Details

analyze1.1s

Algorithm

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

sample29.0ms

Algorithm

intervals

Results

8.0ms	210×	body	80	valid
2.0ms	14×	body	640	valid
2.0ms	18×	body	320	valid
1.0ms	8×	body	1280	valid
1.0ms	31×	body	80	invalid
1.0ms	6×	body	160	valid

simplify78.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4912	13
1	4912	13

prune3.0ms

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: 23.0b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (-.f64 y x) (-.f64 z t))
1.7b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))
16.3b	(/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))

rewrite39.0ms

Algorithm

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:

10.0ms	(*.f64 (-.f64 y x) (-.f64 z t))
13.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))
13.0ms	(/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))

series103.0ms

Counts

3 → 9

Calls

3 calls:

10.0ms	(*.f64 (-.f64 y x) (-.f64 z t))
57.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))
36.0ms	(/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))

simplify43.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	6015	1085

prune90.0ms

Filtered

67 candidates to 88 candidates (-31.3%)

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: 3.9b

Counts

89 → 11

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
1.7b	(*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)))
1.7b	(+.f64 x (*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t))))

rewrite42.0ms

Algorithm

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:

10.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
18.0ms	(*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)))
4.0ms	(+.f64 x (*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t))))

series131.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
42.0ms	(*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)))
70.0ms	(+.f64 x (*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t))))

simplify73.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5068	1606

prune101.0ms

Filtered

85 candidates to 128 candidates (-50.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	122	6	128
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	127	12	139

Merged error: 3.9b

Counts

139 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 z (-.f64 a t))
0.0b	(/.f64 t (-.f64 a t))
1.7b	(*.f64 (-.f64 y x) (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t))))
1.7b	(+.f64 x (*.f64 (-.f64 y x) (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t)))))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

72×	`*-un-lft-identity_binary64`
64×	`add-sqr-sqrt_binary64`
48×	`times-frac_binary64`
28×	`add-cube-cbrt_binary64`
21×	`distribute-lft-out--_binary64`
18×	`associate-r_binary64`
15×	`difference-of-squares_binary64`
12×	`flip3--_binary64` `flip--_binary64`
10×	`associate-/r*_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`associate-/r/_binary64` `frac-times_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `associate-/l*_binary64`
5×	`associate-l_binary64`
4×	`sub-neg_binary64` `associate-*r/_binary64` `div-inv_binary64`
3×	`distribute-rgt-out--_binary64` `sub-div_binary64` `frac-sub_binary64`
2×	`cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `associate-+r+_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 138

Calls

4 calls:

6.0ms	(/.f64 z (-.f64 a t))
6.0ms	(/.f64 t (-.f64 a t))
38.0ms	(*.f64 (-.f64 y x) (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t))))
14.0ms	(+.f64 x (*.f64 (-.f64 y x) (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t)))))

series120.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/.f64 z (-.f64 a t))
6.0ms	(/.f64 t (-.f64 a t))
39.0ms	(*.f64 (-.f64 y x) (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t))))
68.0ms	(+.f64 x (*.f64 (-.f64 y x) (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t)))))

simplify49.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5272	1971

prune99.0ms

Filtered

113 candidates to 150 candidates (-32.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	148	2	150
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	150	12	162

Merged error: 3.9b

Counts

162 → 12

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 a t) (-.f64 z t))
1.6b	(/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))
1.7b	(+.f64 x (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t))))

rewrite87.0ms

Algorithm

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:

8.0ms	(/.f64 (-.f64 a t) (-.f64 z t))
20.0ms	(/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))
42.0ms	(+.f64 x (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t))))

series116.0ms

Counts

3 → 9

Calls

3 calls:

10.0ms	(/.f64 (-.f64 a t) (-.f64 z t))
48.0ms	(/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))
58.0ms	(+.f64 x (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t))))

simplify75.0ms

Algorithm

egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5092	5477

prune87.0ms

Filtered

170 candidates to 283 candidates (-66.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	282	1	283
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	285	10	295

Merged error: 3.9b

Counts

295 → 10

regimes360.0ms

Accuracy

20.6% (5.8b remaining)

Error of 10.1b against oracle of 4.2b and baseline of 11.6b

bsearch60.0ms

Steps

Iters	Range		Point
9	2.0403912219521581e-178	7.711630378124323e-172	1.1251105426542038e-172
10	-2.6086151420952097e-126	-5.4491181932067845e-136	-9.099639368291585e-136

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	90	39
1	90	39

end0.0ms

sample830.0ms

Algorithm

intervals

Results

284.0ms	6563×	body	80	valid
72.0ms	483×	body	640	valid
52.0ms	1241×	body	80	invalid
50.0ms	246×	body	1280	valid
46.0ms	410×	body	320	valid
21.0ms	277×	body	160	valid
5.0ms	21×	body	2560	valid

Details

analyze1.1s

sample29.0ms

simplify78.0ms

prune3.0ms

localize9.0ms

rewrite39.0ms

series103.0ms

simplify43.0ms

prune90.0ms

localize9.0ms

rewrite42.0ms

series131.0ms

simplify73.0ms

prune101.0ms

localize14.0ms

rewrite70.0ms

series120.0ms

simplify49.0ms

prune99.0ms

localize11.0ms

rewrite87.0ms

series116.0ms

simplify75.0ms

prune87.0ms

regimes360.0ms

bsearch60.0ms

simplify3.0ms

end0.0ms

sample830.0ms

Profiling