Details

sample279.0ms

Algorithm

intervals

Results

211.0ms	87×	body	80	nan
26.0ms	279×	body	80	valid

simplify409.0ms

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

prune6.0ms

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: 20.7b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.9b	(+ (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)))

rewrite27.0ms

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	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify118.0ms

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	586

prune185.0ms

Filtered

60 candidates to 75 candidates (-25.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	69	6	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	6	76

Merged error: 7.1b

Counts

76 → 6

localize24.0ms

Local error

Found 4 expressions with local error:

11.4b	(+ (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)))

rewrite16.0ms

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))))))
3.0ms	(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)))

series59.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify112.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (104.0ms)

Iter	Nodes	Cost
0	227	677
1	876	574
2	3665	562
3	5003	558

prune200.0ms

Filtered

58 candidates to 70 candidates (-20.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	70	6	76

Merged error: 7.1b

Counts

76 → 6

localize26.0ms

Local error

Found 4 expressions with local error:

5.9b	(- (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)))

rewrite15.0ms

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

series105.0ms

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)))
25.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
29.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (34.0ms)

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

prune222.0ms

Filtered

60 candidates to 67 candidates (-11.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	67	6	73

Merged error: 7.1b

Counts

73 → 6

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0b	(/ (* a c) b)
4.2b	(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
13×	`*-un-lft-identity`
9×	`add-cube-cbrt`
8×	`add-log-exp`
6×	`times-frac`
5×	`pow1`
4×	`cbrt-undiv` `div-exp` `associate-/r` `sqrt-prod` `associate-/l`
3×	`flip3--` `flip--`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `div-sub` `neg-log`

Counts

4 → 78

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(/ (* a c) b)
9.0ms	(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series51.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0ms	(/ (* a c) b)
14.0ms	(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify57.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	475	705
1	2162	625
2	5002	624

prune143.0ms

Filtered

66 candidates to 90 candidates (-36.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	88	2	90
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	89	7	96

Merged error: 6.6b

Counts

96 → 7

regimes269.0ms

Accuracy

89.5% (1.4b remaining)

Error of 8.2b against oracle of 6.8b and baseline of 20.1b

bsearch79.0ms

Steps

Iters	Range		Point
9	1.6394144220709393e+93	3.4419594162308654e+101	2.4627655436379285e+99
10	-2.384841974323508e+56	-1.2508512957211805e+42	-1.9760603280802133e+56

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	55
1	54	55

end0.0ms

sample1.3s

Algorithm

intervals

Results

763.0ms	8699×	body	80	valid
219.0ms	2606×	body	80	nan

Details

sample279.0ms

simplify409.0ms

prune6.0ms

localize24.0ms

rewrite27.0ms

series76.0ms

simplify118.0ms

prune185.0ms

localize24.0ms

rewrite16.0ms

series59.0ms

simplify112.0ms

prune200.0ms

localize26.0ms

rewrite15.0ms

series105.0ms

simplify43.0ms

prune222.0ms

localize25.0ms

rewrite27.0ms

series51.0ms

simplify57.0ms

prune143.0ms

regimes269.0ms

bsearch79.0ms

simplify2.0ms

end0.0ms

sample1.3s

Profiling