Details

sample251.0ms

Algorithm

intervals

Results

200.0ms	106×	body	80	nan
28.0ms	273×	body	80	valid

simplify372.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	35	18
1	66	18
2	116	18
3	144	18
4	159	18
5	161	18
6	161	18

prune18.0ms

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: 19.3b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b b) (* (* 4.0 a) c))
1.6b	(- (* b b) (* (* 4.0 a) c))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 54

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
3.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series53.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(- (* b b) (* (* 4.0 a) c))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify86.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	147	474
1	570	446
2	2550	444
3	5001	442

prune175.0ms

Filtered

50 candidates to 66 candidates (-32.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	58	8	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	8	67

Merged error: 7.2b

Counts

67 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

9.5b	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `add-cbrt-cube`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`
2×	`sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `neg-log` `flip-+`

Counts

4 → 58

Calls

4 calls:

4.0ms	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify113.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (105.0ms)

Iter	Nodes	Cost
0	227	677
1	876	574
2	3665	562
3	5003	558

prune213.0ms

Filtered

59 candidates to 70 candidates (-18.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	72	6	78

Merged error: 7.2b

Counts

78 → 6

localize28.0ms

Local error

Found 4 expressions with local error:

10.8b	(- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

4.0ms	(- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series59.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify108.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (100.0ms)

Iter	Nodes	Cost
0	221	722
1	829	631
2	3533	612
3	5001	592

prune215.0ms

Filtered

60 candidates to 72 candidates (-20.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	72	6	78

Merged error: 7.2b

Counts

78 → 6

localize26.0ms

Local error

Found 4 expressions with local error:

8.4b	(- (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod`
5×	`pow1`
4×	`add-exp-log` `cbrt-div` `flip3--` `add-cbrt-cube` `flip--`
3×	`sqrt-prod`
2×	`pow1/3` `sqrt-div` `diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 55

Calls

4 calls:

4.0ms	(- (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
3.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series99.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
26.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
26.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	377	865
1	1397	791
2	5001	755

prune212.0ms

Filtered

60 candidates to 67 candidates (-11.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	67	6	73

Merged error: 7.2b

Counts

73 → 6

regimes240.0ms

Accuracy

93.4% (0.8b remaining)

Error of 8.3b against oracle of 7.5b and baseline of 19.6b

bsearch77.0ms

Steps

Iters	Range		Point
8	2.1355185626412625e+132	7.676000847740815e+134	2.114128053402052e+133
10	-2.952718811484394e+162	-1.3370939268532223e+147	-1.3352973769258214e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	58
1	48	58

end0.0ms

sample1.4s

Algorithm

intervals

Results

769.0ms	8717×	body	80	valid
241.0ms	2829×	body	80	nan

Details

sample251.0ms

simplify372.0ms

prune18.0ms

localize24.0ms

rewrite19.0ms

series53.0ms

simplify86.0ms

prune175.0ms

localize23.0ms

rewrite16.0ms

series58.0ms

simplify113.0ms

prune213.0ms

localize28.0ms

rewrite16.0ms

series59.0ms

simplify108.0ms

prune215.0ms

localize26.0ms

rewrite16.0ms

series99.0ms

simplify43.0ms

prune212.0ms

regimes240.0ms

bsearch77.0ms

simplify2.0ms

end0.0ms

sample1.4s

Profiling