Details

sample1.8s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 23.873901%

Guaranteed chance to sample good point: 81.743836%

Results

23.0ms	256×	body	80	valid
2.0ms	20×	body	80	invalid
1.0ms	12×	body	80	nan

simplify374.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune6.0ms

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: 21.1b

Counts

2 → 1

localize38.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b b) (* (* 4.0 a) c))
1.6b	(- (* b b) (* (* 4.0 a) c))
23.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.3b	(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:

9.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(- (* b b) (* (* 4.0 a) c))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify87.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	147	476
1	564	446
2	2529	444
3	5002	442

prune171.0ms

Filtered

50 candidates to 66 candidates (-32.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	57	9	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	9	67

Merged error: 9.3b

Counts

67 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

10.3b	(- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.3b	(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)))

series57.0ms

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))))))
14.0ms	(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)))

simplify106.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (98.0ms)

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

prune220.0ms

Filtered

60 candidates to 72 candidates (-20.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	71	10	81

Merged error: 9.3b

Counts

81 → 10

localize30.0ms

Local error

Found 4 expressions with local error:

23.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.1b	(cbrt (- (* b b) (* (* 4.0 a) c)))
24.1b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `cbrt-div` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

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

series80.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
25.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
29.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify84.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (77.0ms)

Iter	Nodes	Cost
0	218	604
1	680	574
2	2689	560
3	5002	542

prune280.0ms

Filtered

58 candidates to 68 candidates (-17.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	67	11	78

Merged error: 9.3b

Counts

78 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

11.4b	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.3b	(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))))))
3.0ms	(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)))

series57.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify110.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (103.0ms)

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

prune192.0ms

Filtered

59 candidates to 70 candidates (-18.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	3	5	8
Picked	1	0	1
Done	0	2	2
Total	71	10	81

Merged error: 9.3b

Counts

81 → 10

regimes341.0ms

Accuracy

92% (1.0b remaining)

Error of 8.3b against oracle of 7.3b and baseline of 19.6b

bsearch76.0ms

Steps

Iters	Range		Point
9	2.6344834212533875e+88	9.710826601487366e+96	1.0645936985999334e+96
9	-3.2251985257956323e+159	-1.662564167781351e+151	-1.3325084122913293e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	58
1	48	58

end0.0ms

sample2.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 23.873901%

Guaranteed chance to sample good point: 81.743836%

Results

687.0ms	8000×	body	80	valid
45.0ms	509×	body	80	invalid
32.0ms	381×	body	80	nan

Details

sample1.8s

simplify374.0ms

prune6.0ms

localize38.0ms

rewrite19.0ms

series53.0ms

simplify87.0ms

prune171.0ms

localize23.0ms

rewrite16.0ms

series57.0ms

simplify106.0ms

prune220.0ms

localize30.0ms

rewrite16.0ms

series80.0ms

simplify84.0ms

prune280.0ms

localize23.0ms

rewrite16.0ms

series57.0ms

simplify110.0ms

prune192.0ms

regimes341.0ms

bsearch76.0ms

simplify2.0ms

end0.0ms

sample2.5s

Profiling