Details

analyze593.0ms

Algorithm: search

sample40.0ms

Algorithm

intervals

Results

9.0ms	34×	body	2560	valid
7.0ms	172×	body	80	valid
5.0ms	24×	body	1280	valid
2.0ms	14×	body	640	valid
1.0ms	29×	body	80	nan
1.0ms	16×	body	80	invalid
1.0ms	5×	body	320	valid
1.0ms	7×	body	160	valid

simplify389.0ms

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

prune6.0ms

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: 32.1b

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)
0.4b	(- (* b_2 b_2) (* a c))
1.8b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite49.0ms

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))
7.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series62.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (+ (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)))

simplify142.0ms

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

prune132.0ms

Filtered

69 candidates to 92 candidates (-33.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	85	7	92
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	85	8	93

Merged error: 5.2b

Counts

93 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.5b	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
9.0b	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite50.0ms

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))))
15.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series113.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
41.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
47.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify109.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (80.0ms)

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

prune222.0ms

Filtered

147 candidates to 218 candidates (-48.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	214	4	218
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	218	8	226

Merged error: 5.1b

Counts

226 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.5b	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
3.8b	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite92.0ms

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:

8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.0ms	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
16.0ms	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) 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	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
52.0ms	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify106.0ms

Algorithm

egg-herbie

Counts

503 → 503

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1569	8733
1	5001	8087

prune299.0ms

Filtered

303 candidates to 503 candidates (-66.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	501	2	503
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	504	7	511

Merged error: 5.1b

Counts

511 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b_2 b_2) (* a c))
0.5b	(/ 1 (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
0.6b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 169

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(/ 1 (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
32.0ms	(/ 1 (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
13.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify73.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	618	2273
1	2704	2086
2	5001	1951

prune96.0ms

Filtered

81 candidates to 181 candidates (-123.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	180	1	181
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	182	6	188

Merged error: 5.1b

Counts

188 → 6

regimes334.0ms

Accuracy

95.6% (1.1b remaining)

Error of 6.6b against oracle of 5.6b and baseline of 29.6b

bsearch708.0ms

Steps

Iters	Range	Point
7	7.5269478862554305e+118	1.6623563295692568e+120	3.307552053757527e+119
9	-1.1129268685471683e-201	-1.591206346462726e-208	-1.97023969969262e-208
11	-1.4462310998269807e+156	-1.3640302321346553e+136	-1.6809616024018359e+140

Iters

Range

Point

7.5269478862554305e+118

1.6623563295692568e+120

3.307552053757527e+119

-1.1129268685471683e-201

-1.591206346462726e-208

-1.97023969969262e-208

-1.4462310998269807e+156

-1.3640302321346553e+136

-1.6809616024018359e+140

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	22
1	42	22
2	42	22

end0.0ms

analyze398.0ms

Algorithm: search

sample1.1s

Algorithm

intervals

Results

265.0ms	1044×	body	2560	valid
230.0ms	5216×	body	80	valid
180.0ms	878×	body	1280	valid
73.0ms	455×	body	640	valid
34.0ms	817×	body	80	nan
30.0ms	100×	body	5120	valid
26.0ms	216×	body	320	valid
11.0ms	251×	body	80	invalid
7.0ms	91×	body	160	valid

Details

analyze593.0ms

sample40.0ms

simplify389.0ms

prune6.0ms

localize12.0ms

rewrite49.0ms

series62.0ms

simplify142.0ms

prune132.0ms

localize11.0ms

rewrite50.0ms

series113.0ms

simplify109.0ms

prune222.0ms

localize11.0ms

rewrite92.0ms

series117.0ms

simplify106.0ms

prune299.0ms

localize12.0ms

rewrite35.0ms

series63.0ms

simplify73.0ms

prune96.0ms

regimes334.0ms

bsearch708.0ms

simplify2.0ms

end0.0ms

analyze398.0ms

sample1.1s

Profiling