Details

analyze498.0ms

Algorithm: search

sample35.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
1.0ms	16×	body	80	nan
1.0ms	13×	body	80	invalid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	18
1	79	18
2	136	18
3	161	18
4	173	18
5	177	18
6	177	18

prune4.0ms

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: 21.4b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.9b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b	(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))))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify116.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (106.0ms)

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

prune179.0ms

Filtered

62 candidates to 75 candidates (-21.0%)

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: 6.7b

Counts

76 → 6

localize28.0ms

Local error

Found 4 expressions with local error:

10.0b	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b	(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)))

series57.0ms

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

simplify114.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (104.0ms)

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

prune195.0ms

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: 6.7b

Counts

76 → 6

localize28.0ms

Local error

Found 4 expressions with local error:

8.0b	(+ (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
25.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))
25.2b	(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)))
4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series99.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
26.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	382	835
1	1434	761
2	5002	721

prune215.0ms

Filtered

60 candidates to 66 candidates (-10.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	66	6	72

Merged error: 6.7b

Counts

72 → 6

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.3b	(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
4.4b	(/ (* a c) b)
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite26.0ms

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` `associate-/r*`
5×	`pow1`
4×	`cbrt-undiv` `div-exp` `sqrt-prod`
3×	`flip3--` `flip--`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `associate-/r/` `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` `neg-log`

Counts

4 → 77

Calls

4 calls:

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

series50.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify58.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	447	687
1	2162	609
2	5001	607

prune139.0ms

Filtered

65 candidates to 89 candidates (-36.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	1	2	3
Picked	1	0	1
Done	0	2	2
Total	89	6	95

Merged error: 6.2b

Counts

95 → 6

regimes267.0ms

Accuracy

94% (0.9b remaining)

Error of 7.5b against oracle of 6.7b and baseline of 21.4b

bsearch477.0ms

Steps

Iters	Range		Point
7	6.309826001656731e+109	1.360342274038119e+112	7.978357071485187e+111
8	-2.4676564296332972e+138	-5.366905323104297e+133	-4.925343489467074e+134

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	61
1	56	61

end0.0ms

analyze488.0ms

Algorithm: search

sample982.0ms

Algorithm

intervals

Results

697.0ms	8000×	body	80	valid
58.0ms	697×	body	80	nan
32.0ms	384×	body	80	invalid

Details

analyze498.0ms

sample35.0ms

simplify13.0ms

prune4.0ms

localize22.0ms

rewrite27.0ms

series58.0ms

simplify116.0ms

prune179.0ms

localize28.0ms

rewrite16.0ms

series57.0ms

simplify114.0ms

prune195.0ms

localize28.0ms

rewrite16.0ms

series99.0ms

simplify44.0ms

prune215.0ms

localize28.0ms

rewrite26.0ms

series50.0ms

simplify58.0ms

prune139.0ms

regimes267.0ms

bsearch477.0ms

simplify2.0ms

end0.0ms

analyze488.0ms

sample982.0ms

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