Details

sample45.0ms

Algorithm

intervals

Results

9.0ms	42×	body	2560	valid
8.0ms	191×	body	80	valid
4.0ms	20×	body	1280	valid
3.0ms	96×	body	80	nan
2.0ms	17×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	3×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	9
1	65	9
2	121	9
3	151	9
4	160	9
5	164	9
6	164	9

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b	(- (* b b) (* 4.0 (* a c)))
0.8b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt` `prod-diff`
60×	`*-un-lft-identity`
48×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`neg-mul-1` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 157

Calls

4 calls:

20.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
4.0ms	(- (* b b) (* 4.0 (* a c)))
11.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series302.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
51.0ms	(- (* b b) (* 4.0 (* a c)))
82.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
69.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify76.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	590	3305
1	2101	2212
2	5002	2128

prune374.0ms

Filtered

169 candidates to 89 candidates (52.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.6b	(- (* b b) (* 4.0 (* a c)))
0.8b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 165

Calls

4 calls:

15.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
4.0ms	(- (* b b) (* 4.0 (* a c)))
11.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series291.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
43.0ms	(- (* b b) (* 4.0 (* a c)))
77.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify82.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	656	3422
1	2594	2238
2	5001	2193

prune340.0ms

Filtered

177 candidates to 90 candidates (50.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.2b

localize7.0ms

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

prune16.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.2b

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b	(- (/ c b) (/ b a))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

249×	`times-frac`
202×	`add-sqr-sqrt`
196×	`*-un-lft-identity`
190×	`add-cube-cbrt`
169×	`prod-diff`
27×	`div-inv`
13×	`fma-neg`
4×	`difference-of-squares`
3×	`add-log-exp`
2×	`distribute-lft-out--`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `frac-sub` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

1 → 203

Calls

1 calls:

18.0ms

(- (/ c b) (/ b a))

series28.0ms

Counts

1 → 3

Calls

1 calls:

28.0ms

(- (/ c b) (/ b a))

simplify69.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	687	4502
1	1800	3181
2	5002	2604

prune165.0ms

Filtered

206 candidates to 49 candidates (23.8%)

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 6.2b

regimes290.0ms

Accuracy

81.3% (5.3b remaining)

Error of 11.2b against oracle of 5.9b and baseline of 34.3b

bsearch99.0ms

Steps

Iters	Range		Point
7	9.786063674806627e+75	3.1345211132670796e+77	2.9083064714494895e+77
9	-6.944152938449299e-155	-2.632619076242731e-163	-6.842303289862193e-155

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	16
1	37	16

end0.0ms

sample1.2s

Algorithm

intervals

Results

257.0ms	1079×	body	2560	valid
232.0ms	5913×	body	80	valid
176.0ms	912×	body	1280	valid
111.0ms	2982×	body	80	nan
58.0ms	399×	body	640	valid
34.0ms	114×	body	5120	valid
24.0ms	212×	body	320	valid
7.0ms	97×	body	160	valid