Details

sample246.0ms

Algorithm

intervals

Results

203.0ms	191×	body	80	valid
7.0ms	30×	body	2560	valid
6.0ms	28×	body	1280	valid
4.0ms	98×	body	80	nan
3.0ms	20×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	5×	body	160	valid
0.0ms	1×	body	5120	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	32	7
2	41	7
3	44	7
4	44	7

prune5.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 31.9b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.2b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
21.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 91

Calls

4 calls:

11.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series69.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
22.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(- (* b_2 b_2) (* a c))
22.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	360	964
1	1233	910
2	5002	901

prune137.0ms

Filtered

103 candidates to 72 candidates (30.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	95	8	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	8	104

Merged error: 5.2b

Counts

104 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
2.8b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.6b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
21.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
32×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 184

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
13.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series120.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
41.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
59.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify105.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	704	2894
1	3112	2747
2	5001	2727

prune225.0ms

Filtered

196 candidates to 144 candidates (26.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	193	3	196
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	195	9	204

Merged error: 5.1b

Counts

204 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
2.5b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
2.8b	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
21.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

831×	`times-frac`
545×	`add-sqr-sqrt`
448×	`*-un-lft-identity`
352×	`add-cube-cbrt`
96×	`difference-of-squares`
74×	`associate-/l*`
51×	`sqrt-prod`
48×	`distribute-lft-out--`
25×	`associate-/r*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`pow1` `associate-/r/`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 437

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
22.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series115.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
52.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
43.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify96.0ms

Algorithm

egg-herbie

Counts

449 → 449

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1530	7327
1	5001	6764

prune301.0ms

Filtered

449 candidates to 297 candidates (33.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	447	2	449
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	450	8	458

Merged error: 5.1b

Counts

458 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))
0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.2b	(- (* b_2 b_2) (* a c))
21.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

789×	`times-frac`
493×	`add-sqr-sqrt`
406×	`*-un-lft-identity`
320×	`add-cube-cbrt`
86×	`difference-of-squares`
46×	`sqrt-prod`
44×	`add-exp-log`
43×	`distribute-lft-out--`
40×	`div-inv`
32×	`div-exp`
29×	`associate-/r/`
24×	`associate-/l*`
17×	`flip3--` `flip--`
16×	`add-cbrt-cube`
13×	`associate-/r*`
8×	`cbrt-undiv` `rec-exp` `1-exp` `add-log-exp`
5×	`pow1`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 423

Calls

4 calls:

22.0ms	(/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series62.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))
13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify102.0ms

Algorithm

egg-herbie

Counts

435 → 435

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1748	7648
1	5001	6939

prune280.0ms

Filtered

435 candidates to 173 candidates (60.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	435	0	435
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	435	8	443

Merged error: 5.1b

Counts

443 → 8

regimes289.0ms

Accuracy

94.6% (1.3b remaining)

Error of 7.0b against oracle of 5.7b and baseline of 29.7b

bsearch110.0ms

Steps

Iters	Range		Point
10	4.2917270207488e+96	9.615152778888747e+106	1.8369043176329317e+104
12	-6.7935373210721584e-298	9.28059404710146e-280	8.875671163682851e-299
9	-1.3279209152234913e+54	-5.495259451600425e+45	-1.307112579275623e+54

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	20
1	38	20

end0.0ms

sample1.3s

Algorithm

intervals

Results

252.0ms	1060×	body	2560	valid
244.0ms	5773×	body	80	valid
189.0ms	968×	body	1280	valid
117.0ms	2847×	body	80	nan
71.0ms	440×	body	640	valid
37.0ms	121×	body	5120	valid
28.0ms	247×	body	320	valid
9.0ms	117×	body	160	valid

Details

sample246.0ms

simplify13.0ms

prune5.0ms

localize11.0ms

rewrite32.0ms

series69.0ms

simplify43.0ms

prune137.0ms

localize11.0ms

rewrite44.0ms

series120.0ms

simplify105.0ms

prune225.0ms

localize10.0ms

rewrite74.0ms

series115.0ms

simplify96.0ms

prune301.0ms

localize11.0ms

rewrite66.0ms

series62.0ms

simplify102.0ms

prune280.0ms

regimes289.0ms

bsearch110.0ms

simplify2.0ms

end0.0ms

sample1.3s

Profiling