Details

analyze49.0ms (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)

sample17.0ms (0.3%)

Algorithm

1×

intervals

Results

8.0ms

256×

body

128

valid

Compiler

Compiled 19 to 15 computations (21.1% saved)

simplify10.0ms (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

14.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	14.7b	(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
✓	14.4b	(cbrt.f64 (/.f64 g (*.f64 2 a)))

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`cbrt-prod_binary64`
3×	`*-un-lft-identity_binary64`
3×	`times-frac_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 18

Calls

1 calls:

2.0ms

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

series636.0ms (10.8%)

Counts

1 → 24

Calls

1 calls:

636.0ms

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

simplify82.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

809×	`div-sub_binary64`
664×	`fma-def_binary64`
461×	`fma-neg_binary64`
390×	`times-frac_binary64`
300×	`unswap-sqr_binary64`

Counts

42 → 80

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	74	709
1	117	709
2	178	685
3	426	549
4	960	513
5	2276	513
6	4146	513
7	5010	513

prune33.0ms (0.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	71	9	80
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	71	10	81

Error

0.2b

Counts

81 → 10

Alt Table

Status	Error	Program
✓	14.7b	(cbrt.f64 (/.f64 g (*.f64 2 a)))
	15.0b	(.f64 (cbrt.f64 (.f64 (cbrt.f64 (/.f64 g (.f64 2 a))) (cbrt.f64 (/.f64 g (.f64 2 a))))) (cbrt.f64 (cbrt.f64 (/.f64 g (*.f64 2 a)))))
	14.7b	(*.f64 (cbrt.f64 1/2) (cbrt.f64 (/.f64 g a)))
	39.4b	(.f64 (sqrt.f64 (cbrt.f64 (/.f64 g (.f64 2 a)))) (sqrt.f64 (cbrt.f64 (/.f64 g (*.f64 2 a)))))
▶	0.8b	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))
	36.0b	(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 g) 2)) (cbrt.f64 (/.f64 (sqrt.f64 g) a)))
	4.5b	(.f64 (cbrt.f64 (/.f64 (.f64 (cbrt.f64 g) (cbrt.f64 g)) 2)) (cbrt.f64 (/.f64 (cbrt.f64 g) a)))
	39.4b	(.f64 (cbrt.f64 (sqrt.f64 (/.f64 g (.f64 2 a)))) (cbrt.f64 (sqrt.f64 (/.f64 g (*.f64 2 a)))))
	0.8b	(/.f64 (cbrt.f64 g) (cbrt.f64 (*.f64 2 a)))
	15.3b	(.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)))))

Compiler

Compiled 727 to 530 computations (27.1% 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)))
✓	0.5b	(cbrt.f64 g)
✓	0.6b	(cbrt.f64 (/.f64 1/2 a))

rewrite15.0ms (0.2%)

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

series1.2s (19.7%)

Counts

3 → 48

Calls

3 calls:

715.0ms	(*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))
223.0ms	(cbrt.f64 g)
222.0ms	(cbrt.f64 (/.f64 1/2 a))

simplify104.0ms (1.8%)

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 → 208

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

prune93.0ms (1.6%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	196	12	208
Fresh	4	4	8
Picked	1	0	1
Done	0	1	1
Total	201	17	218

Error

0.0b

Counts

218 → 17

Alt Table

Status	Error	Program
▶	0.8b	(.f64 (.f64 (cbrt.f64 g) (cbrt.f64 (sqrt.f64 1/2))) (cbrt.f64 (/.f64 (sqrt.f64 1/2) 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)))
	0.9b	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 (/.f64 -1 a)) (cbrt.f64 -1/2)))
	39.4b	(.f64 (cbrt.f64 (sqrt.f64 (/.f64 g (.f64 2 a)))) (cbrt.f64 (sqrt.f64 (/.f64 g (*.f64 2 a)))))
	1.5b	(.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))) (cbrt.f64 (.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a))))) (cbrt.f64 (*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))))
	0.9b	(*.f64 (cbrt.f64 g) (/.f64 (cbrt.f64 1/2) (cbrt.f64 a)))
✓	14.7b	(cbrt.f64 (/.f64 g (*.f64 2 a)))
	32.1b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 g)) (sqrt.f64 (cbrt.f64 g))) (cbrt.f64 (/.f64 1/2 a)))
	1.1b	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 (/.f64 (sqrt.f64 1/2) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (cbrt.f64 (/.f64 (sqrt.f64 1/2) (cbrt.f64 a)))))
	1.2b	(.f64 (cbrt.f64 (.f64 (cbrt.f64 g) (cbrt.f64 g))) (*.f64 (cbrt.f64 (cbrt.f64 g)) (cbrt.f64 (/.f64 1/2 a))))
	1.5b	(.f64 (.f64 (cbrt.f64 (cbrt.f64 g)) (cbrt.f64 (cbrt.f64 g))) (*.f64 (cbrt.f64 (cbrt.f64 g)) (cbrt.f64 (/.f64 1/2 a))))
	0.9b	(.f64 (.f64 (cbrt.f64 g) (cbrt.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)))) (cbrt.f64 (/.f64 (cbrt.f64 1/2) a)))
	4.5b	(.f64 (cbrt.f64 (/.f64 (.f64 (cbrt.f64 g) (cbrt.f64 g)) 2)) (cbrt.f64 (/.f64 (cbrt.f64 g) a)))
	0.8b	(/.f64 (cbrt.f64 g) (cbrt.f64 (*.f64 2 a)))
	15.3b	(.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)))))
	1.4b	(.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))))
	0.8b	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 (sqrt.f64 1/2)) (cbrt.f64 (/.f64 (sqrt.f64 1/2) a))))

Compiler

Compiled 2087 to 1390 computations (33.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite12.0ms (0.2%)

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))

series382.0ms (6.5%)

Counts

3 → 12

Calls

3 calls:

370.0ms	(cbrt.f64 (/.f64 (sqrt.f64 1/2) a))
12.0ms	(/.f64 (sqrt.f64 1/2) a)
0.0ms	(cbrt.f64 (sqrt.f64 1/2))

simplify154.0ms (2.6%)

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 → 155

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

prune105.0ms (1.8%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	194	2	196
Fresh	5	10	15
Picked	0	1	1
Done	0	1	1
Total	199	14	213

Error

0.0b

Counts

213 → 14

Alt Table

Status	Error	Program
	1.0b	(.f64 (.f64 (cbrt.f64 g) (cbrt.f64 (sqrt.f64 1/2))) (cbrt.f64 (/.f64 (*.f64 (cbrt.f64 (sqrt.f64 1/2)) (cbrt.f64 (sqrt.f64 1/2))) (/.f64 a (cbrt.f64 (sqrt.f64 1/2))))))
	1.1b	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 (/.f64 (sqrt.f64 1/2) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (cbrt.f64 (/.f64 (sqrt.f64 1/2) (cbrt.f64 a)))))
	0.9b	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 (/.f64 -1 a)) (cbrt.f64 -1/2)))
	39.4b	(.f64 (cbrt.f64 (sqrt.f64 (/.f64 g (.f64 2 a)))) (cbrt.f64 (sqrt.f64 (/.f64 g (*.f64 2 a)))))
	1.5b	(.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))) (cbrt.f64 (.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a))))) (cbrt.f64 (*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))))
	0.9b	(*.f64 (cbrt.f64 g) (/.f64 (cbrt.f64 1/2) (cbrt.f64 a)))
✓	14.7b	(cbrt.f64 (/.f64 g (*.f64 2 a)))
	1.1b	(.f64 (.f64 (cbrt.f64 g) (cbrt.f64 (sqrt.f64 1/2))) (cbrt.f64 (/.f64 (/.f64 (sqrt.f64 1/2) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))))
	1.4b	(.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))))
	32.1b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 g)) (sqrt.f64 (cbrt.f64 g))) (cbrt.f64 (/.f64 1/2 a)))
	1.5b	(.f64 (.f64 (cbrt.f64 (cbrt.f64 g)) (cbrt.f64 (cbrt.f64 g))) (*.f64 (cbrt.f64 (cbrt.f64 g)) (cbrt.f64 (/.f64 1/2 a))))
✓	0.8b	(.f64 (.f64 (cbrt.f64 g) (cbrt.f64 (sqrt.f64 1/2))) (cbrt.f64 (/.f64 (sqrt.f64 1/2) a)))
	4.5b	(.f64 (cbrt.f64 (/.f64 (.f64 (cbrt.f64 g) (cbrt.f64 g)) 2)) (cbrt.f64 (/.f64 (cbrt.f64 g) a)))
▶	0.8b	(/.f64 (cbrt.f64 g) (cbrt.f64 (*.f64 2 a)))

Compiler

Compiled 2756 to 2100 computations (23.8% 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 2 a)))
	0.5b	(cbrt.f64 g)
✓	0.6b	(cbrt.f64 (*.f64 2 a))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`times-frac_binary64`
23×	`cbrt-prod_binary64`
19×	`*-un-lft-identity_binary64`
19×	`add-sqr-sqrt_binary64`
19×	`add-cube-cbrt_binary64`

Counts

2 → 59

Calls

2 calls:

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

series916.0ms (15.5%)

Counts

2 → 36

Calls

2 calls:

675.0ms	(/.f64 (cbrt.f64 g) (cbrt.f64 (*.f64 2 a)))
241.0ms	(cbrt.f64 (*.f64 2 a))

simplify150.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

558×	`fma-def_binary64`
438×	`times-frac_binary64`
415×	`associate-/l/_binary64`
378×	`associate-l_binary64`
353×	`associate-/r*_binary64`

Counts

95 → 180

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	124	1680
1	205	1634
2	380	1598
3	763	1452
4	1689	1416
5	4383	1416
6	4743	1416
7	4916	1416

prune95.0ms (1.6%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	257	5	262
Fresh	3	8	11
Picked	1	0	1
Done	0	2	2
Total	261	15	276

Error

0.0b

Counts

276 → 15

Alt Table

Status	Error	Program
	1.0b	(.f64 (.f64 (cbrt.f64 g) (cbrt.f64 (sqrt.f64 1/2))) (cbrt.f64 (/.f64 (*.f64 (cbrt.f64 (sqrt.f64 1/2)) (cbrt.f64 (sqrt.f64 1/2))) (/.f64 a (cbrt.f64 (sqrt.f64 1/2))))))
	1.1b	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 (/.f64 (sqrt.f64 1/2) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (cbrt.f64 (/.f64 (sqrt.f64 1/2) (cbrt.f64 a)))))
	0.9b	(.f64 (cbrt.f64 g) (.f64 (cbrt.f64 (/.f64 -1 a)) (cbrt.f64 -1/2)))
	1.2b	(/.f64 (/.f64 (cbrt.f64 g) (cbrt.f64 2)) (cbrt.f64 a))
	1.5b	(.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))) (cbrt.f64 (.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a))))) (cbrt.f64 (*.f64 (cbrt.f64 g) (cbrt.f64 (/.f64 1/2 a)))))
	0.9b	(*.f64 (cbrt.f64 g) (/.f64 (cbrt.f64 1/2) (cbrt.f64 a)))
	1.5b	(/.f64 (/.f64 (cbrt.f64 g) (.f64 (cbrt.f64 (cbrt.f64 (.f64 2 a))) (cbrt.f64 (cbrt.f64 (.f64 2 a))))) (cbrt.f64 (cbrt.f64 (.f64 2 a))))
✓	14.7b	(cbrt.f64 (/.f64 g (*.f64 2 a)))
	1.1b	(.f64 (/.f64 (cbrt.f64 (.f64 (cbrt.f64 g) (cbrt.f64 g))) 1) (/.f64 (cbrt.f64 (cbrt.f64 g)) (cbrt.f64 (*.f64 2 a))))
	32.1b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 g)) (sqrt.f64 (cbrt.f64 g))) (cbrt.f64 (/.f64 1/2 a)))
	1.5b	(.f64 (.f64 (cbrt.f64 (cbrt.f64 g)) (cbrt.f64 (cbrt.f64 g))) (*.f64 (cbrt.f64 (cbrt.f64 g)) (cbrt.f64 (/.f64 1/2 a))))
✓	0.8b	(.f64 (.f64 (cbrt.f64 g) (cbrt.f64 (sqrt.f64 1/2))) (cbrt.f64 (/.f64 (sqrt.f64 1/2) a)))
	0.9b	(/.f64 1 (/.f64 (cbrt.f64 (*.f64 2 a)) (cbrt.f64 g)))
	0.8b	(/.f64 (/.f64 (cbrt.f64 g) 1) (cbrt.f64 (*.f64 2 a)))
	1.4b	(.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))))

Compiler

Compiled 2008 to 1269 computations (36.8% saved)

regimes1.1s (19.3%)

Accuracy

Total 0.8b remaining (93.7%)

Threshold costs 0.8b (93.7%)

Compiler

Compiled 16249 to 12636 computations (22.2% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	13	20
2	13	20

end1.0ms (0%)

Compiler: Compiled 14 to 12 computations (14.3% saved)

sample704.0ms (11.9%)

Algorithm

1×

intervals

Results

276.0ms

8000×

body

128

valid

Compiler

Compiled 268 to 207 computations (22.8% saved)

Details

analyze49.0ms (0.8%)

sample17.0ms (0.3%)

simplify10.0ms (0.2%)

prune2.0ms (0%)

localize4.0ms (0.1%)

rewrite3.0ms (0.1%)

series636.0ms (10.8%)

simplify82.0ms (1.4%)

prune33.0ms (0.6%)

localize6.0ms (0.1%)

rewrite15.0ms (0.2%)

series1.2s (19.7%)

simplify104.0ms (1.8%)

prune93.0ms (1.6%)

localize9.0ms (0.2%)

rewrite12.0ms (0.2%)

series382.0ms (6.5%)

simplify154.0ms (2.6%)

prune105.0ms (1.8%)

localize6.0ms (0.1%)

rewrite9.0ms (0.1%)

series916.0ms (15.5%)

simplify150.0ms (2.5%)

prune95.0ms (1.6%)

regimes1.1s (19.3%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample704.0ms (11.9%)

Profiling