Details

sample486.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 5.867544%

Guaranteed chance to sample good point: 42.569946%

Results

15.0ms	34×	body	2560	valid
9.0ms	182×	body	80	valid
8.0ms	38×	body	1280	valid
4.0ms	84×	body	80	nan
2.0ms	11×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	2×	body	160	valid

simplify401.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	7
1	22	7
2	25	7
3	27	7
4	29	7
5	29	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: 35.1b

Counts

2 → 1

localize13.0ms

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))
0.6b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

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))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series71.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
17.0ms	(- (* 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)))

simplify142.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	338	783
1	1216	724
2	4971	703
3	5001	703

prune135.0ms

Filtered

69 candidates to 92 candidates (-33.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	85	7	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	7	93

Merged error: 6.7b

Counts

93 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.1b	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
10.1b	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 206

Calls

4 calls:

8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
14.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series117.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
40.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
51.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify111.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	716	3474
1	3237	3299
2	5002	3273

prune234.0ms

Filtered

147 candidates to 218 candidates (-48.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	217	1	218
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	217	8	225

Merged error: 6.6b

Counts

225 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.0b	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.1b	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

951×	`times-frac`
589×	`add-sqr-sqrt`
588×	`*-un-lft-identity`
392×	`add-cube-cbrt`
98×	`distribute-lft-out--` `difference-of-squares`
83×	`associate-/l*`
52×	`sqrt-prod`
49×	`distribute-rgt-neg-in`
28×	`associate-/r*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
8×	`add-log-exp`
5×	`pow1` `associate-/r/`
2×	`flip3--` `frac-2neg` `sqrt-div` `diff-log` `clear-num` `flip--`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 491

Calls

4 calls:

11.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
25.0ms	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series121.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
48.0ms	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
47.0ms	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify108.0ms

Algorithm

egg-herbie

Counts

503 → 503

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1569	8733
1	5001	8087

prune324.0ms

Filtered

303 candidates to 503 candidates (-66.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	501	2	503
Fresh	1	5	6
Picked	0	1	1
Done	1	0	1
Total	503	8	511

Merged error: 6.6b

Counts

511 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
0.7b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.6b	(/ (* a c) a)
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(/ (* a c) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series37.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.0ms	(/ (* a c) a)
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify38.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	297	457
1	1304	420
2	5001	399

prune74.0ms

Filtered

57 candidates to 78 candidates (-36.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	78	8	86

Merged error: 6.6b

Counts

86 → 8

regimes236.0ms

Accuracy

82.9% (4.5b remaining)

Error of 10.1b against oracle of 5.6b and baseline of 31.8b

bsearch60.0ms

Steps

Iters	Range		Point
9	1.289478017848784e-92	3.0960733146221547e-84	2.4464565658583153e-86
8	-8.382670411051464e+140	-3.442563917519272e+136	-7.018837578197459e+139

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	15
1	35	15

end0.0ms

sample1.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 5.867544%

Guaranteed chance to sample good point: 42.569946%

Results

278.0ms	1096×	body	2560	valid
263.0ms	5777×	body	80	valid
191.0ms	910×	body	1280	valid
95.0ms	2199×	body	80	nan
72.0ms	443×	body	640	valid
38.0ms	111×	body	5120	valid
34.0ms	264×	body	320	valid
9.0ms	111×	body	160	valid

Details

sample486.0ms

simplify401.0ms

prune5.0ms

localize13.0ms

rewrite30.0ms

series71.0ms

simplify142.0ms

prune135.0ms

localize11.0ms

rewrite51.0ms

series117.0ms

simplify111.0ms

prune234.0ms

localize12.0ms

rewrite88.0ms

series121.0ms

simplify108.0ms

prune324.0ms

localize12.0ms

rewrite21.0ms

series37.0ms

simplify38.0ms

prune74.0ms

regimes236.0ms

bsearch60.0ms

simplify2.0ms

end0.0ms

sample1.6s

Profiling