Details

analyze36.0ms (0.9%)

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
50%	50%	0.1%	3
50%	50%	0.1%	4
74.9%	25%	0.1%	5
74.9%	25%	0.1%	6
87.4%	12.5%	0.1%	7
87.4%	12.5%	0.1%	8
93.7%	6.2%	0.1%	9
93.7%	6.2%	0.1%	10
96.8%	3.1%	0.1%	11
96.8%	3.1%	0.1%	12
98.3%	1.6%	0.1%	13
98.3%	1.6%	0.1%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample791.0ms (19.7%)

Results

760.0ms

8256×

body

128

valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`associate-/r*_binary64`
1×	`*-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	10	9
2	12	9
3	12	9

prune2.0ms (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

13.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	13.9b	(cbrt.f64 (/.f64 g (*.f64 2 a)))

Compiler

Compiled 24 to 18 computations (25% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	13.7b	(cbrt.f64 (/.f64 g (*.f64 2 a)))

series368.0ms (9.2%)

Counts

1 → 24

Calls

1 calls:

368.0ms

(cbrt.f64 (/.f64 g (*.f64 2 a)))

rewrite41.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

695×	`log1p-expm1-u_binary64`
695×	`expm1-log1p-u_binary64`
129×	`expm1-udef_binary64`
129×	`log1p-udef_binary64`
115×	`log-pow_binary64`

Counts

1 → 31

Calls

1 calls:

41.0ms

(cbrt.f64 (/.f64 g (*.f64 2 a)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	145	9
2	1811	9
3	4982	9

simplify63.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

801×	`div-sub_binary64`
792×	`fma-def_binary64`
513×	`fma-neg_binary64`
310×	`times-frac_binary64`
268×	`unswap-sqr_binary64`

Counts

55 → 38

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	40	472
1	76	472
2	132	448
3	375	312
4	906	280
5	2132	280
6	4048	280
7	5162	280

prune32.0ms (0.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	28	10	38
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	11	39

Error

0.1b

Counts

39 → 11

Alt Table

Status	Error	Program
✓	13.9b	(cbrt.f64 (/.f64 g (*.f64 2 a)))
	14.3b	(/.f64 1 (cbrt.f64 (/.f64 (*.f64 2 a) g)))
	13.9b	(*.f64 (cbrt.f64 1/2) (cbrt.f64 (/.f64 g a)))
	14.5b	(pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 g (*.f64 2 a)))) 3)
▶	0.8b	(/.f64 (cbrt.f64 (/.f64 g 2)) (cbrt.f64 a))
	0.9b	(/.f64 (cbrt.f64 g) (cbrt.f64 (*.f64 2 a)))
	0.9b	(/.f64 1 (/.f64 (cbrt.f64 (*.f64 2 a)) (cbrt.f64 g)))
	16.8b	(.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 g (.f64 2 a))) 2) 1/3) (cbrt.f64 (cbrt.f64 (/.f64 g (*.f64 2 a)))))
	14.6b	(.f64 (cbrt.f64 (cbrt.f64 (/.f64 g (.f64 2 a)))) (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 g (*.f64 2 a)))) 2))
	0.9b	(.f64 (cbrt.f64 g) (/.f64 1 (cbrt.f64 (.f64 2 a))))
	0.8b	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))

Compiler

Compiled 629 to 485 computations (22.9% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (cbrt.f64 (/.f64 g 2)) (cbrt.f64 a))
✓	0.6b	(cbrt.f64 a)
✓	0.6b	(cbrt.f64 (/.f64 g 2))

series510.0ms (12.7%)

Counts

3 → 48

Calls

3 calls:

439.0ms	(/.f64 (cbrt.f64 (/.f64 g 2)) (cbrt.f64 a))
38.0ms	(cbrt.f64 (/.f64 g 2))
33.0ms	(cbrt.f64 a)

rewrite51.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

801×	`log1p-expm1-u_binary64`
801×	`expm1-log1p-u_binary64`
84×	`egg-rr`
82×	`add-sqr-sqrt_binary64`
78×	`add-cube-cbrt_binary64`

Counts

3 → 84

Calls

3 calls:

50.0ms	(/.f64 (cbrt.f64 (/.f64 g 2)) (cbrt.f64 a))
50.0ms	(cbrt.f64 a)
50.0ms	(cbrt.f64 (/.f64 g 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	169	18
2	2084	18
3	4987	18

simplify69.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

772×	`unswap-sqr_binary64`
605×	`associate-l_binary64`
405×	`fma-def_binary64`
355×	`fma-neg_binary64`
350×	`div-sub_binary64`

Counts

132 → 98

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	51	652
1	111	652
2	195	628
3	500	484
4	1269	468
5	3400	468
6	5338	468

prune68.0ms (1.7%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	89	9	98
Fresh	5	4	9
Picked	0	1	1
Done	0	1	1
Total	94	15	109

Error

0.0b

Counts

109 → 15

Alt Table

Status	Error	Program
	0.9b	(/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 g)) (cbrt.f64 a))
✓	0.8b	(/.f64 (cbrt.f64 (/.f64 g 2)) (cbrt.f64 a))
	1.4b	(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cbrt.f64 a)) 2)) (/.f64 (cbrt.f64 (/.f64 g 2)) (cbrt.f64 (cbrt.f64 a))))
	0.9b	(.f64 (cbrt.f64 g) (/.f64 1 (cbrt.f64 (.f64 2 a))))
	1.6b	(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 g 2))) 2) (.f64 (cbrt.f64 (cbrt.f64 (/.f64 g 2))) (/.f64 1 (cbrt.f64 a))))
	0.8b	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))
	1.4b	(/.f64 (cbrt.f64 (/.f64 g 2)) (*.f64 (cbrt.f64 (cbrt.f64 a)) (pow.f64 (cbrt.f64 (cbrt.f64 a)) 2)))
	1.1b	(/.f64 (/.f64 (cbrt.f64 g) (cbrt.f64 2)) (cbrt.f64 a))
▶	0.8b	(/.f64 (/.f64 1 (cbrt.f64 (/.f64 2 g))) (cbrt.f64 a))
	0.9b	(.f64 (cbrt.f64 1/2) (.f64 (cbrt.f64 (neg.f64 g)) (cbrt.f64 (/.f64 -1 a))))
	0.9b	(/.f64 1 (/.f64 (cbrt.f64 (*.f64 2 a)) (cbrt.f64 g)))
✓	13.9b	(cbrt.f64 (/.f64 g (*.f64 2 a)))
	14.3b	(pow.f64 (cbrt.f64 (/.f64 a (/.f64 g 2))) -1)
	14.6b	(.f64 (cbrt.f64 (cbrt.f64 (/.f64 g (.f64 2 a)))) (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 g (*.f64 2 a)))) 2))
	0.9b	(*.f64 (cbrt.f64 (/.f64 g 2)) (/.f64 1 (cbrt.f64 a)))

Compiler

Compiled 1441 to 1048 computations (27.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (cbrt.f64 (/.f64 2 g)))
✓	0.3b	(/.f64 (/.f64 1 (cbrt.f64 (/.f64 2 g))) (cbrt.f64 a))
	0.6b	(cbrt.f64 a)
✓	0.6b	(cbrt.f64 (/.f64 2 g))

series549.0ms (13.7%)

Counts

3 → 48

Calls

3 calls:

446.0ms	(/.f64 (/.f64 1 (cbrt.f64 (/.f64 2 g))) (cbrt.f64 a))
62.0ms	(/.f64 1 (cbrt.f64 (/.f64 2 g)))
41.0ms	(cbrt.f64 (/.f64 2 g))

rewrite63.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

903×	`log1p-expm1-u_binary64`
903×	`expm1-log1p-u_binary64`
99×	`add-sqr-sqrt_binary64`
95×	`egg-rr`
93×	`add-cbrt-cube_binary64`

Counts

3 → 95

Calls

3 calls:

62.0ms	(/.f64 1 (cbrt.f64 (/.f64 2 g)))
62.0ms	(/.f64 (/.f64 1 (cbrt.f64 (/.f64 2 g))) (cbrt.f64 a))
62.0ms	(cbrt.f64 (/.f64 2 g))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	29
1	207	27
2	2404	27
3	5617	27

simplify78.0ms (2%)

Algorithm

1×	egg-herbie

Rules

488×	`unswap-sqr_binary64`
452×	`fma-neg_binary64`
448×	`fma-def_binary64`
366×	`associate-/l*_binary64`
347×	`div-sub_binary64`

Counts

143 → 109

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	53	756
1	112	720
2	208	696
3	538	552
4	1395	508
5	3399	508
6	4868	508
7	4926	508

prune89.0ms (2.2%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	128	5	133
Fresh	5	7	12
Picked	1	0	1
Done	0	2	2
Total	134	14	148

Error

0.0b

Counts

148 → 14

Alt Table

Status	Error	Program
	0.9b	(/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 g)) (cbrt.f64 a))
✓	0.8b	(/.f64 (cbrt.f64 (/.f64 g 2)) (cbrt.f64 a))
	1.5b	(/.f64 (/.f64 1 (*.f64 (cbrt.f64 (cbrt.f64 (/.f64 2 g))) (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 2 g))) 2))) (cbrt.f64 a))
	0.9b	(/.f64 1 (/.f64 (cbrt.f64 (*.f64 2 a)) (cbrt.f64 g)))
✓	13.9b	(cbrt.f64 (/.f64 g (*.f64 2 a)))
	1.5b	(/.f64 (/.f64 1 (cbrt.f64 (/.f64 2 g))) (pow.f64 (cbrt.f64 (cbrt.f64 a)) 3))
	1.1b	(/.f64 (/.f64 1 (*.f64 (cbrt.f64 2) (cbrt.f64 (/.f64 1 g)))) (cbrt.f64 a))
	0.9b	(.f64 (cbrt.f64 g) (/.f64 1 (cbrt.f64 (.f64 2 a))))
	0.9b	(*.f64 (/.f64 1 (cbrt.f64 (/.f64 2 g))) (/.f64 1 (cbrt.f64 a)))
	1.6b	(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 g 2))) 2) (.f64 (cbrt.f64 (cbrt.f64 (/.f64 g 2))) (/.f64 1 (cbrt.f64 a))))
▶	0.8b	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))
	1.3b	(*.f64 (cbrt.f64 (neg.f64 g)) (/.f64 (cbrt.f64 (/.f64 -1 a)) (cbrt.f64 2)))
	0.9b	(.f64 (cbrt.f64 1/2) (.f64 (cbrt.f64 (neg.f64 g)) (cbrt.f64 (/.f64 -1 a))))
	14.3b	(pow.f64 (cbrt.f64 (/.f64 a (/.f64 g 2))) -1)

Compiler

Compiled 2044 to 1560 computations (23.7% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))
✓	0.5b	(cbrt.f64 (/.f64 1/2 a))
✓	0.6b	(cbrt.f64 g)

series438.0ms (10.9%)

Counts

3 → 48

Calls

3 calls:

377.0ms	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))
33.0ms	(cbrt.f64 (/.f64 1/2 a))
28.0ms	(cbrt.f64 g)

rewrite76.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

687×	`log1p-expm1-u_binary64`
687×	`expm1-log1p-u_binary64`
138×	`expm1-udef_binary64`
138×	`log1p-udef_binary64`
127×	`log-pow_binary64`

Counts

3 → 67

Calls

3 calls:

75.0ms	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))
75.0ms	(cbrt.f64 (/.f64 1/2 a))
75.0ms	(cbrt.f64 g)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	162	18
2	1842	18
3	4987	18
4	5023	18

simplify56.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

688×	`unswap-sqr_binary64`
476×	`times-frac_binary64`
431×	`fma-def_binary64`
347×	`div-sub_binary64`
347×	`fma-neg_binary64`

Counts

115 → 80

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	50	680
1	109	680
2	194	624
3	490	512
4	1293	472
5	2564	472
6	5038	472

prune47.0ms (1.2%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	78	2	80
Fresh	2	9	11
Picked	0	1	1
Done	0	2	2
Total	80	14	94

Error

0.0b

Counts

94 → 14

Alt Table

Status	Error	Program
	0.9b	(/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 g)) (cbrt.f64 a))
✓	0.8b	(/.f64 (cbrt.f64 (/.f64 g 2)) (cbrt.f64 a))
	1.5b	(/.f64 (/.f64 1 (*.f64 (cbrt.f64 (cbrt.f64 (/.f64 2 g))) (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 2 g))) 2))) (cbrt.f64 a))
	0.9b	(/.f64 1 (/.f64 (cbrt.f64 (*.f64 2 a)) (cbrt.f64 g)))
✓	13.9b	(cbrt.f64 (/.f64 g (*.f64 2 a)))
	1.5b	(/.f64 (/.f64 1 (cbrt.f64 (/.f64 2 g))) (pow.f64 (cbrt.f64 (cbrt.f64 a)) 3))
	1.1b	(/.f64 (/.f64 1 (*.f64 (cbrt.f64 2) (cbrt.f64 (/.f64 1 g)))) (cbrt.f64 a))
	0.9b	(.f64 (cbrt.f64 g) (/.f64 1 (cbrt.f64 (.f64 2 a))))
	0.9b	(*.f64 (/.f64 1 (cbrt.f64 (/.f64 2 g))) (/.f64 1 (cbrt.f64 a)))
✓	0.8b	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))
	1.3b	(*.f64 (cbrt.f64 (neg.f64 g)) (/.f64 (cbrt.f64 (/.f64 -1 a)) (cbrt.f64 2)))
	0.8b	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 (/.f64 -1 a)) (cbrt.f64 -1/2)))
	0.8b	(*.f64 (cbrt.f64 g) (/.f64 (cbrt.f64 1/2) (cbrt.f64 a)))
	14.3b	(pow.f64 (cbrt.f64 (/.f64 a (/.f64 g 2))) -1)

Compiler

Compiled 993 to 707 computations (28.8% saved)

regimes399.0ms (9.9%)

Accuracy

Total 0.8b remaining (94.1%)

Threshold costs 0.8b (94.1%)

Counts

80 → 1

Compiler

Compiled 5453 to 4489 computations (17.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	8	11

end150.0ms (3.7%)

Compiler: Compiled 182 to 149 computations (18.1% saved)

Details

analyze36.0ms (0.9%)

sample791.0ms (19.7%)

simplify8.0ms (0.2%)

prune2.0ms (0%)

localize4.0ms (0.1%)

series368.0ms (9.2%)

rewrite41.0ms (1%)

simplify63.0ms (1.6%)

prune32.0ms (0.8%)

localize6.0ms (0.1%)

series510.0ms (12.7%)

rewrite51.0ms (1.3%)

simplify69.0ms (1.7%)

prune68.0ms (1.7%)

localize9.0ms (0.2%)

series549.0ms (13.7%)

rewrite63.0ms (1.6%)

simplify78.0ms (2%)

prune89.0ms (2.2%)

localize6.0ms (0.1%)

series438.0ms (10.9%)

rewrite76.0ms (1.9%)

simplify56.0ms (1.4%)

prune47.0ms (1.2%)

regimes399.0ms (9.9%)

simplify3.0ms (0.1%)

end150.0ms (3.7%)

Profiling