Details

sample47.0ms

Algorithm

intervals

Results

24.0ms	283×	body	80	valid
6.0ms	75×	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: 19.9b

Counts

2 → 1

localize118.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* (* 4.0 a) c))
2.2b	(- (- 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)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

4.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(- (- b) (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)))

series269.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 4.0 a) c))
78.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify119.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (112.0ms)

Iter	Nodes	Cost
0	227	581
1	878	551
2	3814	541
3	5002	538

prune267.0ms

Filtered

72 candidates to 55 candidates (76.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	66	6	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	6	73

Merged error: 8.9b

Counts

73 → 6

localize120.0ms

Local error

Found 4 expressions with local error:

9.3b	(- (- 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	(- (- 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)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (- 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)))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify108.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (101.0ms)

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

prune283.0ms

Filtered

72 candidates to 59 candidates (81.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	72	6	78

Merged error: 8.9b

Counts

78 → 6

localize116.0ms

Local error

Found 4 expressions with local error:

11.7b	(+ (- 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

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)))

series295.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(+ (- 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)))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify109.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (101.0ms)

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

prune272.0ms

Filtered

70 candidates to 59 candidates (84.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	70	6	76

Merged error: 8.9b

Counts

76 → 6

localize119.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.3b	(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
6.5b	(/ (* a c) b)
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite35.0ms

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:

9.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms	(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
5.0ms	(/ (* a c) b)
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
80.0ms	(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
24.0ms	(/ (* a c) b)
66.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify59.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	478	706
1	2176	625
2	5001	623

prune268.0ms

Filtered

90 candidates to 66 candidates (73.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	88	2	90
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	88	8	96

Merged error: 7.0b

Counts

96 → 8

regimes181.0ms

Accuracy

92.5% (1.0b remaining)

Error of 7.6b against oracle of 6.6b and baseline of 19.7b

bsearch179.0ms

Steps

Iters	Range		Point
7	1.3211901385472032e+133	6.376039839231052e+134	7.410553570169163e+133
9	-3.270551254255918e+118	-2.1334538400483563e+110	-2.4928243975796524e+116

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	63
1	57	63

end0.0ms

sample1.1s

Algorithm

intervals

Results

662.0ms	8719×	body	80	valid
203.0ms	2907×	body	80	nan

Details

sample47.0ms

simplify14.0ms

prune4.0ms

localize118.0ms

rewrite21.0ms

series269.0ms

simplify119.0ms

prune267.0ms

localize120.0ms

rewrite17.0ms

series299.0ms

simplify108.0ms

prune283.0ms

localize116.0ms

rewrite17.0ms

series295.0ms

simplify109.0ms

prune272.0ms

localize119.0ms

rewrite35.0ms

series242.0ms

simplify59.0ms

prune268.0ms

regimes181.0ms

bsearch179.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling