Details

sample412.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 5.867564%

Guaranteed chance to sample good point: 43.897396%

Results

24.0ms	278×	body	80	valid
7.0ms	82×	body	80	nan

simplify14.0ms

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: 23.9b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 4.0 a) c))
1.3b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
25.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite26.0ms

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:

7.0ms	(- (* b b) (* (* 4.0 a) c))
7.0ms	(+ (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)))

series59.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* 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)))
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify122.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (115.0ms)

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

prune175.0ms

Filtered

55 candidates to 69 candidates (-25.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	62	7	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	7	70

Merged error: 8.8b

Counts

70 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

1.3b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.8b	(/ (- (neg b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
4.9b	(/ (* a c) b)
25.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
14×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `times-frac`
8×	`add-log-exp`
7×	`associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `div-exp` `associate-/r*` `distribute-lft-out--`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`flip3--` `frac-2neg` `sqrt-div` `prod-exp` `clear-num` `sum-log` `flip--` `cbrt-unprod` `div-inv` `associate-/l/` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `neg-sub0` `associate-+l-` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `div-sub` `neg-log` `flip-+`

Counts

4 → 81

Calls

4 calls:

7.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(/ (- (neg b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
4.0ms	(/ (* a c) b)
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series44.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms	(/ (- (neg b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
5.0ms	(/ (* a c) b)
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify54.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	485	747
1	2165	661
2	5002	654

prune182.0ms

Filtered

68 candidates to 93 candidates (-36.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	89	4	93
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	91	9	100

Merged error: 7.9b

Counts

100 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 2.0 c) (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.3b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/r*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `associate-/r/` `flip--` `flip-+`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 69

Calls

4 calls:

12.0ms	(/ (* 2.0 c) (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
7.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series91.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ (* 2.0 c) (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
9.0ms	(- (* 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)))

simplify43.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	375	757
1	1596	658
2	5001	645

prune173.0ms

Filtered

61 candidates to 81 candidates (-32.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	76	5	81
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	79	11	90

Merged error: 7.8b

Counts

90 → 11

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 2.0 (/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) c))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.3b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

117×	`times-frac`
113×	`*-un-lft-identity`
62×	`add-sqr-sqrt`
61×	`add-cube-cbrt`
26×	`distribute-lft-out`
19×	`associate-/r*`
13×	`distribute-rgt-neg-in`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `div-inv`
3×	`cbrt-undiv` `div-exp` `sqrt-prod` `associate-/l*`
2×	`flip3--` `sqrt-div` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `neg-log` `clear-num` `associate-/r/` `flip-+`

Counts

4 → 136

Calls

4 calls:

12.0ms	(/ 2.0 (/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) c))
3.0ms	(- (* 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)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ 2.0 (/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) c))
8.0ms	(- (* 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)))

simplify70.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	588	1909
1	2460	1816
2	5001	1810

prune234.0ms

Filtered

102 candidates to 148 candidates (-45.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	146	2	148
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	149	10	159

Merged error: 7.6b

Counts

159 → 10

regimes298.0ms

Accuracy

91.2% (1.3b remaining)

Error of 7.3b against oracle of 6.0b and baseline of 21.0b

bsearch68.0ms

Steps

Iters	Range		Point
9	5.540085819974055e+25	1.8898729685964401e+31	1.7986047002629845e+31
8	-3.580435379502479e+155	-9.018124288077145e+152	-6.792199154286955e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	55
1	47	55

end0.0ms

sample1.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 5.867564%

Guaranteed chance to sample good point: 43.897396%

Results

766.0ms	8731×	body	80	valid
176.0ms	2187×	body	80	nan

Details

sample412.0ms

simplify14.0ms

prune4.0ms

localize22.0ms

rewrite26.0ms

series59.0ms

simplify122.0ms

prune175.0ms

localize25.0ms

rewrite28.0ms

series44.0ms

simplify54.0ms

prune182.0ms

localize22.0ms

rewrite28.0ms

series91.0ms

simplify43.0ms

prune173.0ms

localize24.0ms

rewrite32.0ms

series64.0ms

simplify70.0ms

prune234.0ms

regimes298.0ms

bsearch68.0ms

simplify2.0ms

end0.0ms

sample1.7s

Profiling