Details

analyze1.1s (25.3%)

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%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.8%	98%	0.2%	10
7.7%	92.1%	0.2%	11
10.4%	89.4%	0.2%	12
14.9%	84.9%	0.2%	13
16.2%	83.5%	0.3%	14

sample31.0ms (0.7%)

Algorithm

1×

intervals

Results

8.0ms	212×	body	80	valid
2.0ms	11×	body	1280	valid
2.0ms	51×	body	80	invalid
2.0ms	10×	body	640	valid
2.0ms	14×	body	320	valid
1.0ms	8×	body	160	valid
0.0ms	1×	body	2560	valid

simplify61.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4912	13
1	4912	13

prune8.0ms (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: 27.2b

Counts

2 → 1

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (-.f64 y x) (-.f64 z t))
2.4b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))
19.9b	(/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))

rewrite38.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
13×	`flip3--_binary64` `flip--_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`associate-/l/_binary64` `frac-times_binary64`
7×	`add-cube-cbrt_binary64`
5×	`associate-/r_binary64` `add-log-exp_binary64` `pow1_binary64` `associate-r_binary64` `associate-l*_binary64` `times-frac_binary64`
4×	`associate-r/_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `associate-l/_binary64`
2×	`sub-neg_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 79

Calls

3 calls:

17.0ms	(/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))
10.0ms	(*.f64 (-.f64 y x) (-.f64 z t))
8.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

series126.0ms (2.9%)

Counts

3 → 9

Calls

3 calls:

70.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))
44.0ms	(/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))
12.0ms	(*.f64 (-.f64 y x) (-.f64 z t))

simplify43.0ms (1%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	6015	1085

prune145.0ms (3.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	77	11	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	11	89

Merged error: 3.8b

Counts

89 → 11

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
2.4b	(+.f64 x (*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t))))
2.8b	(*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)))

rewrite35.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`add-sqr-sqrt_binary64`
73×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-r_binary64`
27×	`add-cube-cbrt_binary64`
23×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-/r_binary64` `add-log-exp_binary64` `pow1_binary64` `flip3--_binary64` `associate-l_binary64` `associate-/l_binary64` `flip--_binary64`
4×	`associate-/r/_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-r/_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 119

Calls

3 calls:

17.0ms	(*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)))
8.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
4.0ms	(+.f64 x (*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t))))

series129.0ms (2.9%)

Counts

3 → 9

Calls

3 calls:

69.0ms	(+.f64 x (*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t))))
47.0ms	(*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)))
12.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

simplify44.0ms (1%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5068	1606

prune172.0ms (3.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	121	7	128
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	127	12	139

Merged error: 3.8b

Counts

139 → 12

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 a t) (-.f64 z t))
2.4b	(+.f64 x (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t))))
2.8b	(/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))

rewrite85.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

330×	`times-frac_binary64`
323×	`*-un-lft-identity_binary64`
321×	`add-sqr-sqrt_binary64`
113×	`add-cube-cbrt_binary64`
104×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
36×	`associate-/r*_binary64`
15×	`associate-/r/_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
9×	`flip3--_binary64` `flip--_binary64`
8×	`div-inv_binary64`
5×	`add-log-exp_binary64`
4×	`associate-/l/_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`pow1_binary64` `div-sub_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`flip3-+_binary64` `associate-+r-_binary64` `distribute-lft-out_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

3 → 274

Calls

3 calls:

42.0ms	(+.f64 x (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t))))
16.0ms	(/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))
9.0ms	(/.f64 (-.f64 a t) (-.f64 z t))

series146.0ms (3.3%)

Counts

3 → 9

Calls

3 calls:

69.0ms	(+.f64 x (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t))))
65.0ms	(/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))
12.0ms	(/.f64 (-.f64 a t) (-.f64 z t))

simplify77.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5092	5477

prune304.0ms (6.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	279	4	283
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	281	14	295

Merged error: 3.8b

Counts

295 → 14

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (-.f64 a t))
0.3b	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
2.8b	(.f64 (-.f64 y x) (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))))
3.6b	(+.f64 x (.f64 (-.f64 y x) (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))))

rewrite47.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64`
44×	`*-un-lft-identity_binary64`
32×	`add-exp-log_binary64` `times-frac_binary64`
25×	`add-cube-cbrt_binary64`
22×	`associate-r_binary64`
20×	`add-cbrt-cube_binary64` `frac-times_binary64`
17×	`flip3--_binary64` `flip--_binary64`
13×	`prod-exp_binary64`
12×	`pow1_binary64`
10×	`associate-r/_binary64` `associate-l_binary64` `associate-l/_binary64`
9×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
7×	`cbrt-unprod_binary64`
6×	`add-log-exp_binary64` `div-exp_binary64`
5×	`associate-/r*_binary64`
4×	`pow-prod-down_binary64` `associate-/r/_binary64` `un-div-inv_binary64`
3×	`1-exp_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `rec-exp_binary64` `associate-/l*_binary64`
2×	`div-inv_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `+-commutative_binary64` `pow-flip_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 146

Calls

4 calls:

16.0ms	(.f64 (-.f64 y x) (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))))
15.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
6.0ms	(/.f64 1 (-.f64 a t))
5.0ms	(+.f64 x (.f64 (-.f64 y x) (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))))

series137.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

71.0ms	(+.f64 x (.f64 (-.f64 y x) (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))))
45.0ms	(.f64 (-.f64 y x) (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))))
15.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
6.0ms	(/.f64 1 (-.f64 a t))

simplify48.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5748	1773

prune151.0ms (3.4%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	158	14	172

Merged error: 3.8b

Counts

172 → 14

regimes546.0ms (12.4%)

Accuracy

Total 6.7b remaining (62.6%)

Threshold costs 0b (0%)

bsearch54.0ms (1.2%)

Steps

Iters	Range		Point
9	3.460757096827721e-129	4.2348902560365425e-123	3.517675129380762e-129
10	-3.2471889374812983e-75	-4.9152245920875165e-88	-8.259863305585935e-85

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	81	35
1	81	35

end0.0ms (0%)

sample817.0ms (18.6%)

Algorithm

1×

intervals

Results

271.0ms	6545×	body	80	valid
74.0ms	448×	body	640	valid
52.0ms	265×	body	1280	valid
47.0ms	426×	body	320	valid
46.0ms	1183×	body	80	invalid
22.0ms	292×	body	160	valid
5.0ms	24×	body	2560	valid

Details

analyze1.1s (25.3%)

sample31.0ms (0.7%)

simplify61.0ms (1.4%)

prune8.0ms (0.2%)

localize9.0ms (0.2%)

rewrite38.0ms (0.9%)

series126.0ms (2.9%)

simplify43.0ms (1%)

prune145.0ms (3.3%)

localize10.0ms (0.2%)

rewrite35.0ms (0.8%)

series129.0ms (2.9%)

simplify44.0ms (1%)

prune172.0ms (3.9%)

localize9.0ms (0.2%)

rewrite85.0ms (1.9%)

series146.0ms (3.3%)

simplify77.0ms (1.7%)

prune304.0ms (6.9%)

localize11.0ms (0.2%)

rewrite47.0ms (1.1%)

series137.0ms (3.1%)

simplify48.0ms (1.1%)

prune151.0ms (3.4%)

regimes546.0ms (12.4%)

bsearch54.0ms (1.2%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample817.0ms (18.6%)

Profiling