Details

analyze731.0ms

Algorithm: search

sample38.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
1.0ms	13×	body	80	nan
1.0ms	10×	body	80	invalid

simplify367.0ms

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: 20.1b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* (* 4.0 a) c))
2.2b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

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

series74.0ms

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)))
37.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify123.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (116.0ms)

Iter	Nodes	Cost
0	231	531
1	915	501
2	4084	489
3	5002	486

prune218.0ms

Filtered

55 candidates to 69 candidates (-25.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	63	6	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	6	70

Merged error: 8.6b

Counts

70 → 6

localize24.0ms

Local error

Found 4 expressions with local error:

11.5b	(- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b	(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)))

series61.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify106.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	221	722
1	829	631
2	3533	612
3	5001	595

prune220.0ms

Filtered

63 candidates to 72 candidates (-14.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	71	7	78

Merged error: 8.6b

Counts

78 → 7

localize28.0ms

Local error

Found 4 expressions with local error:

8.3b	(- (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.3b	(cbrt (- (* b b) (* (* 4.0 a) c)))
24.3b	(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))))))
4.0ms	(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)))

series103.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (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)))
25.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
26.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (33.0ms)

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

prune233.0ms

Filtered

60 candidates to 67 candidates (-11.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	66	8	74

Merged error: 8.6b

Counts

74 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* (* 4.0 a) c))
3.1b	(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
6.6b	(/ (* a c) b)
23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`times-frac` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp` `associate-/r` `associate-/l`
3×	`flip3--` `sqrt-prod` `flip--`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `div-sub`

Counts

4 → 72

Calls

4 calls:

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

series43.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* (* 4.0 a) c))
16.0ms	(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
5.0ms	(/ (* a c) b)
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	423	596
1	1940	520
2	5002	518

prune128.0ms

Filtered

61 candidates to 84 candidates (-37.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	83	9	92

Merged error: 7.0b

Counts

92 → 9

regimes281.0ms

Accuracy

92.3% (1.1b remaining)

Error of 7.9b against oracle of 6.8b and baseline of 21.1b

bsearch596.0ms

Steps

Iters	Range		Point
9	5.861930467183623e+87	5.1667852289507864e+94	3.888274402711614e+94
9	-2.3923055925670283e+82	-1.2794925325132113e+74	-2.3516286670485864e+82

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	55
1	56	55

end0.0ms

analyze549.0ms

Algorithm: search

sample964.0ms

Algorithm

intervals

Results

682.0ms	8000×	body	80	valid
54.0ms	671×	body	80	nan
32.0ms	396×	body	80	invalid

Details

analyze731.0ms

sample38.0ms

simplify367.0ms

prune6.0ms

localize23.0ms

rewrite22.0ms

series74.0ms

simplify123.0ms

prune218.0ms

localize24.0ms

rewrite16.0ms

series61.0ms

simplify106.0ms

prune220.0ms

localize28.0ms

rewrite16.0ms

series103.0ms

simplify42.0ms

prune233.0ms

localize24.0ms

rewrite22.0ms

series43.0ms

simplify49.0ms

prune128.0ms

regimes281.0ms

bsearch596.0ms

simplify2.0ms

end0.0ms

analyze549.0ms

sample964.0ms

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