Details

Time bar (total: 18.3s)

sample128.0ms

Algorithm
intervals
Results
22.0ms42×body2560valid
16.0ms173×body80valid
10.0ms25×body1280valid
5.0ms18×body640valid
5.0ms69×body80nan
2.0ms11×body320valid
1.0ms2×body5120valid
0.0ms2×body160valid

simplify87.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
01013
11813
23213
34113
44413
done4413

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b
(- (* b_2 b_2) (* a c))
24.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite160.0ms

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:
92.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
42.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms
(- (* b_2 b_2) (* a c))
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series386.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
106.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
45.0ms
(- (* b_2 b_2) (* a c))
98.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.2s

Counts
103 → 103
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01561821
13661727
210051611
327701595
done50011593

prune422.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.2b

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b_2 b_2) (* a c))
2.4b
(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.8b
(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
24.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite225.0ms

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:
9.0ms
(- (* b_2 b_2) (* a c))
108.0ms
(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
85.0ms
(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
18.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series626.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(- (* b_2 b_2) (* a c))
249.0ms
(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
250.0ms
(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
68.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.7s

Counts
136 → 136
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02372999
15862794
219382466
done50012460

prune542.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ c 1) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
0.4b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.2b
(- (* b_2 b_2) (* a c))
24.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite192.0ms

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:
83.0ms
(/ (/ c 1) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
69.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms
(- (* b_2 b_2) (* a c))
17.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series548.0ms

Counts
4 → 12
Calls
4 calls:
295.0ms
(/ (/ c 1) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
102.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
55.0ms
(- (* b_2 b_2) (* a c))
96.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.7s

Counts
169 → 169
Iterations

Useful iterations: done (2.7s)

IterNodesCost
02623935
15913277
211393153
325163149
done50003137

prune394.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.8b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b
(- (* b_2 b_2) (* a c))
24.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite183.0ms

Algorithm
rewrite-expression-head
Rules
165×times-frac
130×add-sqr-sqrt
129×*-un-lft-identity
77×add-cube-cbrt
27×associate-/r*
26×distribute-lft-out-- difference-of-squares
16×sqrt-prod
15×add-exp-log
13×distribute-rgt-neg-in
10×add-log-exp
9×associate-/r/ add-cbrt-cube
7×flip3-- div-exp flip--
6×pow1
5×div-inv
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 → 177
Calls
4 calls:
98.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
48.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms
(- (* b_2 b_2) (* a c))
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series450.0ms

Counts
4 → 12
Calls
4 calls:
184.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
128.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
70.0ms
(- (* b_2 b_2) (* a c))
69.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify3.1s

Counts
189 → 189
Iterations

Useful iterations: 3 (1.6s)

IterNodesCost
02664484
15773936
213803617
338543507
done50003507

prune382.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 4.2b

regimes240.0ms

Accuracy

94.8% (1.3b remaining)

Error of 6.6b against oracle of 5.4b and baseline of 29.6b

bsearch230.0ms

Steps
ItersRangePoint
5
1.7897742140858872e+53
5.1194650287633095e+53
5.031608061939103e+53
9
9.448397398655464e-278
1.4829972419072586e-270
8.216265756828381e-276
9
-1.4642911230069481e+159
-8.435593739772907e+149
-3.5132588248780117e+152

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03357
13955
done3955

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.3s5843×body80valid
623.0ms1104×body2560valid
361.0ms2938×body80nan
295.0ms860×body1280valid
183.0ms492×body640valid
105.0ms226×body320valid
88.0ms107×body5120valid
13.0ms106×body160valid