Details

Time bar (total: 5.9s)

sample364.0ms

Algorithm
intervals
Results
8.0ms187×body80valid
8.0ms40×body2560valid
5.0ms31×body1280valid
3.0ms96×body80nan
2.0ms8×body5120valid
1.0ms9×body640valid
1.0ms6×body320valid
0.0ms3×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0187
1327
2417
3447
4447

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b
(- (* b_2 b_2) (* a c))
0.9b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
28.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite109.0ms

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:
64.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms
(- (* b_2 b_2) (* a c))
22.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series243.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
31.0ms
(- (* b_2 b_2) (* a c))
66.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
68.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0368965
11241910
25001901

prune245.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.4b

localize11.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.6b
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.6b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
28.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite205.0ms

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:
40.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
90.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
55.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series434.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
139.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
172.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
57.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify104.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
07302960
132002803
250012783

prune477.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.3b

localize10.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.1b
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
3.6b
(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
28.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite202.0ms

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:
39.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
42.0ms
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
74.0ms
(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series398.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
154.0ms
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
127.0ms
(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
54.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify92.0ms

Algorithm
egg-herbie
Counts
452 → 452
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
015717388
150016820

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
0.8b
(- (* b_2 b_2) (* a c))
1.4b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
28.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
8×add-exp-log sqrt-prod add-log-exp
6×pow1 associate-/r* add-cbrt-cube
5×distribute-lft-out--
4×flip3-- flip--
3×associate-/l*
2×sub-neg sqrt-div diff-log div-exp associate-/r/
1×cbrt-undiv rem-sqrt-square rec-exp pow-flip frac-2neg sqrt-pow1 pow1/2 1-exp clear-num div-inv inv-pow
Counts
4 → 87
Calls
4 calls:
46.0ms
(/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
8.0ms
(- (* b_2 b_2) (* a c))
42.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series224.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
34.0ms
(- (* b_2 b_2) (* a c))
61.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
57.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify40.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0334836
11204767
25001738

prune175.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 8.3b

regimes214.0ms

Accuracy

94.9% (1.2b remaining)

Error of 6.8b against oracle of 5.6b and baseline of 29.9b

bsearch76.0ms

Steps
ItersRangePoint
6
4.231934083523606e+52
2.717919616353272e+53
2.043334298601045e+53
3
2.62163126713661e-290
3.6876397702511455e-290
2.9547589243599016e-290
6
-1.0492990687338703e+133
-1.6798826367412696e+132
-4.4804386899137485e+132

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04123
14123

end0.0ms

sample1.1s

Algorithm
intervals
Results
200.0ms1050×body2560valid
197.0ms5881×body80valid
141.0ms923×body1280valid
83.0ms2795×body80nan
51.0ms425×body640valid
26.0ms111×body5120valid
21.0ms232×body320valid
6.0ms102×body160valid