Details

sample44.0ms

Algorithm

intervals

Results

9.0ms	33×	body	2560	valid
8.0ms	172×	body	80	valid
7.0ms	31×	body	1280	valid
3.0ms	73×	body	80	nan
2.0ms	14×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	9×	body	320	valid
1.0ms	11×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	32	7
2	41	7
3	44	7
4	44	7

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 36.1b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.4b	(- (* b_2 b_2) (* a c))
2.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 91

Calls

4 calls:

10.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series240.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
34.0ms	(- (* b_2 b_2) (* a c))
65.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify41.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	368	965
1	1241	910
2	5001	901

prune213.0ms

Filtered

103 candidates to 72 candidates (69.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	93	10	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	10	104

Merged error: 5.5b

Counts

104 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.5b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.2b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
150×	`add-sqr-sqrt`
115×	`*-un-lft-identity`
81×	`add-cube-cbrt`
34×	`difference-of-squares`
27×	`associate-/l*`
20×	`sqrt-prod`
17×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`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 → 187

Calls

4 calls:

7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series470.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
153.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
187.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify111.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	730	2960
1	3200	2803
2	5001	2783

prune445.0ms

Filtered

199 candidates to 148 candidates (74.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	194	5	199
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	201	8	209

Merged error: 5.5b

Counts

209 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b_2 b_2) (* a c))
1.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0b	(/ a (* a c))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
8×	`add-log-exp`
7×	`add-cube-cbrt`
5×	`pow1`
4×	`sqrt-prod`
3×	`flip3--` `times-frac` `flip--` `associate-/l*`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `difference-of-squares`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv` `distribute-lft-out--`

Counts

4 → 63

Calls

4 calls:

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

series171.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(/ a (* a c))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify129.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (122.0ms)

Iter	Nodes	Cost
0	277	415
1	944	374
2	4178	369
3	5002	368

prune154.0ms

Filtered

75 candidates to 54 candidates (72.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	75	8	83

Merged error: 5.5b

Counts

83 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.3b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
4.5b	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

831×	`times-frac`
549×	`add-sqr-sqrt`
450×	`*-un-lft-identity`
352×	`add-cube-cbrt`
98×	`difference-of-squares`
74×	`associate-/l*`
52×	`sqrt-prod`
49×	`distribute-lft-out--`
25×	`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 → 440

Calls

4 calls:

7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
11.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
23.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
167.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
137.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify93.0ms

Algorithm

egg-herbie

Counts

452 → 452

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1571	7388
1	5001	6820

prune887.0ms

Filtered

452 candidates to 301 candidates (66.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	451	1	452
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	452	8	460

Merged error: 5.5b

Counts

460 → 8

regimes186.0ms

Accuracy

88.7% (3.0b remaining)

Error of 8.5b against oracle of 5.5b and baseline of 32.3b

bsearch130.0ms

Steps

Iters	Range	Point
7	6.011887282010727e+43	5.675568733030414e+45	5.6015260252764486e+45
8	-2.5434321915683498e-300	-1.516458467021275e-303	-1.5468287913800058e-303
6	-1.178837026734108e+72	-2.0363184654676703e+71	-2.143742921108664e+71

Iters

Range

Point

6.011887282010727e+43

5.675568733030414e+45

5.6015260252764486e+45

-2.5434321915683498e-300

-1.516458467021275e-303

-1.5468287913800058e-303

-1.178837026734108e+72

-2.0363184654676703e+71

-2.143742921108664e+71

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	23
1	41	23

end0.0ms

sample1.3s

Algorithm

intervals

Results

287.0ms	1066×	body	2560	valid
271.0ms	5798×	body	80	valid
201.0ms	924×	body	1280	valid
131.0ms	2899×	body	80	nan
79.0ms	465×	body	640	valid
31.0ms	92×	body	5120	valid
30.0ms	236×	body	320	valid
11.0ms	120×	body	160	valid

Details

sample44.0ms

simplify8.0ms

prune2.0ms

localize12.0ms

rewrite28.0ms

series240.0ms

simplify41.0ms

prune213.0ms

localize13.0ms

rewrite46.0ms

series470.0ms

simplify111.0ms

prune445.0ms

localize11.0ms

rewrite20.0ms

series171.0ms

simplify129.0ms

prune154.0ms

localize13.0ms

rewrite84.0ms

series438.0ms

simplify93.0ms

prune887.0ms

regimes186.0ms

bsearch130.0ms

simplify2.0ms

end0.0ms

sample1.3s

Profiling