Details

sample39.0ms

Algorithm

intervals

Results

19.0ms	276×	body	80	valid
4.0ms	85×	body	80	nan

simplify15.0ms

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

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: 21.0b

Counts

2 → 1

localize112.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
1.0b	(- (* b b) (* (* 4.0 a) c))
23.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite15.0ms

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

series227.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* b b) (* (* 4.0 a) c))
46.0ms	(- (* b b) (* (* 4.0 a) c))
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify79.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (73.0ms)

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

prune229.0ms

Filtered

66 candidates to 50 candidates (75.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	59	7	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	7	67

Merged error: 10.6b

Counts

67 → 7

localize134.0ms

Local error

Found 4 expressions with local error:

6.8b	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.1b	(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	(- (- 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)))

series280.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify104.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	225	725
1	835	631
2	3414	609
3	5001	589

prune268.0ms

Filtered

72 candidates to 60 candidates (83.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	73	6	79

Merged error: 10.6b

Counts

79 → 6

localize116.0ms

Local error

Found 4 expressions with local error:

9.9b	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
23.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0b	(cbrt (- (* b b) (* (* 4.0 a) c)))
24.0b	(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` `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	(+ (- 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)))
4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
94.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
93.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (38.0ms)

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

prune334.0ms

Filtered

66 candidates to 59 candidates (89.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	65	7	72

Merged error: 10.6b

Counts

72 → 7

localize121.0ms

Local error

Found 4 expressions with local error:

22.9b	(+ (- b) (* (fabs (exp (log (cbrt (- (* b b) (* (* 4.0 a) c)))))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
23.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0b	(cbrt (- (* b b) (* (* 4.0 a) c)))
24.0b	(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` `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	(+ (- b) (* (fabs (exp (log (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)))
4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series337.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(+ (- b) (* (fabs (exp (log (cbrt (- (* b b) (* (* 4.0 a) c)))))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
93.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
94.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	370	843
1	1473	749
2	5001	713

prune345.0ms

Filtered

66 candidates to 59 candidates (89.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	66	7	73

Merged error: 10.6b

Counts

73 → 7

regimes162.0ms

Accuracy

93.3% (0.8b remaining)

Error of 8.6b against oracle of 7.8b and baseline of 19.8b

bsearch168.0ms

Steps

Iters	Range		Point
8	2.000287750443077e+147	1.6365741300291856e+150	1.091736019600057e+148
8	-7.940186999589029e+157	-2.4392292464634512e+153	-1.3442754169306616e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	59
1	51	59

end0.0ms

sample851.0ms

Algorithm

intervals

Results

459.0ms	8710×	body	80	valid
139.0ms	2898×	body	80	nan