Details

sample49.0ms

Algorithm

intervals

Results

25.0ms	277×	body	80	valid
6.0ms	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

prune4.0ms

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: 18.3b

Counts

2 → 1

localize22.0ms

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)))

rewrite23.0ms

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:

3.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series53.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify118.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (111.0ms)

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

prune183.0ms

Filtered

55 candidates to 72 candidates (-30.9%)

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

localize26.0ms

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)))

rewrite17.0ms

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)))
3.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
5.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series100.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (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)))
24.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
26.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (34.0ms)

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

prune252.0ms

Filtered

60 candidates to 67 candidates (-11.7%)

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

localize29.0ms

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)))

rewrite15.0ms

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

series68.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify82.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (75.0ms)

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

prune284.0ms

Filtered

59 candidates to 70 candidates (-18.6%)

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

localize25.0ms

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)))

rewrite17.0ms

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)))
5.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series93.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ (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)))
24.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
24.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	382	835
1	1434	761
2	5002	721

prune209.0ms

Filtered

60 candidates to 66 candidates (-10.0%)

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

regimes271.0ms

Accuracy

92% (1.0b remaining)

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

bsearch79.0ms

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

sample1.5s

Algorithm

intervals

Results

796.0ms	8677×	body	80	valid
257.0ms	3007×	body	80	nan

Details

sample49.0ms

simplify14.0ms

prune4.0ms

localize22.0ms

rewrite23.0ms

series53.0ms

simplify118.0ms

prune183.0ms

localize26.0ms

rewrite17.0ms

series100.0ms

simplify42.0ms

prune252.0ms

localize29.0ms

rewrite15.0ms

series68.0ms

simplify82.0ms

prune284.0ms

localize25.0ms

rewrite17.0ms

series93.0ms

simplify42.0ms

prune209.0ms

regimes271.0ms

bsearch79.0ms

simplify2.0ms

end0.0ms

sample1.5s

Profiling