Details

sample41.0ms

Algorithm

intervals

Results

20.0ms	276×	body	80	valid
5.0ms	77×	body	80	nan

simplify15.0ms

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

prune3.0ms

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: 18.0b

Counts

2 → 1

localize158.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 4.0 a) c))
0.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite19.0ms

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:

3.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(- (- 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)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 4.0 a) c))
89.0ms	(- (- b) (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)))

simplify120.0ms

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

prune248.0ms

Filtered

72 candidates to 55 candidates (76.4%)

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: 6.6b

Counts

73 → 7

localize121.0ms

Local error

Found 4 expressions with local error:

13.2b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.7b	(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	(+ (- 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)))

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))))))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
66.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify110.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (103.0ms)

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

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	70	7	77

Merged error: 6.6b

Counts

77 → 7

localize126.0ms

Local error

Found 4 expressions with local error:

5.8b	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.5b	(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	(- (- 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)))
4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
99.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
102.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	363	835
1	1402	760
2	5001	731

prune330.0ms

Filtered

67 candidates to 59 candidates (88.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	65	2	67
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	65	9	74

Merged error: 6.5b

Counts

74 → 9

localize128.0ms

Local error

Found 4 expressions with local error:

14.3b	(- (- b) (* (fabs (exp (log (cbrt (- (* b b) (* (* 4.0 a) c)))))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.5b	(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	(- (- b) (* (fabs (exp (log (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)))

series353.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(- (- b) (* (fabs (exp (log (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

67 → 67

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	365	877
1	1404	784
2	5001	744

prune338.0ms

Filtered

67 candidates to 59 candidates (88.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	67	9	76

Merged error: 6.5b

Counts

76 → 9

regimes197.0ms

Accuracy

87.9% (1.5b remaining)

Error of 9.2b against oracle of 7.7b and baseline of 20.1b

bsearch128.0ms

Steps

Iters	Range		Point
7	3.0106008231332273e+28	3.853441604264477e+30	3.7841174599135035e+30
5	-2.783673024614503e+98	-8.233152822480874e+97	-2.720129631643668e+98

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	58
1	49	58

end0.0ms

sample1.1s

Algorithm

intervals

Results

618.0ms	8737×	body	80	valid
192.0ms	2866×	body	80	nan