify182.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

1787×	`distribute-rgt-in_binary64`
1640×	`fma-neg_binary64`
693×	`unsub-neg_binary64`
564×	`fma-def_binary64`
479×	`distribute-lft-in_binary64`

Counts

42 → 37

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	48
1	21	48
2	35	48
3	60	48
4	101	48
5	124	48
6	141	48
7	206	48
8	341	48
9	620	48
10	1343	48
11	1444	48
12	1554	48
13	1606	48
14	1628	48
15	1633	48
16	4089	48
17	3873	48
18	3937	48
19	4105	48
20	4161	48
21	4161	48
22	4361	48
23	4307	48
24	4311	48
25	4317	48
26	5262	48

prune23.0ms (0.6%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	34	3	37
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	36	12	48

Error

0.0b

Counts

48 → 12

Alt Table

Status	Error	Program
	3.0b	(expm1.f64 (log1p.f64 (*.f64 x (log.f64 x))))
	33.5b	(.f64 (sqrt.f64 (log.f64 x)) (.f64 (sqrt.f64 (log.f64 x)) x))
	33.9b	(.f64 (pow.f64 (.f64 (cbrt.f64 (*.f64 x (log.f64 x))) (cbrt.f64 x)) 3/2) (pow.f64 (cbrt.f64 (log.f64 x)) 3/2))
▶	1.3b	(.f64 (.f64 x (pow.f64 (cbrt.f64 (log.f64 x)) 2)) (cbrt.f64 (log.f64 x)))
✓	0.6b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 x)))
	33.5b	(pow.f64 (sqrt.f64 (*.f64 x (log.f64 x))) 2)
	32.3b	(.f64 (cbrt.f64 (.f64 x x)) (*.f64 (cbrt.f64 x) (log.f64 x)))
	21.8b	(.f64 (sqrt.f64 x) (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 x) (log.f64 x)) 3)))
	33.6b	(.f64 (sqrt.f64 x) (pow.f64 (sqrt.f64 (.f64 (sqrt.f64 x) (log.f64 x))) 2))
	1.4b	(.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (.f64 (sqrt.f64 x) (log.f64 x))) 3))
	1.7b	(pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 3)) 3)
✓	0.3b	(*.f64 x (log.f64 x))

Compiler

Compiled 585 to 293 computations (49.9% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 x (pow.f64 (cbrt.f64 (log.f64 x)) 2))
✓	0.4b	(.f64 (.f64 x (pow.f64 (cbrt.f64 (log.f64 x)) 2)) (cbrt.f64 (log.f64 x)))
✓	0.5b	(cbrt.f64 (log.f64 x))
✓	0.6b	(pow.f64 (cbrt.f64 (log.f64 x)) 2)

series1.3s (35%)

Counts

4 → 48

Calls

4 calls:

480.0ms	(cbrt.f64 (log.f64 x))
457.0ms	(pow.f64 (cbrt.f64 (log.f64 x)) 2)
369.0ms	(*.f64 x (pow.f64 (cbrt.f64 (log.f64 x)) 2))
23.0ms	(.f64 (.f64 x (pow.f64 (cbrt.f64 (log.f64 x)) 2)) (cbrt.f64 (log.f64 x)))

rewrite80.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

602×	`log1p-expm1-u_binary64`
602×	`expm1-log1p-u_binary64`
355×	`log-prod_binary64`
125×	`expm1-udef_binary64`
125×	`log1p-udef_binary64`

Counts

4 → 83

Calls

4 calls:

79.0ms	(*.f64 x (pow.f64 (cbrt.f64 (log.f64 x)) 2))
79.0ms	(.f64 (.f64 x (pow.f64 (cbrt.f64 (log.f64 x)) 2)) (cbrt.f64 (log.f64 x)))
79.0ms	(cbrt.f64 (log.f64 x))
79.0ms	(pow.f64 (cbrt.f64 (log.f64 x)) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	30
1	156	26
2	1628	26
3	4972	26
4	4960	26
0	0	0
1	0	0

simplify87.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

898×	`fma-def_binary64`
770×	`unsub-neg_binary64`
614×	`fma-neg_binary64`
403×	`neg-sub0_binary64`
396×	`unswap-sqr_binary64`

Counts

131 → 97

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	360
1	79	360
2	130	360
3	316	360
4	1019	360
5	2755	360
6	3679	360
7	4516	360
8	4973	360

prune62.0ms (1.6%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	122	4	126
Fresh	3	6	9
Picked	0	1	1
Done	0	2	2
Total	125	13	138

Error

0.0b

Counts

138 → 13

Alt Table

Status	Error	Program
	1.1b	(.f64 (.f64 x (pow.f64 (pow.f64 (log.f64 x) 2) 1/3)) (cbrt.f64 (log.f64 x)))
	1.7b	(pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (*.f64 x (log.f64 x))) 3)) 3)
✓	1.3b	(.f64 (.f64 x (pow.f64 (cbrt.f64 (log.f64 x)) 2)) (cbrt.f64 (log.f64 x)))
	33.5b	(.f64 (sqrt.f64 (log.f64 x)) (.f64 (sqrt.f64 (log.f64 x)) x))
✓	0.6b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (log.f64 x)))
	33.5b	(pow.f64 (sqrt.f64 (*.f64 x (log.f64 x))) 2)
	21.8b	(.f64 (sqrt.f64 x) (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 x) (log.f64 x)) 3)))
	33.6b	(.f64 (sqrt.f64 x) (pow.f64 (sqrt.f64 (.f64 (sqrt.f64 x) (log.f64 x))) 2))
	1.4b	(.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (.f64 (sqrt.f64 x) (log.f64 x))) 3))
	41.3b	(cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (log.f64 x) 3)))
	33.9b	(.f64 (.f64 x (pow.f64 (cbrt.f64 (log.f64 x)) 2)) (exp.f64 (log.f64 (cbrt.f64 (log.f64 x)))))
	0.8b	(.f64 (.f64 x (cbrt.f64 (pow.f64 (log.f64 x) 2))) (cbrt.f64 (log.f64 x)))
✓	0.3b	(*.f64 x (log.f64 x))

Compiler

Compiled 1883 to 925 computations (50.9% saved)

regimes50.0ms (1.3%)

Accuracy

Total 0.2b remaining (85.7%)

Threshold costs 0.2b (85.7%)

Counts

25 → 1

Compiler

Compiled 550 to 374 computations (32% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	5	6
2	5	6

end136.0ms (3.6%)

Compiler: Compiled 150 to 99 computations (34% saved)

Details

analyze4.0ms (0.1%)

sample713.0ms (18.8%)

simplify6.0ms (0.2%)

prune1.0ms (0%)

localize3.0ms (0.1%)

series31.0ms (0.8%)

rewrite72.0ms (1.9%)

simplify166.0ms (4.4%)

prune11.0ms (0.3%)

localize6.0ms (0.1%)

series555.0ms (14.6%)

rewrite47.0ms (1.2%)

simplify83.0ms (2.2%)

prune61.0ms (1.6%)

localize5.0ms (0.1%)

series32.0ms (0.8%)

rewrite45.0ms (1.2%)

simplify182.0ms (4.8%)

prune23.0ms (0.6%)

localize6.0ms (0.2%)

series1.3s (35%)

rewrite80.0ms (2.1%)

simplify87.0ms (2.3%)

prune62.0ms (1.6%)

regimes50.0ms (1.3%)

simplify2.0ms (0%)

end136.0ms (3.6%)

Profiling