Details

sample244.0ms

Algorithm

intervals

Results

198.0ms	214×	body	80	valid
8.0ms	28×	body	2560	valid
4.0ms	19×	body	1280	valid
4.0ms	87×	body	80	nan
2.0ms	10×	body	640	valid
1.0ms	2×	body	5120	valid
0.0ms	4×	body	320	valid
0.0ms	2×	body	160	valid

simplify265.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

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: 32.9b

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)
0.7b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
24.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite31.0ms

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)
8.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series71.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (+ (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))
23.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify141.0ms

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

prune136.0ms

Filtered

92 candidates to 69 candidates (25.0%)

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: 7.5b

Counts

93 → 9

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.7b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.2b	(- (* b_2 b_2) (* a c))
24.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite36.0ms

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)))
9.0ms	(- (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)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(- (* 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 (50.0ms)

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

prune124.0ms

Filtered

174 candidates to 85 candidates (51.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	171	3	174
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	174	9	183

Merged error: 7.4b

Counts

183 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
1.2b	(- (* b_2 b_2) (* a c))
24.7b	(sqrt (- (* b_2 b_2) (* a c)))
24.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 54

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
3.0ms	(- (* b_2 b_2) (* a c))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series40.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify52.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	138	388
1	451	366
2	1533	364
3	5001	362

prune85.0ms

Filtered

66 candidates to 50 candidates (24.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	66	9	75

Merged error: 7.4b

Counts

75 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
1.6b	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
10.9b	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
24.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite46.0ms

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)
14.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series109.0ms

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

simplify108.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 2 (78.0ms)

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

prune194.0ms

Filtered

212 candidates to 141 candidates (33.5%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	211	1	212
Fresh	1	4	5
Picked	0	1	1
Done	0	3	3
Total	212	9	221

Merged error: 7.4b

Counts

221 → 9

regimes366.0ms

Accuracy

91.8% (2.2b remaining)

Error of 8.2b against oracle of 6.0b and baseline of 32.5b

bsearch93.0ms

Steps

Iters	Range	Point
7	1.5733488064158731e+78	9.799352262304037e+79	4.657075857496205e+78
10	-3.421784863608424e-274	-1.3449762450799657e-285	-4.437211336946152e-284
8	-7.483396380019031e+117	-3.515939334884751e+113	-1.0192218364023762e+116

Iters

Range

Point

1.5733488064158731e+78

9.799352262304037e+79

4.657075857496205e+78

-3.421784863608424e-274

-1.3449762450799657e-285

-4.437211336946152e-284

-7.483396380019031e+117

-3.515939334884751e+113

-1.0192218364023762e+116

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	23
1	37	23

end0.0ms

sample1.2s

Algorithm

intervals

Results

290.0ms	6481×	body	80	valid
206.0ms	825×	body	2560	valid
130.0ms	659×	body	1280	valid
111.0ms	2646×	body	80	nan
59.0ms	360×	body	640	valid
31.0ms	96×	body	5120	valid
19.0ms	161×	body	320	valid
7.0ms	89×	body	160	valid

Details

sample244.0ms

simplify265.0ms

prune5.0ms

localize12.0ms

rewrite31.0ms

series71.0ms

simplify141.0ms

prune136.0ms

localize9.0ms

rewrite36.0ms

series64.0ms

simplify68.0ms

prune124.0ms

localize11.0ms

rewrite15.0ms

series40.0ms

simplify52.0ms

prune85.0ms

localize11.0ms

rewrite46.0ms

series109.0ms

simplify108.0ms

prune194.0ms

regimes366.0ms

bsearch93.0ms

simplify2.0ms

end0.0ms

sample1.2s

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