Details

sample1.9s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.280762%

Guaranteed chance to sample good point: 62.857376%

Results

9.0ms	32×	body	2560	valid
7.0ms	34×	body	1280	valid
7.0ms	154×	body	80	valid
3.0ms	18×	body	640	valid
1.0ms	11×	body	320	valid
1.0ms	4×	body	5120	valid
1.0ms	23×	body	80	nan
0.0ms	6×	body	80	invalid
0.0ms	3×	body	160	valid

simplify355.0ms

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: 36.0b

Counts

2 → 1

localize24.0ms

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))))
1.0b	(- (* b_2 b_2) (* a c))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite29.0ms

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:

9.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(+ (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)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
14.0ms	(+ (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)))

simplify138.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (31.0ms)

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

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	84	8	92
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	9	93

Merged error: 6.2b

Counts

93 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
3.0b	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.1b	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite45.0ms

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))
18.0ms	(/ (/ (+ 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))
43.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
48.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify105.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 2 (76.0ms)

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

prune222.0ms

Filtered

142 candidates to 212 candidates (-49.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	209	3	212
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	212	9	221

Merged error: 6.2b

Counts

221 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
2.7b	(/ 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)
22.8b	(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:

3.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
26.0ms	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series118.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
50.0ms	(/ 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)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify107.0ms

Algorithm

egg-herbie

Counts

497 → 497

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1525	8627
1	5002	7984

prune303.0ms

Filtered

298 candidates to 497 candidates (-66.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	495	2	497
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	498	8	506

Merged error: 6.2b

Counts

506 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
2.0b	(/ (cbrt a) (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 241

Calls

4 calls:

8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(/ (cbrt a) (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series150.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(- (* b_2 b_2) (* a c))
117.0ms	(/ (cbrt a) (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify101.0ms

Algorithm

egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	818	4086
1	3317	4004
2	5001	3965

prune167.0ms

Filtered

148 candidates to 253 candidates (-70.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	252	1	253
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	252	9	261

Merged error: 6.2b

Counts

261 → 9

regimes402.0ms

Accuracy

94.3% (1.4b remaining)

Error of 6.8b against oracle of 5.4b and baseline of 30.0b

bsearch114.0ms

Steps

Iters	Range	Point
9	3.6431704190991106e+50	2.902896348134585e+56	1.4879353124997477e+51
9	-6.417038681493137e-284	-8.322916491939974e-290	-1.9916343573940057e-289
8	-5.4768850363821645e+118	-8.462113933920072e+113	-2.677617976630959e+118

Iters

Range

Point

3.6431704190991106e+50

2.902896348134585e+56

1.4879353124997477e+51

-6.417038681493137e-284

-8.322916491939974e-290

-1.9916343573940057e-289

-5.4768850363821645e+118

-8.462113933920072e+113

-2.677617976630959e+118

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	26
1	45	26
2	45	26

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

287.0ms	1080×	body	2560	valid
244.0ms	5115×	body	80	valid
196.0ms	889×	body	1280	valid
77.0ms	449×	body	640	valid
34.0ms	108×	body	5120	valid
33.0ms	239×	body	320	valid
20.0ms	462×	body	80	nan
10.0ms	120×	body	160	valid
9.0ms	182×	body	80	invalid

Details

sample1.9s

simplify355.0ms

prune5.0ms

localize24.0ms

rewrite29.0ms

series67.0ms

simplify138.0ms

prune135.0ms

localize11.0ms

rewrite45.0ms

series111.0ms

simplify105.0ms

prune222.0ms

localize14.0ms

rewrite85.0ms

series118.0ms

simplify107.0ms

prune303.0ms

localize14.0ms

rewrite48.0ms

series150.0ms

simplify101.0ms

prune167.0ms

regimes402.0ms

bsearch114.0ms

simplify2.0ms

end0.0ms

sample2.9s

Profiling