Details

analyze35.0ms (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)

sample808.0ms (19.7%)

Results

777.0ms

8256×

body

128

valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify6.0ms (0.1%)

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

17.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	17.0b	(cbrt.f64 (/.f64 g (*.f64 2 a)))

Compiler

Compiled 24 to 18 computations (25% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 g (*.f64 2 a))
✓	16.5b	(cbrt.f64 (/.f64 g (*.f64 2 a)))

series427.0ms (10.4%)

Counts

2 → 48

Calls

2 calls:

418.0ms	(cbrt.f64 (/.f64 g (*.f64 2 a)))
8.0ms	(/.f64 g (*.f64 2 a))

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`cbrt-prod_binary64`
7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
6×	`*-un-lft-identity_binary64`
6×	`times-frac_binary64`

Counts

2 → 41

Calls

2 calls:

3.0ms	(/.f64 g (*.f64 2 a))
2.0ms	(cbrt.f64 (/.f64 g (*.f64 2 a)))

simplify85.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

729×	`associate-/r/_binary64`
549×	`fma-def_binary64`
530×	`associate-l_binary64`
394×	`associate-r_binary64`
317×	`fma-neg_binary64`

Counts

89 → 74

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	105	1134
1	199	1089
2	490	1064
3	1729	928
4	3552	872
5	4609	872
6	4975	872

prune51.0ms (1.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	65	9	74
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	65	10	75

Error

0.2b

Counts

75 → 10

Alt Table

Status	Error	Program
	16.8b	(*.f64 (cbrt.f64 1/2) (cbrt.f64 (/.f64 g a)))
▶	0.8b	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))
	36.7b	(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 g) 2)) (cbrt.f64 (/.f64 (sqrt.f64 g) a)))
	6.8b	(.f64 (cbrt.f64 (/.f64 (.f64 (cbrt.f64 g) (cbrt.f64 g)) 2)) (cbrt.f64 (/.f64 (cbrt.f64 g) a)))
	1.0b	(/.f64 (cbrt.f64 g) (cbrt.f64 (*.f64 2 a)))
	17.6b	(.f64 (.f64 (cbrt.f64 (cbrt.f64 (/.f64 g (.f64 2 a)))) (cbrt.f64 (cbrt.f64 (/.f64 g (.f64 2 a))))) (cbrt.f64 (cbrt.f64 (/.f64 g (*.f64 2 a)))))
✓	17.0b	(cbrt.f64 (/.f64 g (*.f64 2 a)))
	39.5b	(cbrt.f64 (*.f64 (/.f64 (sqrt.f64 g) 2) (/.f64 (sqrt.f64 g) a)))
	16.9b	(cbrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 g) (cbrt.f64 g)) 2) (/.f64 (cbrt.f64 g) a)))
	40.5b	(.f64 (sqrt.f64 (cbrt.f64 (/.f64 g (.f64 2 a)))) (sqrt.f64 (cbrt.f64 (/.f64 g (*.f64 2 a)))))

Compiler

Compiled 1068 to 736 computations (31.1% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))
✓	0.6b	(cbrt.f64 g)
✓	0.6b	(cbrt.f64 (/.f64 1/2 a))

series489.0ms (11.9%)

Counts

3 → 48

Calls

3 calls:

423.0ms	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))
36.0ms	(cbrt.f64 (/.f64 1/2 a))
30.0ms	(cbrt.f64 g)

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`cbrt-prod_binary64`
35×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
20×	`times-frac_binary64`

Counts

3 → 80

Calls

3 calls:

7.0ms	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))
2.0ms	(cbrt.f64 (/.f64 1/2 a))
1.0ms	(cbrt.f64 g)

simplify86.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

521×	`exp-sum_binary64`
480×	`*-commutative_binary64`
376×	`fma-neg_binary64`
371×	`associate-l_binary64`
306×	`associate-r_binary64`

Counts

128 → 116

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	150	1729
1	260	1725
2	655	1660
3	1644	1530
4	3907	1502
5	5154	1502

prune78.0ms (1.9%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	107	9	116
Fresh	4	4	8
Picked	0	1	1
Done	0	1	1
Total	111	15	126

Error

0.0b

Counts

126 → 15

Alt Table

Status	Error	Program
	36.7b	(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 g) 2)) (cbrt.f64 (/.f64 (sqrt.f64 g) a)))
	0.8b	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 (sqrt.f64 1/2)) (cbrt.f64 (/.f64 (sqrt.f64 1/2) a))))
	1.5b	(.f64 (.f64 (cbrt.f64 g) (*.f64 (cbrt.f64 (cbrt.f64 (/.f64 1/2 a))) (cbrt.f64 (cbrt.f64 (/.f64 1/2 a))))) (cbrt.f64 (cbrt.f64 (/.f64 1/2 a))))
	0.9b	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2))) (cbrt.f64 (/.f64 (cbrt.f64 1/2) a))))
▶	0.8b	(.f64 (.f64 (cbrt.f64 g) (cbrt.f64 1/2)) (cbrt.f64 (/.f64 1 a)))
	16.9b	(cbrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 g) (cbrt.f64 g)) 2) (/.f64 (cbrt.f64 g) a)))
	16.8b	(*.f64 (cbrt.f64 1/2) (cbrt.f64 (/.f64 g a)))
✓	0.8b	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))
	32.8b	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 a))) (cbrt.f64 (/.f64 1/2 (sqrt.f64 a)))))
	1.0b	(/.f64 (cbrt.f64 g) (cbrt.f64 (*.f64 2 a)))
	0.9b	(.f64 (cbrt.f64 g) (cbrt.f64 (.f64 (*.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (/.f64 1/2 a))) (cbrt.f64 (/.f64 1/2 a)))))
✓	17.0b	(cbrt.f64 (/.f64 g (*.f64 2 a)))
	0.9b	(/.f64 (*.f64 (cbrt.f64 g) (cbrt.f64 1/2)) (cbrt.f64 a))
	1.2b	(.f64 (.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a))))) (cbrt.f64 (/.f64 1/2 (cbrt.f64 a))))
	1.5b	(.f64 (.f64 (*.f64 (cbrt.f64 (cbrt.f64 g)) (cbrt.f64 (cbrt.f64 g))) (cbrt.f64 (cbrt.f64 g))) (cbrt.f64 (/.f64 1/2 a)))

Compiler

Compiled 1954 to 1299 computations (33.5% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series493.0ms (12%)

Counts

3 → 48

Calls

3 calls:

426.0ms	(.f64 (.f64 (cbrt.f64 g) (cbrt.f64 1/2)) (cbrt.f64 (/.f64 1 a)))
37.0ms	(*.f64 (cbrt.f64 g) (cbrt.f64 1/2))
30.0ms	(cbrt.f64 (/.f64 1 a))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`cbrt-prod_binary64`
30×	`add-sqr-sqrt_binary64`
22×	`associate-r_binary64`
22×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`

Counts

3 → 89

Calls

3 calls:

7.0ms	(.f64 (.f64 (cbrt.f64 g) (cbrt.f64 1/2)) (cbrt.f64 (/.f64 1 a)))
4.0ms	(*.f64 (cbrt.f64 g) (cbrt.f64 1/2))
2.0ms	(cbrt.f64 (/.f64 1 a))

simplify152.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

744×	`fma-neg_binary64`
489×	`exp-sum_binary64`
365×	`*-commutative_binary64`
212×	`associate-+r+_binary64`
204×	`fma-def_binary64`

Counts

137 → 148

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	136	1902
1	271	1834
2	789	1774
3	1407	1540
4	3526	1483
5	4923	1483
6	4972	1483
7	4944	1483
8	5036	1483

prune110.0ms (2.7%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	162	4	166
Fresh	4	8	12
Picked	0	1	1
Done	0	2	2
Total	166	15	181

Error

0.0b

Counts

181 → 15

Alt Table

Status	Error	Program
	36.7b	(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 g) 2)) (cbrt.f64 (/.f64 (sqrt.f64 g) a)))
▶	0.8b	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 (sqrt.f64 1/2)) (cbrt.f64 (/.f64 (sqrt.f64 1/2) a))))
	1.5b	(.f64 (.f64 (cbrt.f64 g) (*.f64 (cbrt.f64 (cbrt.f64 (/.f64 1/2 a))) (cbrt.f64 (cbrt.f64 (/.f64 1/2 a))))) (cbrt.f64 (cbrt.f64 (/.f64 1/2 a))))
	0.9b	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2))) (cbrt.f64 (/.f64 (cbrt.f64 1/2) a))))
	32.1b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 g)) (*.f64 (cbrt.f64 (sqrt.f64 g)) (cbrt.f64 1/2))) (cbrt.f64 (/.f64 1 a)))
✓	0.8b	(.f64 (.f64 (cbrt.f64 g) (cbrt.f64 1/2)) (cbrt.f64 (/.f64 1 a)))
	16.9b	(cbrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 g) (cbrt.f64 g)) 2) (/.f64 (cbrt.f64 g) a)))
	32.8b	(.f64 (.f64 (cbrt.f64 g) (cbrt.f64 1/2)) (*.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 a))) (cbrt.f64 (sqrt.f64 (/.f64 1 a)))))
✓	0.8b	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))
	0.9b	(.f64 (.f64 (cbrt.f64 g) (cbrt.f64 1/2)) (/.f64 1 (cbrt.f64 a)))
	1.0b	(/.f64 (cbrt.f64 g) (cbrt.f64 (*.f64 2 a)))
	0.9b	(.f64 (cbrt.f64 g) (cbrt.f64 (.f64 (*.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (/.f64 1/2 a))) (cbrt.f64 (/.f64 1/2 a)))))
✓	17.0b	(cbrt.f64 (/.f64 g (*.f64 2 a)))
	0.9b	(.f64 (cbrt.f64 (.f64 1/2 g)) (cbrt.f64 (/.f64 1 a)))
	1.5b	(.f64 (.f64 (*.f64 (cbrt.f64 (cbrt.f64 g)) (cbrt.f64 (cbrt.f64 g))) (cbrt.f64 (cbrt.f64 g))) (cbrt.f64 (/.f64 1/2 a)))

Compiler

Compiled 2892 to 2083 computations (28% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 (sqrt.f64 1/2) a)
	0.6b	(cbrt.f64 g)
✓	0.6b	(cbrt.f64 (/.f64 (sqrt.f64 1/2) a))
✓	1.0b	(cbrt.f64 (sqrt.f64 1/2))

series233.0ms (5.7%)

Counts

3 → 12

Calls

3 calls:

230.0ms	(cbrt.f64 (/.f64 (sqrt.f64 1/2) a))
3.0ms	(/.f64 (sqrt.f64 1/2) a)
0.0ms	(cbrt.f64 (sqrt.f64 1/2))

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64`
33×	`add-sqr-sqrt_binary64`
33×	`add-cube-cbrt_binary64`
28×	`cbrt-prod_binary64`

Counts

3 → 90

Calls

3 calls:

3.0ms	(/.f64 (sqrt.f64 1/2) a)
2.0ms	(cbrt.f64 (/.f64 (sqrt.f64 1/2) a))
1.0ms	(cbrt.f64 (sqrt.f64 1/2))

simplify134.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

718×	`fma-neg_binary64`
434×	`associate-/r*_binary64`
413×	`associate-/r/_binary64`
247×	`*-commutative_binary64`
187×	`fma-def_binary64`

Counts

102 → 111

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	125	1474
1	182	1396
2	393	1371
3	1190	1313
4	2659	1273
5	4257	1273
6	4978	1273
7	4993	1273
8	4998	1273

prune101.0ms (2.5%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	124	5	129
Fresh	4	7	11
Picked	1	0	1
Done	0	3	3
Total	129	15	144

Error

0.0b

Counts

144 → 15

Alt Table

Status	Error	Program
	0.9b	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 (sqrt.f64 1/2)) (cbrt.f64 (*.f64 (fabs.f64 (cbrt.f64 1/2)) (/.f64 (sqrt.f64 (cbrt.f64 1/2)) a)))))
✓	0.8b	(.f64 (.f64 (cbrt.f64 g) (cbrt.f64 1/2)) (cbrt.f64 (/.f64 1 a)))
	32.1b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 g)) (*.f64 (cbrt.f64 (sqrt.f64 g)) (cbrt.f64 1/2))) (cbrt.f64 (/.f64 1 a)))
	16.9b	(cbrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 g) (cbrt.f64 g)) 2) (/.f64 (cbrt.f64 g) a)))
	32.0b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 g)) (cbrt.f64 (sqrt.f64 g))) (*.f64 (cbrt.f64 (sqrt.f64 1/2)) (cbrt.f64 (/.f64 (sqrt.f64 1/2) a))))
	0.9b	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 (sqrt.f64 1/2)) (*.f64 (cbrt.f64 (fabs.f64 (cbrt.f64 1/2))) (cbrt.f64 (/.f64 (sqrt.f64 (cbrt.f64 1/2)) a)))))
	0.9b	(.f64 (.f64 (cbrt.f64 g) (cbrt.f64 1/2)) (/.f64 1 (cbrt.f64 a)))
	32.0b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 g)) (sqrt.f64 (cbrt.f64 g))) (*.f64 (cbrt.f64 (sqrt.f64 1/2)) (cbrt.f64 (/.f64 (sqrt.f64 1/2) a))))
	1.8b	(.f64 (cbrt.f64 g) (.f64 (*.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 1/2))) (cbrt.f64 (sqrt.f64 (sqrt.f64 1/2)))) (cbrt.f64 (/.f64 (sqrt.f64 1/2) a))))
	0.9b	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2))) (cbrt.f64 (/.f64 (cbrt.f64 1/2) a))))
	1.0b	(/.f64 (cbrt.f64 g) (cbrt.f64 (*.f64 2 a)))
	0.9b	(.f64 (cbrt.f64 g) (cbrt.f64 (.f64 (*.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (/.f64 1/2 a))) (cbrt.f64 (/.f64 1/2 a)))))
✓	17.0b	(cbrt.f64 (/.f64 g (*.f64 2 a)))
	0.9b	(.f64 (cbrt.f64 (.f64 1/2 g)) (cbrt.f64 (/.f64 1 a)))
✓	0.8b	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))

Compiler

Compiled 2600 to 1999 computations (23.1% saved)

regimes546.0ms (13.3%)

Accuracy

Total 0.8b remaining (91.9%)

Threshold costs 0.8b (91.9%)

Counts

107 → 1

Compiler

Compiled 8749 to 6961 computations (20.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	9	11
2	9	11

end188.0ms (4.6%)

Compiler: Compiled 245 to 196 computations (20% saved)

Details

analyze35.0ms (0.9%)

sample808.0ms (19.7%)

simplify6.0ms (0.1%)

prune2.0ms (0%)

localize4.0ms (0.1%)

series427.0ms (10.4%)

rewrite6.0ms (0.2%)

simplify85.0ms (2.1%)

prune51.0ms (1.3%)

localize6.0ms (0.1%)

series489.0ms (11.9%)

rewrite13.0ms (0.3%)

simplify86.0ms (2.1%)

prune78.0ms (1.9%)

localize7.0ms (0.2%)

series493.0ms (12%)

rewrite20.0ms (0.5%)

simplify152.0ms (3.7%)

prune110.0ms (2.7%)

localize8.0ms (0.2%)

series233.0ms (5.7%)

rewrite10.0ms (0.3%)

simplify134.0ms (3.3%)

prune101.0ms (2.5%)

regimes546.0ms (13.3%)

simplify2.0ms (0%)

end188.0ms (4.6%)

Profiling