Details

sample296.0ms

Algorithm

intervals

Results

9.0ms	38×	body	2560	valid
8.0ms	188×	body	80	valid
6.0ms	91×	body	80	nan
6.0ms	28×	body	1280	valid
1.0ms	9×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	1×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	7
1	33	7
2	46	7
3	49	7
4	49	7

prune4.0ms

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: 35.1b

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)
0.5b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
24.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
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 → 171

Calls

4 calls:

28.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
10.0ms	(- (- 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)))

series259.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
69.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
33.0ms	(- (* b_2 b_2) (* a c))
75.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify71.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	549	3055
1	1826	2150
2	5001	2063

prune319.0ms

Filtered

183 candidates to 97 candidates (53.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	175	8	183
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	176	8	184

Merged error: 6.8b

Counts

184 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.5b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
24.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
61×	`prod-diff`
54×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`add-exp-log` `associate-r`
11×	`times-frac` `fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `neg-mul-1` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 169

Calls

4 calls:

17.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
10.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
68.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
36.0ms	(- (* b_2 b_2) (* a c))
56.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify76.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	609	2985
1	2334	1993
2	5001	1940

prune269.0ms

Filtered

181 candidates to 96 candidates (53.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	179	2	181
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	180	9	189

Merged error: 6.8b

Counts

189 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.5b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
24.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-sqr-sqrt`
170×	`*-un-lft-identity`
165×	`times-frac`
118×	`add-cube-cbrt`
61×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
15×	`add-exp-log`
11×	`fma-neg`
10×	`add-log-exp`
9×	`associate-/r/` `add-cbrt-cube`
7×	`neg-mul-1` `flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `diff-log` `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` `inv-pow`

Counts

4 → 257

Calls

4 calls:

16.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
10.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series257.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
67.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
32.0ms	(- (* b_2 b_2) (* a c))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify99.0ms

Algorithm

egg-herbie

Counts

269 → 269

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	770	4550
1	3215	3424
2	5002	3236

prune309.0ms

Filtered

269 candidates to 112 candidates (41.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	268	1	269
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	269	9	278

Merged error: 6.7b

Counts

278 → 9

localize4.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify2.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune0.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	6	6
Picked	1	1
Done	2	2
Total	9	9

Merged error: 6.7b

Counts

9 → 9

regimes202.0ms

Accuracy

81.3% (5.3b remaining)

Error of 10.7b against oracle of 5.5b and baseline of 33.7b

bsearch76.0ms

Steps

Iters	Range		Point
7	0.008549975533169097	1.4731263457460937	1.4443031837246074
6	-3.633044971050309e-17	-8.961399793617711e-18	-1.0820642039797266e-17

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	15
1	34	15

end0.0ms

sample1.2s

Algorithm

intervals

Results

278.0ms	1111×	body	2560	valid
258.0ms	5875×	body	80	valid
178.0ms	861×	body	1280	valid
123.0ms	2877×	body	80	nan
70.0ms	439×	body	640	valid
38.0ms	114×	body	5120	valid
25.0ms	210×	body	320	valid
9.0ms	115×	body	160	valid