Details

analyze93.0ms (3.2%)

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
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
50%	37.5%	12.6%	7
56.2%	31.2%	12.6%	8
62.4%	18.7%	18.8%	9
65.6%	15.6%	18.8%	10
68.7%	9.4%	22%	11
70.2%	7.8%	22%	12
71.8%	4.7%	23.5%	13
72.6%	3.9%	23.5%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample732.0ms (24.9%)

Results

681.0ms	8256×	body	128	valid
14.0ms	188×	body	128	invalid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify11.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

13×	`associate-l_binary64`
11×	`associate-r_binary64`
10×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	14	10
2	28	10
3	36	10
4	35	10
5	35	10

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

0.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.3b	(.f64 (.f64 (*.f64 x 3) y) y)

Compiler

Compiled 34 to 22 computations (35.3% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (*.f64 x 3) y) y)
✓	0.3b	(.f64 (.f64 x 3) y)

series15.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(.f64 (.f64 (*.f64 x 3) y) y)
4.0ms	(.f64 (.f64 x 3) y)

rewrite47.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

608×	`log1p-expm1-u_binary64`
608×	`expm1-log1p-u_binary64`
377×	`log-prod_binary64`
126×	`expm1-udef_binary64`
126×	`log1p-udef_binary64`

Counts

2 → 38

Calls

2 calls:

46.0ms	(.f64 (.f64 (*.f64 x 3) y) y)
46.0ms	(.f64 (.f64 x 3) y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	142	17
2	1625	17
3	4944	17
0	0	0
1	0	0

simplify169.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

1104×	`sqr-pow_binary64`
661×	`fabs-mul_binary64`
628×	`pow-sqr_binary64`
611×	`cube-prod_binary64`
311×	`*-commutative_binary64`

Counts

86 → 41

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	408
1	23	408
2	42	408
3	76	408
4	189	408
5	547	408
6	650	408
7	887	408
8	912	408
9	1022	408
10	1140	408
11	1307	408
12	1471	408
13	1699	408
14	2033	408
15	2428	408
16	2986	408
17	3670	408
18	3895	408
19	4160	408
20	4252	408
21	4286	408
22	4307	408
23	4990	408

prune29.0ms (1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	35	6	41
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	35	7	42

Error

0.1b

Counts

42 → 7

Alt Table

Status	Error	Program
	0.3b	(.f64 3 (.f64 y (*.f64 y x)))
	13.7b	(.f64 3 (.f64 (pow.f64 y 2) x))
▶	0.3b	(.f64 (.f64 3 (*.f64 y x)) y)
✓	0.3b	(.f64 (.f64 (*.f64 x 3) y) y)
	38.1b	(cbrt.f64 (.f64 (pow.f64 y 3) (pow.f64 (.f64 (*.f64 x 3) y) 3)))
	30.3b	(pow.f64 (.f64 (sqrt.f64 (.f64 x 3)) y) 2)
	29.5b	(.f64 (pow.f64 (sqrt.f64 (.f64 (*.f64 x 3) y)) 2) y)

Compiler

Compiled 592 to 410 computations (30.7% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 3 (*.f64 y x)) y)
✓	0.2b	(.f64 3 (.f64 y x))

series13.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

9.0ms	(.f64 (.f64 3 (*.f64 y x)) y)
4.0ms	(.f64 3 (.f64 y x))

rewrite46.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

623×	`log1p-expm1-u_binary64`
623×	`expm1-log1p-u_binary64`
386×	`log-prod_binary64`
128×	`expm1-udef_binary64`
128×	`log1p-udef_binary64`

Counts

2 → 36

Calls

2 calls:

45.0ms	(.f64 (.f64 3 (*.f64 y x)) y)
45.0ms	(.f64 3 (.f64 y x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	143	17
2	1658	17
3	4967	17
0	0	0
1	0	0

simplify150.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

1104×	`sqr-pow_binary64`
661×	`fabs-mul_binary64`
628×	`pow-sqr_binary64`
611×	`cube-prod_binary64`
310×	`cube-mult_binary64`

Counts

60 → 38

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	240
1	17	240
2	35	240
3	72	240
4	173	240
5	497	240
6	628	240
7	865	240
8	890	240
9	1000	240
10	1118	240
11	1285	240
12	1449	240
13	1677	240
14	2011	240
15	2406	240
16	2964	240
17	3648	240
18	3873	240
19	4138	240
20	4230	240
21	4264	240
22	4285	240
23	4968	240

prune29.0ms (1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	36	2	38
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	36	9	45

Error

0.0b

Counts

45 → 9

Alt Table

Status	Error	Program
▶	0.3b	(.f64 3 (.f64 y (*.f64 y x)))
	13.7b	(.f64 3 (.f64 (pow.f64 y 2) x))
✓	0.3b	(.f64 (.f64 3 (*.f64 y x)) y)
✓	0.3b	(.f64 (.f64 (*.f64 x 3) y) y)
	1.0b	(pow.f64 (cbrt.f64 (.f64 y (.f64 3 (*.f64 y x)))) 3)
	43.0b	(.f64 (+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 3) (.f64 y x)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 3) (*.f64 y x))))) y)
	38.1b	(cbrt.f64 (.f64 (pow.f64 y 3) (pow.f64 (.f64 (*.f64 x 3) y) 3)))
	30.3b	(pow.f64 (.f64 (sqrt.f64 (.f64 x 3)) y) 2)
	29.5b	(.f64 (pow.f64 (sqrt.f64 (.f64 (*.f64 x 3) y)) 2) y)

Compiler

Compiled 620 to 396 computations (36.1% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 y (.f64 y x))
✓	0.3b	(.f64 3 (.f64 y (*.f64 y x)))

series20.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

13.0ms	(.f64 3 (.f64 y (*.f64 y x)))
7.0ms	(.f64 y (.f64 y x))

rewrite45.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

610×	`log1p-expm1-u_binary64`
610×	`expm1-log1p-u_binary64`
379×	`log-prod_binary64`
126×	`expm1-udef_binary64`
126×	`log1p-udef_binary64`

Counts

2 → 36

Calls

2 calls:

44.0ms	(.f64 y (.f64 y x))
44.0ms	(.f64 3 (.f64 y (*.f64 y x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	142	17
2	1629	17
3	4954	17
0	0	0
1	0	0

simplify168.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

1104×	`sqr-pow_binary64`
661×	`fabs-mul_binary64`
628×	`pow-sqr_binary64`
611×	`cube-prod_binary64`
310×	`cube-mult_binary64`

Counts

84 → 40

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	408
1	17	408
2	35	408
3	72	408
4	173	408
5	497	408
6	628	408
7	865	408
8	890	408
9	1000	408
10	1118	408
11	1285	408
12	1449	408
13	1677	408
14	2011	408
15	2406	408
16	2964	408
17	3648	408
18	3873	408
19	4138	408
20	4230	408
21	4264	408
22	4285	408
23	4968	408

prune32.0ms (1.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	39	1	40
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	39	10	49

Error

0.0b

Counts

49 → 10

Alt Table

Status	Error	Program
✓	0.3b	(.f64 3 (.f64 y (*.f64 y x)))
	13.7b	(.f64 3 (.f64 (pow.f64 y 2) x))
✓	0.3b	(.f64 (.f64 3 (*.f64 y x)) y)
▶	1.0b	(.f64 3 (pow.f64 (cbrt.f64 (.f64 y (*.f64 y x))) 3))
✓	0.3b	(.f64 (.f64 (*.f64 x 3) y) y)
	1.0b	(pow.f64 (cbrt.f64 (.f64 y (.f64 3 (*.f64 y x)))) 3)
	43.0b	(.f64 (+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 3) (.f64 y x)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 3) (*.f64 y x))))) y)
	38.1b	(cbrt.f64 (.f64 (pow.f64 y 3) (pow.f64 (.f64 (*.f64 x 3) y) 3)))
	30.3b	(pow.f64 (.f64 (sqrt.f64 (.f64 x 3)) y) 2)
	29.5b	(.f64 (pow.f64 (sqrt.f64 (.f64 (*.f64 x 3) y)) 2) y)

Compiler

Compiled 635 to 355 computations (44.1% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 y (.f64 y x))
✓	0.3b	(.f64 3 (pow.f64 (cbrt.f64 (.f64 y (*.f64 y x))) 3))
✓	0.5b	(pow.f64 (cbrt.f64 (.f64 y (.f64 y x))) 3)
✓	17.2b	(cbrt.f64 (.f64 y (.f64 y x)))

series875.0ms (29.8%)

Counts

3 → 72

Calls

3 calls:

444.0ms	(pow.f64 (cbrt.f64 (.f64 y (.f64 y x))) 3)
405.0ms	(cbrt.f64 (.f64 y (.f64 y x)))
27.0ms	(.f64 3 (pow.f64 (cbrt.f64 (.f64 y (*.f64 y x))) 3))

rewrite99.0ms (3.4%)

Algorithm

2×	batch-egg-rewrite

Rules

702×	`log1p-expm1-u_binary64`
702×	`expm1-log1p-u_binary64`
139×	`expm1-udef_binary64`
139×	`log1p-udef_binary64`
129×	`log-pow_binary64`

Counts

3 → 81

Calls

3 calls:

97.0ms	(.f64 3 (pow.f64 (cbrt.f64 (.f64 y (*.f64 y x))) 3))
97.0ms	(pow.f64 (cbrt.f64 (.f64 y (.f64 y x))) 3)
97.0ms	(cbrt.f64 (.f64 y (.f64 y x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	26
1	168	26
2	1879	26
3	4960	26
4	4928	26
0	0	0
1	0	0

simplify59.0ms (2%)

Algorithm

1×	egg-herbie

Rules

698×	`unswap-sqr_binary64`
316×	`unsub-neg_binary64`
282×	`associate-l_binary64`
281×	`fma-neg_binary64`
273×	`exp-sum_binary64`

Counts

153 → 98

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	52	1132
1	133	1052
2	249	996
3	738	676
4	2640	676
5	5089	676

prune86.0ms (2.9%)

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	116	3	119
Fresh	1	5	6
Picked	0	1	1
Done	0	3	3
Total	117	12	129

Error

0.0b

Counts

129 → 12

Alt Table

Status	Error	Program
	31.5b	(.f64 3 (.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (.f64 y x))))
	13.7b	(.f64 3 (.f64 (pow.f64 y 2) x))
	1.0b	(.f64 3 (.f64 (pow.f64 (cbrt.f64 (.f64 y x)) 2) (.f64 (cbrt.f64 (*.f64 y x)) y)))
✓	0.3b	(.f64 (.f64 3 (*.f64 y x)) y)
✓	0.3b	(.f64 3 (.f64 y (*.f64 y x)))
	14.4b	(.f64 3 (pow.f64 (.f64 (cbrt.f64 (*.f64 y y)) (cbrt.f64 x)) 3))
✓	1.0b	(.f64 3 (pow.f64 (cbrt.f64 (.f64 y (*.f64 y x))) 3))
✓	0.3b	(.f64 (.f64 (*.f64 x 3) y) y)
	1.0b	(pow.f64 (cbrt.f64 (.f64 y (.f64 3 (*.f64 y x)))) 3)
	38.1b	(cbrt.f64 (.f64 (pow.f64 y 3) (pow.f64 (.f64 (*.f64 x 3) y) 3)))
	30.3b	(pow.f64 (.f64 (sqrt.f64 (.f64 x 3)) y) 2)
	29.5b	(.f64 (pow.f64 (sqrt.f64 (.f64 (*.f64 x 3) y)) 2) y)

Compiler

Compiled 1711 to 894 computations (47.7% saved)

regimes73.0ms (2.5%)

Accuracy

Total 0.2b remaining (90.1%)

Threshold costs 0.2b (90.1%)

Counts

16 → 1

Compiler

Compiled 848 to 608 computations (28.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	10	10
2	10	10

end119.0ms (4.1%)

Compiler: Compiled 157 to 111 computations (29.3% saved)

Details

analyze93.0ms (3.2%)

sample732.0ms (24.9%)

simplify11.0ms (0.4%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

series15.0ms (0.5%)

rewrite47.0ms (1.6%)

simplify169.0ms (5.7%)

prune29.0ms (1%)

localize9.0ms (0.3%)

series13.0ms (0.4%)

rewrite46.0ms (1.6%)

simplify150.0ms (5.1%)

prune29.0ms (1%)

localize4.0ms (0.1%)

series20.0ms (0.7%)

rewrite45.0ms (1.5%)

simplify168.0ms (5.7%)

prune32.0ms (1.1%)

localize7.0ms (0.2%)

series875.0ms (29.8%)

rewrite99.0ms (3.4%)

simplify59.0ms (2%)

prune86.0ms (2.9%)

regimes73.0ms (2.5%)

simplify2.0ms (0.1%)

end119.0ms (4.1%)

Profiling