Details

analyze260.0ms

Algorithm

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

sample39.0ms

Algorithm

intervals

Results

14.0ms	125×	body	160	valid
8.0ms	291×	pre	80	true
6.0ms	131×	body	80	valid
2.0ms	35×	body	80	nan

simplify220.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (218.0ms)

Iter	Nodes	Cost
0	1833	16
1	1833	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: 25.2b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.3b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
25.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite30.0ms

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:

4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

series82.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
32.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
21.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

simplify64.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4900	1294
1	4900	1294

prune103.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	75	7	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	75	8	83

Merged error: 0.4b

Counts

83 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.3b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
0.3b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64`
17×	`cbrt-undiv_binary64` `div-exp_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64`
11×	`associate-/l*_binary64`
10×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64`
6×	`associate-/r/_binary64`
5×	`associate-/r*_binary64` `distribute-lft-out_binary64`
4×	`flip3-+_binary64` `pow1_binary64` `div-inv_binary64` `flip-+_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 98

Calls

4 calls:

6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
14.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
12.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

series159.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
55.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
74.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

simplify53.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4949	2008
1	4949	2008

prune150.0ms

Filtered

75 candidates to 110 candidates (-46.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	100	10	110
Fresh	6	0	6
Picked	1	0	1
Done	1	0	1
Total	108	10	118

Merged error: 0b

Counts

118 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
0.2b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
0.2b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-lft-out_binary64`
4×	`associate-/r*_binary64`
3×	`associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 71

Calls

4 calls:

5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
8.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series108.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
19.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
60.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
11.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify71.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4904	1292
1	4904	1292

prune119.0ms

Filtered

64 candidates to 83 candidates (-29.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	84	9	93

Merged error: 0b

Counts

93 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 c (+.f64 b (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 (.f64 c a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
0.3b	(.f64 a (.f64 c (.f64 (.f64 c a) 16)))
0.3b	(.f64 c (.f64 (*.f64 c a) 16))
0.4b	(/.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 (.f64 c a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
27×	`pow1_binary64`
23×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
21×	`times-frac_binary64`
16×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
7×	`associate-/r*_binary64`
6×	`associate-l_binary64` `associate-/l*_binary64`
4×	`add-log-exp_binary64` `distribute-lft-out_binary64` `associate-/r/_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `associate-r_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `*-commutative_binary64`
1×	`flip3--_binary64` `div-sub_binary64` `flip--_binary64`

Counts

4 → 110

Calls

4 calls:

15.0ms	(/.f64 c (+.f64 b (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 (.f64 c a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
10.0ms	(.f64 a (.f64 c (.f64 (.f64 c a) 16)))
7.0ms	(.f64 c (.f64 (*.f64 c a) 16))
13.0ms	(/.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 (.f64 c a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4))))

series121.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/.f64 c (+.f64 b (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 (.f64 c a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
10.0ms	(.f64 a (.f64 c (.f64 (.f64 c a) 16)))
5.0ms	(.f64 c (.f64 (*.f64 c a) 16))
27.0ms	(/.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 (.f64 c a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4))))

simplify57.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5016	2716

prune140.0ms

Filtered

84 candidates to 122 candidates (-45.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	122	9	131

Merged error: 0b

Counts

131 → 9

regimes191.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	95	30
1	95	30

end0.0ms

sample1.1s

Algorithm

intervals

Results

411.0ms	4485×	body	160	valid
247.0ms	8829×	pre	80	true
170.0ms	3515×	body	80	valid
42.0ms	829×	body	80	nan

Details

analyze260.0ms

sample39.0ms

simplify220.0ms

prune7.0ms

localize10.0ms

rewrite30.0ms

series82.0ms

simplify64.0ms

prune103.0ms

localize14.0ms

rewrite41.0ms

series159.0ms

simplify53.0ms

prune150.0ms

localize12.0ms

rewrite26.0ms

series108.0ms

simplify71.0ms

prune119.0ms

localize20.0ms

rewrite50.0ms

series121.0ms

simplify57.0ms

prune140.0ms

regimes191.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling