Details

sample44.0ms

Algorithm

intervals

Results

18.0ms	276×	body	80	valid
7.0ms	101×	body	80	nan

simplify14.0ms

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

prune4.0ms

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: 21.6b

Counts

2 → 1

localize120.0ms

Local error

Found 4 expressions with local error:

1.1b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.3b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
78.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify112.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (104.0ms)

Iter	Nodes	Cost
0	246	646
1	890	606
2	3700	588
3	5001	584

prune273.0ms

Filtered

75 candidates to 60 candidates (80.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	67	8	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	8	76

Merged error: 8.0b

Counts

76 → 8

localize116.0ms

Local error

Found 4 expressions with local error:

12.8b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b	(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	(+ (- 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	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (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)))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify111.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (104.0ms)

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

prune264.0ms

Filtered

70 candidates to 58 candidates (82.9%)

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: 8.0b

Counts

78 → 8

localize120.0ms

Local error

Found 4 expressions with local error:

6.6b	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite17.0ms

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:

5.0ms	(- (- 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)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
66.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify104.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (96.0ms)

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

prune266.0ms

Filtered

72 candidates to 58 candidates (80.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	72	8	80

Merged error: 8.0b

Counts

80 → 8

localize119.0ms

Local error

Found 4 expressions with local error:

8.9b	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
25.1b	(cbrt (- (* b b) (* (* 4.0 a) c)))
25.1b	(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))))))
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)))

series362.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
95.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
99.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (37.0ms)

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

prune300.0ms

Filtered

66 candidates to 59 candidates (89.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	66	8	74

Merged error: 8.0b

Counts

74 → 8

regimes174.0ms

Accuracy

91.8% (1.0b remaining)

Error of 9.1b against oracle of 8.1b and baseline of 20.4b

bsearch190.0ms

Steps

Iters	Range		Point
6	6.333441064762502e+69	2.6854631551896503e+70	2.6171947504708796e+70
11	-4.6778596556519216e+169	-3.105074477202361e+149	-1.7929580539303616e+153

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	58
1	48	58

end0.0ms

sample1.1s

Algorithm

intervals

Results

604.0ms	8706×	body	80	valid
192.0ms	2921×	body	80	nan