Details

analyze474.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

sample45.0ms

Algorithm

intervals

Results

13.0ms	37×	body	2560	valid
9.0ms	166×	body	80	valid
5.0ms	20×	body	1280	valid
4.0ms	20×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	22×	body	80	nan
1.0ms	7×	body	320	valid
1.0ms	12×	body	80	invalid
0.0ms	2×	body	160	valid

simplify209.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (206.0ms)

Iter	Nodes	Cost
0	1784	16
1	1784	16

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 36.7b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3.0 a) c))) b) (.f64 3.0 a))
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))
1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))) b)
26.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
6×	`difference-of-squares_binary64` `associate-/l*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
5×	`pow1_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`associate-/r*_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 70

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3.0 a) c))) b) (.f64 3.0 a))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

series77.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3.0 a) c))) b) (.f64 3.0 a))
10.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))
18.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))) b)
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

simplify38.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4931	1311
1	4931	1311

prune127.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	72	10	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	10	83

Merged error: 5.2b

Counts

83 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

1.5b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))))
3.9b	(/.f64 (/.f64 (neg.f64 (.f64 (.f64 3.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3.0 a) c))))) (.f64 3.0 a))
9.3b	(/.f64 (neg.f64 (.f64 (.f64 3.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))))
26.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac_binary64`
79×	`*-un-lft-identity_binary64`
40×	`add-sqr-sqrt_binary64`
39×	`add-cube-cbrt_binary64`
36×	`associate-/l*_binary64`
20×	`distribute-lft-out_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
5×	`associate-/r*_binary64` `pow1_binary64`
4×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
3×	`div-sub_binary64` `distribute-frac-neg_binary64` `sqrt-prod_binary64`
2×	`cbrt-unprod_binary64` `neg-sub0_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 159

Calls

4 calls:

6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))))
14.0ms	(/.f64 (/.f64 (neg.f64 (.f64 (.f64 3.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3.0 a) c))))) (.f64 3.0 a))
16.0ms	(/.f64 (neg.f64 (.f64 (.f64 3.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

series158.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))))
52.0ms	(/.f64 (/.f64 (neg.f64 (.f64 (.f64 3.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3.0 a) c))))) (.f64 3.0 a))
69.0ms	(/.f64 (neg.f64 (.f64 (.f64 3.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))))
17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

simplify60.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4996	3913
1	4996	3913

prune222.0ms

Filtered

128 candidates to 171 candidates (-33.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	168	3	171
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	171	10	181

Merged error: 5.1b

Counts

181 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 3.0 a) c)
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))
1.5b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))))
26.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64` `sqrt-prod_binary64`
2×	`flip3--_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 56

Calls

4 calls:

5.0ms	(.f64 (.f64 3.0 a) c)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

series53.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(.f64 (.f64 3.0 a) c)
12.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))
19.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))))
17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

simplify29.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5122	753

prune83.0ms

Filtered

48 candidates to 68 candidates (-41.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	68	10	78

Merged error: 5.1b

Counts

78 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

1.5b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))))
1.7b	(.f64 (neg.f64 (.f64 3.0 a)) (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))))))
3.9b	(/.f64 (.f64 (neg.f64 (.f64 3.0 a)) (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3.0 a) c)))))) (.f64 3.0 a))
26.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`associate-r_binary64`
14×	`add-cube-cbrt_binary64` `times-frac_binary64`
9×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64`
4×	`distribute-lft-out_binary64`
3×	`sqrt-prod_binary64`
2×	`flip3-+_binary64` `associate-*r/_binary64` `distribute-lft-neg-out_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `div-inv_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `associate-/r_binary64` `pow1/2_binary64` `flip3--_binary64` `neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `sqrt-pow1_binary64` `distribute-rgt-neg-in_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `+-commutative_binary64` `distribute-frac-neg_binary64` `flip--_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 95

Calls

4 calls:

6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))))
14.0ms	(.f64 (neg.f64 (.f64 3.0 a)) (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))))))
15.0ms	(/.f64 (.f64 (neg.f64 (.f64 3.0 a)) (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3.0 a) c)))))) (.f64 3.0 a))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

series162.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))))
68.0ms	(.f64 (neg.f64 (.f64 3.0 a)) (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c))))))
56.0ms	(/.f64 (.f64 (neg.f64 (.f64 3.0 a)) (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3.0 a) c)))))) (.f64 3.0 a))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3.0 a) c)))

simplify55.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4964	1769
1	4964	1769

prune95.0ms

Filtered

75 candidates to 107 candidates (-42.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	107	10	117

Merged error: 5.1b

Counts

117 → 10

regimes426.0ms

Accuracy

96.1% (0.9b remaining)

Error of 6.6b against oracle of 5.7b and baseline of 29.5b

bsearch87.0ms

Steps

Iters	Range	Point
7	7.023815571878041e+127	3.7086927817372e+129	2.7144293381871665e+129
10	-1.0074435914629907e-302	1.2174472353976405e-303	-4.511854892223982e-306
8	-5.886835373009713e+149	-1.5910644516223008e+147	-1.3740666575718133e+149

Iters

Range

Point

7.023815571878041e+127

3.7086927817372e+129

2.7144293381871665e+129

-1.0074435914629907e-302

1.2174472353976405e-303

-4.511854892223982e-306

-5.886835373009713e+149

-1.5910644516223008e+147

-1.3740666575718133e+149

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	120	59
1	120	59

end0.0ms

sample1.3s

Algorithm

intervals

Results

316.0ms	1048×	body	2560	valid
272.0ms	5111×	body	80	valid
227.0ms	924×	body	1280	valid
98.0ms	494×	body	640	valid
39.0ms	106×	body	5120	valid
35.0ms	670×	body	80	nan
32.0ms	224×	body	320	valid
21.0ms	395×	body	80	invalid
9.0ms	93×	body	160	valid

Details

analyze474.0ms

sample45.0ms

simplify209.0ms

prune7.0ms

localize9.0ms

rewrite32.0ms

series77.0ms

simplify38.0ms

prune127.0ms

localize11.0ms

rewrite46.0ms

series158.0ms

simplify60.0ms

prune222.0ms

localize10.0ms

rewrite22.0ms

series53.0ms

simplify29.0ms

prune83.0ms

localize13.0ms

rewrite43.0ms

series162.0ms

simplify55.0ms

prune95.0ms

regimes426.0ms

bsearch87.0ms

simplify3.0ms

end0.0ms

sample1.3s

Profiling