Details

sample1.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 23.873901%

Guaranteed chance to sample good point: 69.504911%

Results

13.0ms	44×	body	2560	valid
8.0ms	152×	body	80	valid
6.0ms	25×	body	1280	valid
3.0ms	15×	body	640	valid
2.0ms	6×	body	5120	valid
1.0ms	9×	body	320	valid
1.0ms	17×	body	80	nan
1.0ms	14×	body	80	invalid
1.0ms	5×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	9
1	42	9
2	76	9
3	94	9
4	102	9
5	102	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: 36.3b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.0b	(- (* b b) (* (* 3.0 a) c))
1.5b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
26.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite26.0ms

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:

11.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
3.0ms	(- (* b b) (* (* 3.0 a) c))
7.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
8.0ms	(- (* b b) (* (* 3.0 a) c))
15.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	391	774
1	1518	684
2	5001	674

prune156.0ms

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: 5.3b

Counts

83 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 3.0 a) c))
4.4b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
9.8b	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
26.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite43.0ms

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

series119.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* (* 3.0 a) c))
44.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
53.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify114.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	634	2582
1	3155	2341
2	5002	2328

prune273.0ms

Filtered

106 candidates to 160 candidates (-50.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	158	2	160
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	158	11	169

Merged error: 5.2b

Counts

169 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b	(- (* b b) (* (* 3.0 a) c))
15.6b	(/ (* 3.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
26.1b	(sqrt (- (* b b) (* (* 3.0 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) (* (* 3.0 a) c))))
3.0ms	(- (* b b) (* (* 3.0 a) c))
16.0ms	(/ (* 3.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series83.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
11.0ms	(- (* b b) (* (* 3.0 a) c))
42.0ms	(/ (* 3.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify74.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (65.0ms)

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

prune130.0ms

Filtered

58 candidates to 84 candidates (-44.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	2	6	8
Picked	1	0	1
Done	0	2	2
Total	86	9	95

Merged error: 5.2b

Counts

95 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 3.0 (/ (* 1 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) c))
0.3b	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b	(- (* b b) (* (* 3.0 a) c))
26.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

11.0ms	(/ 3.0 (/ (* 1 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) c))
8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(- (* b b) (* (* 3.0 a) c))
6.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series72.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ 3.0 (/ (* 1 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) c))
15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
8.0ms	(- (* b b) (* (* 3.0 a) c))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify65.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	548	1187
1	2335	1075
2	5001	1075

prune159.0ms

Filtered

80 candidates to 106 candidates (-32.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	103	3	106
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	104	11	115

Merged error: 5.2b

Counts

115 → 11

regimes617.0ms

Accuracy

94.5% (1.3b remaining)

Error of 7.1b against oracle of 5.8b and baseline of 30.2b

bsearch121.0ms

Steps

Iters	Range	Point
9	6.998369980341823e+52	3.884464804506573e+61	1.4025338698895464e+57
9	-7.853937664262267e-274	-3.1271971898085402e-279	-1.4555990037767983e-278
10	-3.2251985257956323e+159	-1.6184271943407125e+144	-7.892954506325459e+152

Iters

Range

Point

6.998369980341823e+52

3.884464804506573e+61

1.4025338698895464e+57

-7.853937664262267e-274

-3.1271971898085402e-279

-1.4555990037767983e-278

-3.2251985257956323e+159

-1.6184271943407125e+144

-7.892954506325459e+152

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	30
1	51	30
2	51	30

end0.0ms

sample2.9s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 23.873901%

Guaranteed chance to sample good point: 69.504911%

Results

336.0ms	1076×	body	2560	valid
287.0ms	5154×	body	80	valid
220.0ms	877×	body	1280	valid
92.0ms	454×	body	640	valid
41.0ms	111×	body	5120	valid
37.0ms	232×	body	320	valid
26.0ms	479×	body	80	invalid
23.0ms	392×	body	80	nan
10.0ms	96×	body	160	valid

Details

sample1.6s

simplify10.0ms

prune4.0ms

localize14.0ms

rewrite26.0ms

series64.0ms

simplify45.0ms

prune156.0ms

localize15.0ms

rewrite43.0ms

series119.0ms

simplify114.0ms

prune273.0ms

localize16.0ms

rewrite33.0ms

series83.0ms

simplify74.0ms

prune130.0ms

localize15.0ms

rewrite32.0ms

series72.0ms

simplify65.0ms

prune159.0ms

regimes617.0ms

bsearch121.0ms

simplify2.0ms

end0.0ms

sample2.9s

Profiling