Details

sample2.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.280762%

Guaranteed chance to sample good point: 62.857376%

Results

9.0ms	33×	body	2560	valid
7.0ms	161×	body	80	valid
7.0ms	31×	body	1280	valid
3.0ms	16×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	9×	body	320	valid
1.0ms	25×	body	80	nan
0.0ms	7×	body	80	invalid
0.0ms	2×	body	160	valid

simplify363.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	32	7
2	41	7
3	44	7
4	44	7

prune5.0ms

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: 33.2b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
1.0b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

10.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
7.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	360	964
1	1233	910
2	5002	901

prune134.0ms

Filtered

72 candidates to 103 candidates (-43.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	95	8	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	8	104

Merged error: 5.7b

Counts

104 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.7b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.5b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
150×	`add-sqr-sqrt`
115×	`*-un-lft-identity`
81×	`add-cube-cbrt`
34×	`difference-of-squares`
27×	`associate-/l*`
20×	`sqrt-prod`
17×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 187

Calls

4 calls:

7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series122.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
41.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
56.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify101.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	704	2957
1	3098	2807
2	5001	2787

prune233.0ms

Filtered

148 candidates to 199 candidates (-34.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	196	3	199
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	196	11	207

Merged error: 5.7b

Counts

207 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.8b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
2.7b	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

831×	`times-frac`
549×	`add-sqr-sqrt`
450×	`*-un-lft-identity`
352×	`add-cube-cbrt`
98×	`difference-of-squares`
74×	`associate-/l*`
52×	`sqrt-prod`
49×	`distribute-lft-out--`
25×	`associate-/r*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`pow1` `associate-/r/`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 440

Calls

4 calls:

7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
11.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
26.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series124.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
54.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
39.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify97.0ms

Algorithm

egg-herbie

Counts

452 → 452

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1557	7387
1	5001	6822

prune307.0ms

Filtered

301 candidates to 452 candidates (-50.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	450	2	452
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	454	9	463

Merged error: 5.7b

Counts

463 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
0.6b	(- (* b_2 b_2) (* a c))
1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
121×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
68×	`add-cube-cbrt`
26×	`difference-of-squares`
22×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`div-exp`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `flip3--` `flip--` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/r/` `inv-pow`

Counts

4 → 154

Calls

4 calls:

11.0ms	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
4.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series57.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
7.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify66.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	586	1942
1	2438	1777
2	5001	1652

prune92.0ms

Filtered

80 candidates to 166 candidates (-107.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	166	9	175

Merged error: 5.7b

Counts

175 → 9

regimes303.0ms

Accuracy

93.3% (1.6b remaining)

Error of 7.1b against oracle of 5.5b and baseline of 29.6b

bsearch92.0ms

Steps

Iters	Range		Point
8	7.786515903648168e+33	8.243245634482105e+36	8.138872639988856e+36
9	1.5418353768342275e-282	5.305196384710469e-273	1.5079584948694994e-279
6	-4.7059157791950687e+83	-5.694770959789599e+82	-3.718440583315633e+83

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	22
1	40	22

end0.0ms

sample2.9s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.280762%

Guaranteed chance to sample good point: 62.857376%

Results

282.0ms	1088×	body	2560	valid
233.0ms	5136×	body	80	valid
174.0ms	840×	body	1280	valid
75.0ms	461×	body	640	valid
40.0ms	124×	body	5120	valid
29.0ms	230×	body	320	valid
23.0ms	489×	body	80	nan
10.0ms	121×	body	160	valid
8.0ms	186×	body	80	invalid

Details

sample2.0s

simplify363.0ms

prune5.0ms

localize11.0ms

rewrite49.0ms

series58.0ms

simplify42.0ms

prune134.0ms

localize11.0ms

rewrite44.0ms

series122.0ms

simplify101.0ms

prune233.0ms

localize10.0ms

rewrite80.0ms

series124.0ms

simplify97.0ms

prune307.0ms

localize10.0ms

rewrite32.0ms

series57.0ms

simplify66.0ms

prune92.0ms

regimes303.0ms

bsearch92.0ms

simplify2.0ms

end0.0ms

sample2.9s

Profiling