Details

analyze38.0ms (0.8%)

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)

sample836.0ms (17.7%)

Results

805.0ms

8256×

body

128

valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify7.0ms (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

16.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	16.6b	(cbrt.f64 (/.f64 g (*.f64 2 a)))

Compiler

Compiled 24 to 18 computations (25% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 g (*.f64 2 a))
✓	15.7b	(cbrt.f64 (/.f64 g (*.f64 2 a)))

series432.0ms (9.1%)

Counts

2 → 48

Calls

2 calls:

423.0ms	(cbrt.f64 (/.f64 g (*.f64 2 a)))
9.0ms	(/.f64 g (*.f64 2 a))

rewrite7.0ms (0.1%)

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)))

simplify82.0ms (1.7%)

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

prune56.0ms (1.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	62	12	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	12	75

Error

0.2b

Counts

75 → 12

Alt Table

Status	Error	Program
▶	0.8b	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))
	16.1b	(*.f64 (cbrt.f64 1/2) (cbrt.f64 (/.f64 g a)))
	16.1b	(cbrt.f64 (*.f64 g (/.f64 1/2 a)))
	38.0b	(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 g) 2)) (cbrt.f64 (/.f64 (sqrt.f64 g) a)))
	17.0b	(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 g (.f64 a 2))) 2)) (cbrt.f64 (cbrt.f64 (/.f64 g (*.f64 a 2)))))
	1.3b	(/.f64 (cbrt.f64 g) (cbrt.f64 (*.f64 2 a)))
	17.2b	(.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)))))
	42.2b	(cbrt.f64 (.f64 (sqrt.f64 (/.f64 g (.f64 2 a))) (sqrt.f64 (/.f64 g (*.f64 2 a)))))
	16.7b	(cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (/.f64 g (.f64 a 2))) 2) (cbrt.f64 (/.f64 g (*.f64 a 2)))))
	16.8b	(cbrt.f64 (/.f64 (.f64 (cbrt.f64 g) (cbrt.f64 g)) (/.f64 (.f64 2 a) (cbrt.f64 g))))
	6.0b	(.f64 (cbrt.f64 (/.f64 (.f64 (cbrt.f64 g) (cbrt.f64 g)) 2)) (cbrt.f64 (/.f64 (cbrt.f64 g) a)))
	42.4b	(.f64 (cbrt.f64 (sqrt.f64 (/.f64 g (.f64 2 a)))) (cbrt.f64 (sqrt.f64 (/.f64 g (*.f64 2 a)))))

Compiler

Compiled 1158 to 808 computations (30.2% 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)))
✓	0.5b	(cbrt.f64 (/.f64 1/2 a))
✓	0.6b	(cbrt.f64 g)

series487.0ms (10.3%)

Counts

3 → 48

Calls

3 calls:

421.0ms	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))
36.0ms	(cbrt.f64 (/.f64 1/2 a))
29.0ms	(cbrt.f64 g)

rewrite15.0ms (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)

simplify87.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

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

Counts

128 → 108

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

prune86.0ms (1.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	96	12	108
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	103	17	120

Error

0.0b

Counts

120 → 17

Alt Table

Status	Error	Program
	1.1b	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (cbrt.f64 (/.f64 1/2 (cbrt.f64 a)))))
	34.3b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 g)) (cbrt.f64 (sqrt.f64 g))) (cbrt.f64 (/.f64 1/2 a)))
	0.9b	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 (sqrt.f64 1/2)) (cbrt.f64 (/.f64 (sqrt.f64 1/2) a))))
	1.2b	(.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 g) (cbrt.f64 g))) (cbrt.f64 (cbrt.f64 g))) (cbrt.f64 (/.f64 1/2 a)))
	1.2b	(.f64 (.f64 (cbrt.f64 g) (cbrt.f64 (*.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (/.f64 1/2 a))))) (cbrt.f64 (cbrt.f64 (/.f64 1/2 a))))
	31.3b	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 a))) (cbrt.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 a)))))
	16.7b	(cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (/.f64 g (.f64 a 2))) 2) (cbrt.f64 (/.f64 g (*.f64 a 2)))))
	33.9b	(.f64 (sqrt.f64 (.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))) (sqrt.f64 (*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))))
	16.1b	(*.f64 (cbrt.f64 1/2) (cbrt.f64 (/.f64 g a)))
	0.9b	(.f64 (.f64 (cbrt.f64 g) (cbrt.f64 (sqrt.f64 1/2))) (cbrt.f64 (/.f64 (sqrt.f64 1/2) a)))
	42.4b	(.f64 (cbrt.f64 (sqrt.f64 (/.f64 g (.f64 2 a)))) (cbrt.f64 (sqrt.f64 (/.f64 g (*.f64 2 a)))))
	1.3b	(/.f64 (cbrt.f64 g) (cbrt.f64 (*.f64 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 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 g))
	0.8b	(/.f64 (*.f64 (cbrt.f64 g) (cbrt.f64 1/2)) (cbrt.f64 a))
	1.5b	(.f64 (cbrt.f64 g) (.f64 (*.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)))))
	16.1b	(cbrt.f64 (*.f64 g (/.f64 1/2 a)))

Compiler

Compiled 1939 to 1328 computations (31.5% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 g))
	0.5b	(cbrt.f64 (/.f64 1/2 a))
	0.6b	(cbrt.f64 g)

series418.0ms (8.8%)

Counts

1 → 24

Calls

1 calls:

417.0ms

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

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`associate-l_binary64`
11×	`times-frac_binary64`
11×	`*-un-lft-identity_binary64`

Counts

1 → 43

Calls

1 calls:

7.0ms

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

simplify92.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

838×	`div-sub_binary64`
567×	`times-frac_binary64`
520×	`fma-def_binary64`
489×	`fma-neg_binary64`
216×	`sqr-pow_binary64`

Counts

67 → 71

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	115	1128
1	196	1128
2	345	1096
3	664	959
4	1364	935
5	2590	928
6	4244	928
7	5174	928

prune103.0ms (2.2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	118	3	121
Fresh	3	13	16
Picked	1	0	1
Done	0	0	0
Total	122	16	138

Error

0.0b

Counts

138 → 16

Alt Table

Status	Error	Program
	1.1b	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (cbrt.f64 (/.f64 1/2 (cbrt.f64 a)))))
	34.3b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 g)) (cbrt.f64 (sqrt.f64 g))) (cbrt.f64 (/.f64 1/2 a)))
	31.3b	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 a))) (cbrt.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 a)))))
	16.7b	(cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (/.f64 g (.f64 a 2))) 2) (cbrt.f64 (/.f64 g (*.f64 a 2)))))
	0.9b	(.f64 (cbrt.f64 (/.f64 (.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) 1)) (*.f64 (cbrt.f64 (/.f64 (cbrt.f64 1/2) a)) (cbrt.f64 g)))
	33.9b	(.f64 (sqrt.f64 (.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))) (sqrt.f64 (*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))))
	16.1b	(*.f64 (cbrt.f64 1/2) (cbrt.f64 (/.f64 g a)))
	1.0b	(.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (.f64 (*.f64 (cbrt.f64 g) (cbrt.f64 g)) (cbrt.f64 g))))
	0.9b	(.f64 (.f64 (cbrt.f64 g) (cbrt.f64 (sqrt.f64 1/2))) (cbrt.f64 (/.f64 (sqrt.f64 1/2) a)))
	42.4b	(.f64 (cbrt.f64 (sqrt.f64 (/.f64 g (.f64 2 a)))) (cbrt.f64 (sqrt.f64 (/.f64 g (*.f64 2 a)))))
	1.3b	(/.f64 (cbrt.f64 g) (cbrt.f64 (*.f64 2 a)))
	1.2b	(.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 g) (cbrt.f64 g))) (cbrt.f64 (cbrt.f64 g))) (cbrt.f64 (/.f64 1/2 a)))
	0.9b	(.f64 (cbrt.f64 (/.f64 (sqrt.f64 1/2) 1)) (.f64 (cbrt.f64 (/.f64 (sqrt.f64 1/2) a)) (cbrt.f64 g)))
▶	0.8b	(/.f64 (*.f64 (cbrt.f64 g) (cbrt.f64 1/2)) (cbrt.f64 a))
	1.5b	(.f64 (cbrt.f64 g) (.f64 (*.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)))))
	16.1b	(cbrt.f64 (*.f64 g (/.f64 1/2 a)))

Compiler

Compiled 2138 to 1448 computations (32.3% 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 a))
✓	0.5b	(*.f64 (cbrt.f64 g) (cbrt.f64 1/2))
	0.6b	(cbrt.f64 g)
✓	0.6b	(cbrt.f64 a)

series495.0ms (10.5%)

Counts

3 → 48

Calls

3 calls:

425.0ms	(/.f64 (*.f64 (cbrt.f64 g) (cbrt.f64 1/2)) (cbrt.f64 a))
39.0ms	(*.f64 (cbrt.f64 g) (cbrt.f64 1/2))
30.0ms	(cbrt.f64 a)

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
10×	`add-exp-log_binary64`

Counts

3 → 72

Calls

3 calls:

6.0ms	(*.f64 (cbrt.f64 g) (cbrt.f64 1/2))
4.0ms	(/.f64 (*.f64 (cbrt.f64 g) (cbrt.f64 1/2)) (cbrt.f64 a))
1.0ms	(cbrt.f64 a)

simplify81.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

876×	`times-frac_binary64`
474×	`associate-/l*_binary64`
338×	`associate-l_binary64`
287×	`associate-r_binary64`
231×	`associate-/r*_binary64`

Counts

120 → 124

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	136	1629
1	266	1546
2	858	1496
3	4046	1340
4	4968	1340

prune98.0ms (2.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	137	5	142
Fresh	3	12	15
Picked	1	0	1
Done	0	0	0
Total	141	17	158

Error

0.0b

Counts

158 → 17

Alt Table

Status	Error	Program
	1.1b	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (cbrt.f64 (/.f64 1/2 (cbrt.f64 a)))))
	34.3b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 g)) (cbrt.f64 (sqrt.f64 g))) (cbrt.f64 (/.f64 1/2 a)))
	31.3b	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 a))) (cbrt.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 a)))))
	16.7b	(cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (/.f64 g (.f64 a 2))) 2) (cbrt.f64 (/.f64 g (*.f64 a 2)))))
	0.9b	(.f64 (cbrt.f64 (/.f64 (.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) 1)) (*.f64 (cbrt.f64 (/.f64 (cbrt.f64 1/2) a)) (cbrt.f64 g)))
	33.9b	(.f64 (sqrt.f64 (.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))) (sqrt.f64 (*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))))
	1.0b	(.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (.f64 (*.f64 (cbrt.f64 g) (cbrt.f64 g)) (cbrt.f64 g))))
	16.1b	(cbrt.f64 (*.f64 g (/.f64 1/2 a)))
	31.2b	(/.f64 (/.f64 (*.f64 (cbrt.f64 g) (cbrt.f64 1/2)) (sqrt.f64 (cbrt.f64 a))) (sqrt.f64 (cbrt.f64 a)))
	42.4b	(.f64 (cbrt.f64 (sqrt.f64 (/.f64 g (.f64 2 a)))) (cbrt.f64 (sqrt.f64 (/.f64 g (*.f64 2 a)))))
	16.1b	(cbrt.f64 (/.f64 (*.f64 g 1/2) a))
	31.3b	(/.f64 (/.f64 (*.f64 (cbrt.f64 g) (cbrt.f64 1/2)) (cbrt.f64 (sqrt.f64 a))) (cbrt.f64 (sqrt.f64 a)))
	1.3b	(/.f64 (cbrt.f64 g) (cbrt.f64 (*.f64 2 a)))
	1.2b	(.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 g) (cbrt.f64 g))) (cbrt.f64 (cbrt.f64 g))) (cbrt.f64 (/.f64 1/2 a)))
	0.9b	(.f64 (cbrt.f64 (/.f64 (sqrt.f64 1/2) 1)) (.f64 (cbrt.f64 (/.f64 (sqrt.f64 1/2) a)) (cbrt.f64 g)))
	1.0b	(/.f64 (.f64 (cbrt.f64 (.f64 (*.f64 (cbrt.f64 g) (cbrt.f64 g)) (cbrt.f64 g))) (cbrt.f64 1/2)) (cbrt.f64 a))
	0.8b	(/.f64 (cbrt.f64 (*.f64 g 1/2)) (cbrt.f64 a))

Compiler

Compiled 2047 to 1215 computations (40.6% saved)

regimes1.1s (22.3%)

Accuracy

Total 0.8b remaining (91.5%)

Threshold costs 0.8b (91.5%)

Counts

171 → 1

Compiler

Compiled 12541 to 9735 computations (22.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	11
1	14	11
2	13	11

end197.0ms (4.2%)

Compiler: Compiled 272 to 200 computations (26.5% saved)

Details

analyze38.0ms (0.8%)

sample836.0ms (17.7%)

simplify7.0ms (0.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series432.0ms (9.1%)

rewrite7.0ms (0.1%)

simplify82.0ms (1.7%)

prune56.0ms (1.2%)

localize6.0ms (0.1%)

series487.0ms (10.3%)

rewrite15.0ms (0.3%)

simplify87.0ms (1.8%)

prune86.0ms (1.8%)

localize7.0ms (0.1%)

series418.0ms (8.8%)

rewrite10.0ms (0.2%)

simplify92.0ms (1.9%)

prune103.0ms (2.2%)

localize7.0ms (0.2%)

series495.0ms (10.5%)

rewrite14.0ms (0.3%)

simplify81.0ms (1.7%)

prune98.0ms (2.1%)

regimes1.1s (22.3%)

simplify3.0ms (0.1%)

end197.0ms (4.2%)

Profiling