Details

sample233.0ms

Algorithm

intervals

Results

192.0ms	196×	body	80	valid
7.0ms	26×	body	2560	valid
5.0ms	26×	body	1280	valid
3.0ms	75×	body	80	nan
3.0ms	16×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	4×	body	160	valid

simplify14.0ms

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

Filtered

1 candidates to 0 candidates (100.0%)

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: 31.8b

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)
1.2b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b	(- (* b_2 b_2) (* a c))
21.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite32.0ms

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:

11.0ms	(/ (+ (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)))

series72.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
23.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(- (* b_2 b_2) (* a c))
22.0ms	(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

prune135.0ms

Filtered

92 candidates to 69 candidates (25.0%)

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: 6.3b

Counts

93 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

1.9b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0b	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
9.6b	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
21.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite53.0ms

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))))
17.0ms	(/ (/ (+ 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)))

series116.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
39.0ms	(/ (/ (+ 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)))

simplify112.0ms

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

218 candidates to 147 candidates (32.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	217	1	218
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	219	7	226

Merged error: 6.2b

Counts

226 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

1.9b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.2b	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
4.0b	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
21.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite91.0ms

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))))
16.0ms	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
27.0ms	(/ (/ 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:

13.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
50.0ms	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
46.0ms	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify112.0ms

Algorithm

egg-herbie

Counts

503 → 503

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1569	8733
1	5001	8087

prune297.0ms

Filtered

503 candidates to 303 candidates (39.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	503	0	503
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	503	7	510

Merged error: 6.2b

Counts

510 → 7

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
1.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.4b	(- (* b_2 b_2) (* a c))
21.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `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` `inv-pow`

Counts

4 → 162

Calls

4 calls:

13.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series62.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
12.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify68.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	564	2096
1	2553	1897
2	5001	1761

prune98.0ms

Filtered

174 candidates to 86 candidates (50.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	174	7	181

Merged error: 6.2b

Counts

181 → 7

regimes358.0ms

Accuracy

82.3% (4.7b remaining)

Error of 9.7b against oracle of 5.0b and baseline of 31.6b

bsearch52.0ms

Steps

Iters	Range		Point
8	3.4713192377217875e-36	1.5663447360869123e-31	2.8203535769129045e-33
7	-6.682283173913537e+118	-3.724757707733592e+117	-2.4933470885408413e+118

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	14
1	30	14

end0.0ms

sample1.3s

Algorithm

intervals

Results

247.0ms	5848×	body	80	valid
244.0ms	1000×	body	2560	valid
184.0ms	924×	body	1280	valid
122.0ms	3009×	body	80	nan
63.0ms	406×	body	640	valid
36.0ms	123×	body	5120	valid
31.0ms	264×	body	320	valid
11.0ms	134×	body	160	valid

Details

sample233.0ms

simplify14.0ms

prune5.0ms

localize12.0ms

rewrite32.0ms

series72.0ms

simplify142.0ms

prune135.0ms

localize11.0ms

rewrite53.0ms

series116.0ms

simplify112.0ms

prune222.0ms

localize11.0ms

rewrite91.0ms

series121.0ms

simplify112.0ms

prune297.0ms

localize9.0ms

rewrite34.0ms

series62.0ms

simplify68.0ms

prune98.0ms

regimes358.0ms

bsearch52.0ms

simplify2.0ms

end0.0ms

sample1.3s

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