Details

Time bar (total: 5.6s)

sample37.0ms

Algorithm
intervals
Results
7.0ms35×body2560valid
7.0ms194×body80valid
4.0ms27×body1280valid
3.0ms84×body80nan
2.0ms14×body640valid
1.0ms9×body320valid
1.0ms3×body5120valid
0.0ms3×body160valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0187
1327
2417
3447
4447

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b
(- (* b_2 b_2) (* a c))
0.9b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite56.0ms

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:
32.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms
(- (* b_2 b_2) (* a c))
15.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series249.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
33.0ms
(- (* b_2 b_2) (* a c))
70.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
63.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0368965
11241910
25001901

prune245.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.5b

localize11.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.1b
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
8.2b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite98.0ms

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:
20.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
40.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
23.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
6.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series476.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
151.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
193.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
59.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify108.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
07302960
132002803
250012783

prune506.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.5b

localize11.0ms

Local error

Found 4 expressions with local error:

1.2b
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
1.2b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.1b
(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
22.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite123.0ms

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:
21.0ms
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
17.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
46.0ms
(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series431.0ms

Counts
4 → 12
Calls
4 calls:
165.0ms
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
71.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
136.0ms
(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
58.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify95.0ms

Algorithm
egg-herbie
Counts
452 → 452
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
015717389
150026821

prune1.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.5b

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.7b
(/ a (* a c))
22.5b
(sqrt (- (* b_2 b_2) (* a c)))
22.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×*-un-lft-identity
9×add-exp-log add-cbrt-cube
8×add-cube-cbrt
7×sqrt-prod
6×pow1 add-log-exp
4×sqrt-div
3×flip3-- times-frac flip-- associate-/l*
2×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp difference-of-squares
1×sub-neg frac-2neg diff-log prod-exp clear-num associate-/r* cbrt-unprod div-inv distribute-lft-out--
Counts
4 → 66
Calls
4 calls:
21.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.0ms
(/ a (* a c))
3.0ms
(sqrt (- (* b_2 b_2) (* a c)))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series202.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
6.0ms
(/ a (* a c))
63.0ms
(sqrt (- (* b_2 b_2) (* a c)))
59.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify119.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 3 (113.0ms)

IterNodesCost
0264445
1894411
23925404
35001402

prune234.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 4.5b

regimes247.0ms

Accuracy

89.7% (2.7b remaining)

Error of 8.1b against oracle of 5.4b and baseline of 31.9b

bsearch140.0ms

Steps
ItersRangePoint
6
1.1594993669073426e+93
1.3006782908792091e+94
6.518249790659283e+93
9
1.0330294288086087e-261
2.084324433095697e-255
1.3863010340691693e-261
9
-4.759771033625146e+59
-5.495242732878052e+53
-9.101461187998734e+58

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04123
14123

end0.0ms

sample1.1s

Algorithm
intervals
Results
213.0ms1037×body2560valid
203.0ms5813×body80valid
154.0ms911×body1280valid
97.0ms2949×body80nan
59.0ms452×body640valid
31.0ms125×body5120valid
21.0ms222×body320valid
8.0ms126×body160valid