Details

analyze1.0s

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

sample35.0ms

Algorithm

intervals

Results

13.0ms	212×	body	80	valid
2.0ms	51×	body	80	invalid
2.0ms	11×	body	1280	valid
1.0ms	14×	body	320	valid
1.0ms	10×	body	640	valid
1.0ms	8×	body	160	valid
0.0ms	1×	body	2560	valid

simplify63.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4912	13
1	4912	13

prune4.0ms

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: 27.2b

Counts

2 → 1

localize9.0ms

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))

rewrite33.0ms

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))
8.0ms	(+.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))

series120.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(*.f64 (-.f64 y x) (-.f64 z t))
65.0ms	(+.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))

simplify43.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	6015	1085

prune129.0ms

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: 3.8b

Counts

89 → 11

localize9.0ms

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)))

rewrite37.0ms

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:

8.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
4.0ms	(+.f64 x (*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t))))
20.0ms	(*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)))

series118.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
65.0ms	(+.f64 x (*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t))))
41.0ms	(*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)))

simplify45.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5068	1606

prune131.0ms

Filtered

85 candidates to 128 candidates (-50.6%)

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

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)))

rewrite84.0ms

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))
43.0ms	(+.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)))

series133.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(/.f64 (-.f64 a t) (-.f64 z t))
63.0ms	(+.f64 x (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t))))
59.0ms	(/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))

simplify74.0ms

Algorithm

egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5092	5477

prune207.0ms

Filtered

170 candidates to 283 candidates (-66.5%)

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

localize10.0ms

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)))))

rewrite48.0ms

Algorithm

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:

6.0ms	(/.f64 1 (-.f64 a t))
14.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
16.0ms	(.f64 (-.f64 y x) (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))))
5.0ms	(+.f64 x (.f64 (-.f64 y x) (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))))

series125.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/.f64 1 (-.f64 a t))
11.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
44.0ms	(.f64 (-.f64 y x) (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))))
64.0ms	(+.f64 x (.f64 (-.f64 y x) (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))))

simplify48.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5748	1773

prune99.0ms

Filtered

99 candidates to 158 candidates (-59.6%)

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

regimes556.0ms

Accuracy

14.6% (6.7b remaining)

Error of 10.6b against oracle of 4.0b and baseline of 11.8b

bsearch52.0ms

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

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	81	35
1	81	35

end0.0ms

sample776.0ms

Algorithm

intervals

Results

257.0ms	6545×	body	80	valid
62.0ms	448×	body	640	valid
54.0ms	1183×	body	80	invalid
50.0ms	265×	body	1280	valid
44.0ms	426×	body	320	valid
21.0ms	292×	body	160	valid
5.0ms	24×	body	2560	valid

Details

analyze1.0s

sample35.0ms

simplify63.0ms

prune4.0ms

localize9.0ms

rewrite33.0ms

series120.0ms

simplify43.0ms

prune129.0ms

localize9.0ms

rewrite37.0ms

series118.0ms

simplify45.0ms

prune131.0ms

localize9.0ms

rewrite84.0ms

series133.0ms

simplify74.0ms

prune207.0ms

localize10.0ms

rewrite48.0ms

series125.0ms

simplify48.0ms

prune99.0ms

regimes556.0ms

bsearch52.0ms

simplify2.0ms

end0.0ms

sample776.0ms

Profiling