Details

sample346.0ms

Algorithm

intervals

Results

22.0ms	281×	body	80	valid
6.0ms	87×	body	80	nan

simplify18.0ms

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

prune29.0ms

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: 20.8b

Counts

2 → 1

localize146.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite33.0ms

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:

13.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(+ (neg b) (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)))

series397.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
103.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
93.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
105.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify117.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (109.0ms)

Iter	Nodes	Cost
0	248	644
1	898	606
2	3865	590
3	5001	588

prune436.0ms

Filtered

75 candidates to 62 candidates (17.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	68	7	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	7	76

Merged error: 7.5b

Counts

76 → 7

localize145.0ms

Local error

Found 4 expressions with local error:

8.9b	(- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0b	(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:

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)))

series375.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
92.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
93.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
94.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify110.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (100.0ms)

Iter	Nodes	Cost
0	221	725
1	823	631
2	3496	612
3	5001	592

prune428.0ms

Filtered

72 candidates to 58 candidates (19.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	72	7	79

Merged error: 7.5b

Counts

79 → 7

localize146.0ms

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))))))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.8b	(cbrt (- (* b b) (* (* 4.0 a) c)))
23.8b	(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	(+ (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)))
3.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series420.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(+ (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
89.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
116.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
119.0ms	(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	366	804
1	1468	730
2	5001	697

prune587.0ms

Filtered

66 candidates to 59 candidates (10.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	66	7	73

Merged error: 7.5b

Counts

73 → 7

localize145.0ms

Local error

Found 4 expressions with local error:

1.4b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.7b	(exp (log (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `add-log-exp`
7×	`pow1`
6×	`sqrt-prod`
5×	`log-prod` `exp-sum`
4×	`add-exp-log` `exp-prod` `sqrt-div` `add-cbrt-cube` `distribute-lft-out`
2×	`rem-sqrt-square` `log-div` `flip3--` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `exp-diff` `sum-log` `flip--` `flip-+`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-log` `log-pow` `rem-exp-log`

Counts

4 → 64

Calls

4 calls:

8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(exp (log (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series395.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
103.0ms	(exp (log (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
94.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
97.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify108.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (101.0ms)

Iter	Nodes	Cost
0	249	652
1	880	611
2	3511	575
3	5001	565

prune408.0ms

Filtered

76 candidates to 59 candidates (22.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	76	7	83

Merged error: 7.5b

Counts

83 → 7

regimes314.0ms

Accuracy

92.2% (0.9b remaining)

Error of 8.5b against oracle of 7.6b and baseline of 19.8b

bsearch217.0ms

Steps

Iters	Range		Point
9	5.514542683406611e+77	2.3545344307669661e+86	4.3318565542540646e+83
8	-6.668740644957453e+156	-5.936809638808374e+152	-1.332209997956342e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	58
1	48	58

end0.0ms

sample1.2s

Algorithm

intervals

Results

598.0ms	8739×	body	80	valid
187.0ms	2908×	body	80	nan

Details

sample346.0ms

simplify18.0ms

prune29.0ms

localize146.0ms

rewrite33.0ms

series397.0ms

simplify117.0ms

prune436.0ms

localize145.0ms

rewrite17.0ms

series375.0ms

simplify110.0ms

prune428.0ms

localize146.0ms

rewrite16.0ms

series420.0ms

simplify46.0ms

prune587.0ms

localize145.0ms

rewrite26.0ms

series395.0ms

simplify108.0ms

prune408.0ms

regimes314.0ms

bsearch217.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling