Details

sample238.0ms

Algorithm

intervals

Results

192.0ms	191×	body	80	valid
8.0ms	32×	body	2560	valid
6.0ms	30×	body	1280	valid
4.0ms	97×	body	80	nan
2.0ms	14×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	7
1	22	7
2	25	7
3	27	7
4	29	7
5	29	7

prune6.0ms

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: 33.2b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.9b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
21.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/l*`
3×	`associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 80

Calls

4 calls:

10.0ms	(/ (+ (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:

21.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
20.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(- (* b_2 b_2) (* a c))
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify140.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	338	783
1	1216	724
2	4971	703
3	5001	703

prune153.0ms

Filtered

92 candidates to 69 candidates (25.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	82	10	92
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	82	11	93

Merged error: 5.1b

Counts

93 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
3.0b	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
9.9b	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
21.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

186×	`times-frac`
154×	`add-sqr-sqrt`
153×	`*-un-lft-identity`
89×	`add-cube-cbrt`
32×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-rgt-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*` `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 → 200

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series109.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
39.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
51.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify108.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	708	3365
1	3231	3197
2	5001	3171

prune245.0ms

Filtered

212 candidates to 142 candidates (33.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	210	2	212
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	214	9	223

Merged error: 5.1b

Counts

223 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
2.1b	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.0b	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
21.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

951×	`times-frac`
585×	`add-sqr-sqrt`
584×	`*-un-lft-identity`
392×	`add-cube-cbrt`
96×	`distribute-lft-out--` `difference-of-squares`
83×	`associate-/l*`
51×	`sqrt-prod`
48×	`distribute-rgt-neg-in`
28×	`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 → 485

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
25.0ms	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) 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))
50.0ms	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
46.0ms	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify102.0ms

Algorithm

egg-herbie

Counts

497 → 497

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1525	8627
1	5002	7984

prune341.0ms

Filtered

497 candidates to 298 candidates (40.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	496	1	497
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	498	8	506

Merged error: 5.1b

Counts

506 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
1.3b	(/ (/ (cbrt a) (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) (cbrt a))
21.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

2862×	`times-frac`
1645×	`add-sqr-sqrt`
1644×	`*-un-lft-identity`
1136×	`add-cube-cbrt`
993×	`cbrt-prod`
254×	`distribute-lft-out--` `difference-of-squares`
155×	`associate-/l*`
130×	`sqrt-prod`
127×	`distribute-rgt-neg-in`
50×	`div-inv`
13×	`add-exp-log`
10×	`add-log-exp`
8×	`add-cbrt-cube`
7×	`associate-/r/`
6×	`cbrt-undiv` `div-exp` `associate-/r*`
5×	`pow1`
3×	`flip3--` `diff-log` `flip--`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 1153

Calls

4 calls:

8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
50.0ms	(/ (/ (cbrt a) (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) (cbrt a))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series79.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(- (* b_2 b_2) (* a c))
47.0ms	(/ (/ (cbrt a) (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) (cbrt a))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify263.0ms

Algorithm

egg-herbie

Counts

1165 → 1165

Iterations

Useful iterations: 1 (54.0ms)

Iter	Nodes	Cost
0	2923	27910
1	5001	26669

prune862.0ms

Filtered

1165 candidates to 678 candidates (41.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	1165	0	1165
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	1165	8	1173

Merged error: 5.1b

Counts

1173 → 8

regimes453.0ms

Accuracy

93.7% (1.6b remaining)

Error of 7.3b against oracle of 5.7b and baseline of 31.0b

bsearch113.0ms

Steps

Iters	Range		Point
10	4.2917270207488e+96	9.615152778888747e+106	5.2249784563665464e+104
10	1.5449499907901935e-212	3.426440312001654e-201	1.610651904509826e-212
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	43	26
1	45	26
2	45	26

end0.0ms

sample1.4s

Algorithm

intervals

Results

270.0ms	1066×	body	2560	valid
262.0ms	5871×	body	80	valid
182.0ms	853×	body	1280	valid
119.0ms	2842×	body	80	nan
78.0ms	450×	body	640	valid
32.0ms	97×	body	5120	valid
30.0ms	246×	body	320	valid
10.0ms	124×	body	160	valid

Details

sample238.0ms

simplify14.0ms

prune6.0ms

localize12.0ms

rewrite30.0ms

series69.0ms

simplify140.0ms

prune153.0ms

localize14.0ms

rewrite44.0ms

series109.0ms

simplify108.0ms

prune245.0ms

localize11.0ms

rewrite84.0ms

series115.0ms

simplify102.0ms

prune341.0ms

localize14.0ms

rewrite187.0ms

series79.0ms

simplify263.0ms

prune862.0ms

regimes453.0ms

bsearch113.0ms

simplify2.0ms

end0.0ms

sample1.4s

Profiling