Details

sample257.0ms

Algorithm

intervals

Results

202.0ms	75×	body	80	nan
31.0ms	278×	body	80	valid

simplify19.0ms

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

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: 18.6b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* (* 4.0 a) c))
1.9b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite24.0ms

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	(- (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)))

series68.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
30.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify123.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (115.0ms)

Iter	Nodes	Cost
0	223	579
1	875	551
2	3958	543
3	5001	540

prune188.0ms

Filtered

72 candidates to 55 candidates (23.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	65	7	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	7	73

Merged error: 8.4b

Counts

73 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

8.2b	(- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.3b	(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	(- (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)))

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))))))
13.0ms	(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)))

simplify106.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (98.0ms)

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

prune213.0ms

Filtered

72 candidates to 59 candidates (18.1%)

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: 8.4b

Counts

79 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

10.7b	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite18.0ms

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)))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series56.0ms

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))))))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify109.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (102.0ms)

Iter	Nodes	Cost
0	227	680
1	870	574
2	3628	562
3	5001	558

prune203.0ms

Filtered

70 candidates to 59 candidates (15.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	71	6	77

Merged error: 8.4b

Counts

77 → 6

localize30.0ms

Local error

Found 4 expressions with local error:

7.2b	(- (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.1b	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.1b	(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` `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)))

series97.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
25.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify41.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	377	866
1	1391	791
2	5001	755

prune211.0ms

Filtered

67 candidates to 60 candidates (10.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	67	6	73

Merged error: 8.4b

Counts

73 → 6

regimes237.0ms

Accuracy

92.5% (0.9b remaining)

Error of 8.1b against oracle of 7.2b and baseline of 19.5b

bsearch88.0ms

Steps

Iters	Range		Point
8	1.2099936426732458e+107	2.3384458119324726e+110	1.8771340102380541e+109
11	-2.766539085620364e+156	-7.786185162824564e+124	-2.9565804549553922e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	58
1	48	58

end0.0ms

sample1.6s

Algorithm

intervals

Results

876.0ms	8698×	body	80	valid
291.0ms	3010×	body	80	nan

Details

sample257.0ms

simplify19.0ms

prune6.0ms

localize26.0ms

rewrite24.0ms

series68.0ms

simplify123.0ms

prune188.0ms

localize25.0ms

rewrite16.0ms

series59.0ms

simplify106.0ms

prune213.0ms

localize25.0ms

rewrite18.0ms

series56.0ms

simplify109.0ms

prune203.0ms

localize30.0ms

rewrite16.0ms

series97.0ms

simplify41.0ms

prune211.0ms

regimes237.0ms

bsearch88.0ms

simplify2.0ms

end0.0ms

sample1.6s

Profiling