Details

Time bar (total: 14.4s)

sample133.0ms

Algorithm
intervals
Results
15.0ms41×body2560valid
13.0ms178×body80valid
8.0ms26×body1280valid
4.0ms75×body80nan
4.0ms14×body640valid
1.0ms7×body320valid
0.0ms3×body160valid

simplify59.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01013
11813
23213
34113
44413
done4413

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize16.0ms

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))))
24.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite169.0ms

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:
90.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
16.0ms
(- (* b_2 b_2) (* a c))
33.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series408.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
63.0ms
(- (* b_2 b_2) (* a c))
111.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
108.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts
103 → 103
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01561821
13661727
210051611
327731595
done50011593

prune411.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b_2 b_2) (* a c))
3.2b
(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.9b
(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
24.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite211.0ms

Algorithm
rewrite-expression-head
Rules
66×times-frac
53×add-sqr-sqrt
40×*-un-lft-identity
28×add-cube-cbrt
18×add-exp-log add-cbrt-cube
13×associate-/l*
12×difference-of-squares
10×associate-/r/
9×associate-/r* sqrt-prod
7×cbrt-undiv flip3-- div-exp flip--
6×div-inv distribute-lft-out-- add-log-exp
5×pow1
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/l/
Counts
4 → 124
Calls
4 calls:
13.0ms
(- (* b_2 b_2) (* a c))
98.0ms
(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
72.0ms
(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
18.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series686.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* b_2 b_2) (* a c))
258.0ms
(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
272.0ms
(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
111.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts
136 → 136
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02372999
15862794
219382466
done50012460

prune446.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ c 1) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
0.6b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b
(- (* b_2 b_2) (* a c))
24.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite164.0ms

Algorithm
rewrite-expression-head
Rules
141×times-frac
129×add-sqr-sqrt
98×*-un-lft-identity
68×add-cube-cbrt
30×difference-of-squares
18×sqrt-prod
15×distribute-lft-out--
13×associate-/l*
11×add-exp-log
9×add-cbrt-cube
8×div-inv add-log-exp
6×associate-/r*
5×pow1 div-exp
4×flip3-- flip--
3×cbrt-undiv
2×sub-neg sqrt-div diff-log associate-/r/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 1-exp clear-num associate-/l/
Counts
4 → 157
Calls
4 calls:
69.0ms
(/ (/ c 1) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
62.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms
(- (* b_2 b_2) (* a c))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series504.0ms

Counts
4 → 12
Calls
4 calls:
254.0ms
(/ (/ c 1) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
115.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
55.0ms
(- (* b_2 b_2) (* a c))
79.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.3s

Counts
169 → 169
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02623935
15913277
211393153
325163149
done50003137

prune372.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b_2 b_2) (* a c))
6.2b
(- (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))) b_2)
24.6b
(sqrt (- (* b_2 b_2) (* a c)))
24.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
1×difference-of-squares
Counts
4 → 55
Calls
4 calls:
15.0ms
(- (* b_2 b_2) (* a c))
100.0ms
(- (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))) b_2)
17.0ms
(sqrt (- (* b_2 b_2) (* a c)))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series323.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* b_2 b_2) (* a c))
95.0ms
(- (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))) b_2)
89.0ms
(sqrt (- (* b_2 b_2) (* a c)))
91.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.7s

Counts
67 → 67
Iterations

Useful iterations: done (1.7s)

IterNodesCost
0901109
1212805
2604747
31714742
done5000736

prune258.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.3b

regimes237.0ms

Accuracy

95.9% (1.0b remaining)

Error of 6.5b against oracle of 5.5b and baseline of 29.7b

bsearch214.0ms

Steps
ItersRangePoint
9
5.30600492772346e+88
5.894388948599132e+93
3.3616367997262596e+93
10
1.8932238735467414e-306
6.8449465898973125e-295
3.657998399682532e-302
8
-5.7211821970331905e+156
-1.4082798590396656e+153
-1.0772396285489054e+154

simplify9.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
03051
13549
done3549

end0.0ms

sample1.6s

Algorithm
intervals
Results
283.0ms1061×body2560valid
277.0ms5876×body80valid
191.0ms854×body1280valid
132.0ms2976×body80nan
87.0ms471×body640valid
37.0ms113×body5120valid
31.0ms242×body320valid
11.0ms125×body160valid