Details

sample45.0ms

Algorithm

intervals

Results

22.0ms	282×	body	80	valid
6.0ms	98×	body	80	nan

simplify15.0ms

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

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 19.7b

Counts

2 → 1

localize115.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* (* 4.0 a) c))
1.4b	(- (* b b) (* (* 4.0 a) c))
21.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.5b	(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:

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

series230.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 4.0 a) c))
46.0ms	(- (* b b) (* (* 4.0 a) c))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify81.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	149	476
1	576	446
2	2486	444
3	5001	440

prune247.0ms

Filtered

66 candidates to 50 candidates (75.8%)

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: 7.8b

Counts

67 → 9

localize120.0ms

Local error

Found 4 expressions with local error:

9.7b	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
21.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite17.0ms

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

series290.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
67.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify113.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (106.0ms)

Iter	Nodes	Cost
0	232	680
1	883	574
2	3567	559
3	5001	555

prune297.0ms

Filtered

70 candidates to 59 candidates (84.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	70	9	79

Merged error: 7.8b

Counts

79 → 9

localize123.0ms

Local error

Found 4 expressions with local error:

6.5b	(+ (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
21.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.2b	(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))))))
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)))

series367.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(+ (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
100.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
106.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	368	805
1	1471	730
2	5001	697

prune338.0ms

Filtered

66 candidates to 59 candidates (89.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	66	9	75

Merged error: 7.8b

Counts

75 → 9

localize128.0ms

Local error

Found 4 expressions with local error:

7.8b	(- (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
21.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.2b	(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))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series356.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(- (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
98.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
98.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	363	835
1	1402	760
2	5001	731

prune313.0ms

Filtered

67 candidates to 59 candidates (88.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	67	9	76

Merged error: 7.8b

Counts

76 → 9

regimes232.0ms

Accuracy

91.5% (1.0b remaining)

Error of 8.8b against oracle of 7.8b and baseline of 19.7b

bsearch189.0ms

Steps

Iters	Range		Point
10	1.4182100026226751e+88	1.1634796338171106e+98	4.1260465808756976e+97
7	-5.2837056453951795e+85	-2.8556980563007357e+84	-1.2187632957767726e+85

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	59
1	51	59

end0.0ms

sample1.1s

Algorithm

intervals

Results

608.0ms	8713×	body	80	valid
199.0ms	2897×	body	80	nan

Details

sample45.0ms

simplify15.0ms

prune3.0ms

localize115.0ms

rewrite19.0ms

series230.0ms

simplify81.0ms

prune247.0ms

localize120.0ms

rewrite17.0ms

series290.0ms

simplify113.0ms

prune297.0ms

localize123.0ms

rewrite17.0ms

series367.0ms

simplify47.0ms

prune338.0ms

localize128.0ms

rewrite17.0ms

series356.0ms

simplify46.0ms

prune313.0ms

regimes232.0ms

bsearch189.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling