Details

sample78.0ms

Algorithm

intervals

Results

41.0ms	277×	body	80	valid
10.0ms	75×	body	80	nan

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	18
1	79	18
2	136	18
3	161	18
4	173	18
5	177	18
6	177	18

prune7.0ms

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: 18.3b

Counts

2 → 1

localize44.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* (* 4.0 a) c))
1.9b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

7.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series75.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
26.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify135.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (125.0ms)

Iter	Nodes	Cost
0	223	579
1	875	551
2	3958	543
3	5001	540

prune296.0ms

Filtered

72 candidates to 55 candidates (23.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	64	8	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	8	73

Merged error: 8.4b

Counts

73 → 8

localize33.0ms

Local error

Found 4 expressions with local error:

9.2b	(- (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
20.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.1b	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.1b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite33.0ms

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:

8.0ms	(- (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
10.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series133.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
34.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
33.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify54.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (38.0ms)

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

prune344.0ms

Filtered

67 candidates to 60 candidates (10.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	65	2	67
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	67	8	75

Merged error: 8.4b

Counts

75 → 8

localize48.0ms

Local error

Found 4 expressions with local error:

20.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.1b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series74.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify99.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (92.0ms)

Iter	Nodes	Cost
0	218	570
1	680	547
2	2689	538
3	5002	527

prune356.0ms

Filtered

70 candidates to 59 candidates (15.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	70	8	78

Merged error: 8.4b

Counts

78 → 8

localize53.0ms

Local error

Found 4 expressions with local error:

7.3b	(+ (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
20.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.1b	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.1b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite21.0ms

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` `add-cbrt-cube`
3×	`flip3--` `sqrt-prod` `flip--`
2×	`pow1/3` `sqrt-div` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 54

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)))
3.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series107.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (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)))
29.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
32.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify55.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	382	836
1	1428	761
2	5002	721

prune286.0ms

Filtered

66 candidates to 60 candidates (9.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	65	9	74

Merged error: 8.4b

Counts

74 → 9

regimes342.0ms

Accuracy

92% (1.0b remaining)

Error of 8.2b against oracle of 7.2b and baseline of 19.6b

bsearch70.0ms

Steps

Iters	Range		Point
8	1.2099936426732458e+107	2.3384458119324726e+110	3.3163232856065444e+109
9	-2.766539085620364e+156	-8.384876061532889e+150	-1.3459151444301705e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	68
1	54	68

end0.0ms

sample1.8s

Algorithm

intervals

Results

960.0ms	8677×	body	80	valid
312.0ms	3007×	body	80	nan

Details

sample78.0ms

simplify14.0ms

prune7.0ms

localize44.0ms

rewrite43.0ms

series75.0ms

simplify135.0ms

prune296.0ms

localize33.0ms

rewrite33.0ms

series133.0ms

simplify54.0ms

prune344.0ms

localize48.0ms

rewrite22.0ms

series74.0ms

simplify99.0ms

prune356.0ms

localize53.0ms

rewrite21.0ms

series107.0ms

simplify55.0ms

prune286.0ms

regimes342.0ms

bsearch70.0ms

simplify2.0ms

end0.0ms

sample1.8s

Profiling