Details

analyze500.0ms (11.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	93.6%	6.4%	7
3.1%	84.2%	12.7%	8
12.5%	67.1%	20.5%	9
16%	63.5%	20.5%	10
17.9%	57.7%	24.4%	11
22.6%	48.7%	28.7%	12
28.7%	37.8%	33.6%	13
30.4%	35.9%	33.7%	14

sample29.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	80	valid
3.0ms	90×	body	80	nan
1.0ms	26×	body	80	invalid

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	14	8
1	14	8

prune7.0ms (0.2%)

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

Merged error: 18.8b

Counts

2 → 1

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

1.6b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
6.0b	(/.f64 A (*.f64 V l))
13.6b	(sqrt.f64 (/.f64 A (*.f64 V l)))

rewrite19.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
15×	`sqrt-prod_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`associate-r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`times-frac_binary64`
6×	`pow1_binary64`
3×	`add-log-exp_binary64` `associate-l_binary64` `associate-/l*_binary64` `div-inv_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `associate-/r_binary64` `pow1/2_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`

Counts

3 → 66

Calls

3 calls:

9.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
5.0ms	(/.f64 A (*.f64 V l))
4.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))

series38.0ms (0.9%)

Counts

3 → 9

Calls

3 calls:

20.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
12.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))
6.0ms	(/.f64 A (*.f64 V l))

simplify77.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5085	561

prune136.0ms (3.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	61	14	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	14	76

Merged error: 5.6b

Counts

76 → 14

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.6b	(.f64 c0 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))))
2.1b	(/.f64 V (/.f64 (cbrt.f64 A) l))
3.1b	(/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))
13.6b	(sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l))))

rewrite116.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

849×	`times-frac_binary64`
358×	`add-sqr-sqrt_binary64`
331×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
157×	`sqrt-prod_binary64`
146×	`cbrt-prod_binary64`
93×	`associate-/r*_binary64`
79×	`associate-r_binary64`
32×	`add-exp-log_binary64`
24×	`div-inv_binary64`
23×	`add-cbrt-cube_binary64`
15×	`cbrt-undiv_binary64` `div-exp_binary64`
8×	`associate-/r/_binary64`
7×	`pow1_binary64`
6×	`unswap-sqr_binary64`
5×	`rem-sqrt-square_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `associate-/l*_binary64`
3×	`associate-l_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `-commutative_binary64`

Counts

4 → 463

Calls

4 calls:

32.0ms	(.f64 c0 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))))
21.0ms	(/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))
18.0ms	(sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l))))
8.0ms	(/.f64 V (/.f64 (cbrt.f64 A) l))

series81.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

27.0ms	(/.f64 V (/.f64 (cbrt.f64 A) l))
26.0ms	(.f64 c0 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))))
16.0ms	(sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l))))
11.0ms	(/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))

simplify109.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

475 → 475

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4973	7292
1	4973	7292

prune572.0ms (13.3%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	462	13	475
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	468	21	489

Merged error: 1.8b

Counts

489 → 21

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 A)
1.6b	(.f64 c0 (.f64 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V))) (sqrt.f64 (/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V))))))
1.7b	(/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V)))
5.6b	(sqrt.f64 (/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V))))

rewrite26.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-exp-log_binary64` `add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
12×	`times-frac_binary64` `cbrt-prod_binary64`
11×	`add-cbrt-cube_binary64`
10×	`pow1_binary64` `sqrt-prod_binary64`
6×	`associate-/l*_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
3×	`pow-prod-down_binary64` `associate-l_binary64`
2×	`cbrt-undiv_binary64` `associate-*r/_binary64` `div-inv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`associate-/r_binary64` `pow1/2_binary64` `associate-r_binary64` `pow1/3_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`

Counts

4 → 78

Calls

4 calls:

10.0ms	(.f64 c0 (.f64 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V))) (sqrt.f64 (/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V))))))
8.0ms	(/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V)))
5.0ms	(sqrt.f64 (/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V))))
1.0ms	(cbrt.f64 A)

series137.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

62.0ms	(.f64 c0 (.f64 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V))) (sqrt.f64 (/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V))))))
37.0ms	(sqrt.f64 (/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V))))
20.0ms	(/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V)))
18.0ms	(cbrt.f64 A)

simplify66.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4953	988
1	4953	988

prune167.0ms (3.9%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	86	4	90
Fresh	3	17	20
Picked	0	1	1
Done	0	0	0
Total	89	22	111

Merged error: 1.3b

Counts

111 → 22

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.7b	(/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V)))
1.7b	(/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V)))
6.0b	(cbrt.f64 (/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V))))
6.0b	(cbrt.f64 (/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V))))

rewrite27.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`cbrt-prod_binary64`
24×	`times-frac_binary64`
18×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
14×	`add-exp-log_binary64`
12×	`associate-/l*_binary64`
8×	`add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64`
2×	`cbrt-div_binary64` `associate-/r*_binary64` `cbrt-unprod_binary64` `pow1/3_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64`

Counts

4 → 92

Calls

4 calls:

8.0ms	(/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V)))
6.0ms	(/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V)))
5.0ms	(cbrt.f64 (/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V))))
5.0ms	(cbrt.f64 (/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V))))

series106.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

32.0ms	(cbrt.f64 (/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V))))
32.0ms	(cbrt.f64 (/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V))))
23.0ms	(/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V)))
20.0ms	(/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V)))

simplify57.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4932	946
1	4932	946

prune107.0ms (2.5%)

Pruning

22 alts after pruning (20 fresh and 2 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	20	20
Picked	0	1	1
Done	0	1	1
Total	104	22	126

Merged error: 1.3b

Counts

126 → 22

regimes1.1s (24.9%)

Accuracy

Total 4.8b remaining (74.3%)

Threshold costs 0b (0%)

bsearch46.0ms (1.1%)

Steps

Iters	Range		Point
9	7.740698859183003e+215	6.150527533442182e+220	8.068698780946028e+215
5	2.460894195652485e+142	5.653024837172955e+142	5.565384703489568e+142

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	59
1	42	59

end0.0ms (0%)

sample745.0ms (17.4%)

Algorithm

1×

intervals

Results

309.0ms	8000×	body	80	valid
101.0ms	2835×	body	80	nan
33.0ms	895×	body	80	invalid

Details

analyze500.0ms (11.6%)

sample29.0ms (0.7%)

simplify5.0ms (0.1%)

prune7.0ms (0.2%)

localize7.0ms (0.2%)

rewrite19.0ms (0.5%)

series38.0ms (0.9%)

simplify77.0ms (1.8%)

prune136.0ms (3.2%)

localize10.0ms (0.2%)

rewrite116.0ms (2.7%)

series81.0ms (1.9%)

simplify109.0ms (2.5%)

prune572.0ms (13.3%)

localize13.0ms (0.3%)

rewrite26.0ms (0.6%)

series137.0ms (3.2%)

simplify66.0ms (1.5%)

prune167.0ms (3.9%)

localize17.0ms (0.4%)

rewrite27.0ms (0.6%)

series106.0ms (2.5%)

simplify57.0ms (1.3%)

prune107.0ms (2.5%)

regimes1.1s (24.9%)

bsearch46.0ms (1.1%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample745.0ms (17.4%)

Profiling