Details

sample4.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.402832%

Guaranteed chance to sample good point: 74.774996%

Results

11.0ms	37×	body	2560	valid
8.0ms	35×	body	1280	valid
8.0ms	156×	body	80	valid
3.0ms	17×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	5×	body	320	valid
1.0ms	14×	body	80	nan
1.0ms	12×	body	80	invalid
0.0ms	2×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

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: 36.1b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.0b	(- (* b b) (* (* 4.0 a) c))
1.0b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite30.0ms

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-/l*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

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

series65.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
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)))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	396	773
1	1550	683
2	5002	673

prune155.0ms

Filtered

63 candidates to 82 candidates (-30.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	74	9	83

Merged error: 6.4b

Counts

83 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
4.0b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
11.1b	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
20×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
10×	`distribute-rgt-neg-in`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 148

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
16.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
12.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series131.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* (* 4.0 a) c))
46.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
62.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify114.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	637	2580
1	3184	2341
2	5001	2328

prune278.0ms

Filtered

106 candidates to 160 candidates (-50.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	157	3	160
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	159	10	169

Merged error: 6.3b

Counts

169 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

7.9b	(- (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
10.8b	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))))))
24.9b	(cbrt (- (* b b) (* (* 4.0 a) c)))
24.9b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
8×	`add-log-exp`
6×	`add-exp-log` `cbrt-prod` `add-cbrt-cube`
4×	`pow1` `cbrt-div` `flip3--` `flip--`
3×	`associate-/r` `associate-/l`
2×	`pow1/3` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `sub-neg` `frac-2neg` `flip3-+` `div-exp` `neg-log` `clear-num` `flip-+` `div-inv`

Counts

4 → 71

Calls

4 calls:

4.0ms	(- (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
7.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))))))
3.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
197.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))))))
24.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
29.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify108.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	675	1807
1	3140	1638
2	5001	1626

prune300.0ms

Filtered

77 candidates to 83 candidates (-7.8%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	83	10	93

Merged error: 6.3b

Counts

93 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b	(- (* b b) (* (* 4.0 a) c))
18.0b	(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
24.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series86.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(- (* b b) (* (* 4.0 a) c))
44.0ms	(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify78.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	486	952
1	2894	749
2	5002	741

prune109.0ms

Filtered

58 candidates to 84 candidates (-44.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	3	3	6
Picked	0	1	1
Done	1	2	3
Total	87	7	94

Merged error: 6.3b

Counts

94 → 7

regimes323.0ms

Accuracy

93.5% (1.6b remaining)

Error of 7.2b against oracle of 5.7b and baseline of 29.7b

bsearch165.0ms

Steps

Iters	Range	Point
7	850397597643135.8	2.0562449637825846e+17	2.011680736595535e+17
10	-2.973470857770798e-211	-3.182603443154487e-221	-3.2184009596459657e-221
8	-2.0262981865872775e+105	-1.6132765285057123e+101	-1.0833883752928771e+105

Iters

Range

Point

850397597643135.8

2.0562449637825846e+17

2.011680736595535e+17

-2.973470857770798e-211

-3.182603443154487e-221

-3.2184009596459657e-221

-2.0262981865872775e+105

-1.6132765285057123e+101

-1.0833883752928771e+105

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	27
1	49	27
2	49	27

end0.0ms

sample5.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.402832%

Guaranteed chance to sample good point: 74.774996%

Results

306.0ms	1022×	body	2560	valid
276.0ms	5142×	body	80	valid
220.0ms	893×	body	1280	valid
86.0ms	456×	body	640	valid
42.0ms	116×	body	5120	valid
35.0ms	245×	body	320	valid
17.0ms	346×	body	80	nan
16.0ms	304×	body	80	invalid
12.0ms	126×	body	160	valid

Details

sample4.0s

simplify10.0ms

prune4.0ms

localize12.0ms

rewrite30.0ms

series65.0ms

simplify45.0ms

prune155.0ms

localize19.0ms

rewrite41.0ms

series131.0ms

simplify114.0ms

prune278.0ms

localize21.0ms

rewrite20.0ms

series286.0ms

simplify108.0ms

prune300.0ms

localize16.0ms

rewrite33.0ms

series86.0ms

simplify78.0ms

prune109.0ms

regimes323.0ms

bsearch165.0ms

simplify2.0ms

end0.0ms

sample5.5s

Profiling