Details

sample1.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 23.294067%

Guaranteed chance to sample good point: 69.854784%

Results

11.0ms	39×	body	2560	valid
9.0ms	164×	body	80	valid
6.0ms	28×	body	1280	valid
6.0ms	12×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	18×	body	80	nan
1.0ms	15×	body	80	invalid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify374.0ms

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: 35.7b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
25.0b	(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)
7.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
13.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(- (* b_2 b_2) (* a c))
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify137.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (30.0ms)

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

prune151.0ms

Filtered

69 candidates to 92 candidates (-33.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	83	9	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	9	93

Merged error: 5.0b

Counts

93 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
3.0b	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
9.3b	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
25.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

186×	`times-frac`
154×	`add-sqr-sqrt`
153×	`*-un-lft-identity`
89×	`add-cube-cbrt`
32×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-rgt-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*` `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 → 200

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
12.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series111.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
40.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
52.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify107.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	708	3365
1	3231	3197
2	5001	3171

prune242.0ms

Filtered

142 candidates to 212 candidates (-49.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	210	2	212
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	213	8	221

Merged error: 4.9b

Counts

221 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
2.1b	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.0b	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
25.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

951×	`times-frac`
585×	`add-sqr-sqrt`
584×	`*-un-lft-identity`
392×	`add-cube-cbrt`
96×	`distribute-lft-out--` `difference-of-squares`
83×	`associate-/l*`
51×	`sqrt-prod`
48×	`distribute-rgt-neg-in`
28×	`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 → 485

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(/ 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:

9.0ms	(- (* b_2 b_2) (* a c))
50.0ms	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
50.0ms	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify105.0ms

Algorithm

egg-herbie

Counts

497 → 497

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1525	8627
1	5002	7984

prune330.0ms

Filtered

298 candidates to 497 candidates (-66.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	495	2	497
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	497	8	505

Merged error: 4.9b

Counts

505 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 c))
0.5b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
25.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

897×	`times-frac`
528×	`add-sqr-sqrt`
527×	`*-un-lft-identity`
355×	`add-cube-cbrt`
86×	`distribute-lft-out--` `difference-of-squares`
46×	`sqrt-prod`
44×	`add-exp-log`
43×	`distribute-rgt-neg-in` `div-inv`
32×	`div-exp`
29×	`associate-/r/`
27×	`associate-/l*`
17×	`flip3--` `flip--`
16×	`add-cbrt-cube`
13×	`associate-/r*`
10×	`add-log-exp`
8×	`cbrt-undiv` `rec-exp` `1-exp`
5×	`pow1`
3×	`diff-log`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 468

Calls

4 calls:

22.0ms	(/ (/ 1 (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 c))
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (/ 1 (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 c))
14.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify113.0ms

Algorithm

egg-herbie

Counts

480 → 480

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1777	8958
1	5001	8170

prune302.0ms

Filtered

173 candidates to 480 candidates (-177.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	478	2	480
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	479	9	488

Merged error: 4.9b

Counts

488 → 9

regimes291.0ms

Accuracy

96% (1.0b remaining)

Error of 6.3b against oracle of 5.3b and baseline of 29.7b

bsearch106.0ms

Steps

Iters	Range	Point
8	8.682293476141014e+121	6.775453802686609e+124	1.3429984501400026e+124
10	-1.2526338037432968e-195	-1.8255193213693471e-209	-1.8528253350851652e-209
6	-2.2997956104207656e+129	-1.671933652309897e+128	-1.6971779938868822e+128

Iters

Range

Point

8.682293476141014e+121

6.775453802686609e+124

1.3429984501400026e+124

-1.2526338037432968e-195

-1.8255193213693471e-209

-1.8528253350851652e-209

-2.2997956104207656e+129

-1.671933652309897e+128

-1.6971779938868822e+128

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	23
1	42	23

end0.0ms

sample2.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 23.294067%

Guaranteed chance to sample good point: 69.854784%

Results

313.0ms	1108×	body	2560	valid
251.0ms	5079×	body	80	valid
209.0ms	933×	body	1280	valid
78.0ms	430×	body	640	valid
38.0ms	109×	body	5120	valid
30.0ms	226×	body	320	valid
23.0ms	512×	body	80	nan
21.0ms	425×	body	80	invalid
10.0ms	115×	body	160	valid

Details

sample1.7s

simplify374.0ms

prune5.0ms

localize12.0ms

rewrite30.0ms

series70.0ms

simplify137.0ms

prune151.0ms

localize14.0ms

rewrite44.0ms

series111.0ms

simplify107.0ms

prune242.0ms

localize12.0ms

rewrite85.0ms

series121.0ms

simplify105.0ms

prune330.0ms

localize12.0ms

rewrite74.0ms

series67.0ms

simplify113.0ms

prune302.0ms

regimes291.0ms

bsearch106.0ms

simplify2.0ms

end0.0ms

sample2.7s

Profiling