Details

Time bar (total: 17.3s)

sample49.0ms

Algorithm
intervals
Results
10.0ms40×body2560valid
8.0ms181×body80valid
5.0ms27×body1280valid
4.0ms92×body80nan
2.0ms7×body5120valid
2.0ms13×body640valid
1.0ms5×body320valid
0.0ms3×body160valid

simplify22.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01013
11813
23213
34113
44413
done4413

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b
(- (* b_2 b_2) (* a c))
1.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite149.0ms

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)
9.0ms
(- (* b_2 b_2) (* a c))
36.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series417.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
65.0ms
(- (* b_2 b_2) (* a c))
132.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
90.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.9s

Counts
103 → 103
Iterations

Useful iterations: done (2.9s)

IterNodesCost
01561821
13661727
210051611
327731595
done50011593

prune391.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.3b

localize27.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.9b
(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
8.4b
(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite306.0ms

Algorithm
rewrite-expression-head
Rules
66×times-frac
57×add-sqr-sqrt
42×*-un-lft-identity
28×add-cube-cbrt
18×add-exp-log add-cbrt-cube
14×difference-of-squares
13×associate-/l*
10×sqrt-prod associate-/r/
9×associate-/r*
7×cbrt-undiv flip3-- div-exp flip-- distribute-lft-out--
6×div-inv 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 → 127
Calls
4 calls:
76.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
129.0ms
(/ (/ (* 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))
20.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series811.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
301.0ms
(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
281.0ms
(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
95.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.8s

Counts
139 → 139
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02393118
15932899
219412569
done50002563

prune449.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ c 1) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
0.2b
(- (* b_2 b_2) (* a c))
1.1b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite155.0ms

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:
62.0ms
(/ (/ c 1) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
15.0ms
(- (* b_2 b_2) (* a c))
60.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series568.0ms

Counts
4 → 12
Calls
4 calls:
283.0ms
(/ (/ c 1) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
47.0ms
(- (* b_2 b_2) (* a c))
121.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
117.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts
169 → 169
Iterations

Useful iterations: done (2.4s)

IterNodesCost
02623935
15913277
211393153
325143149
done50013137

prune343.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(* c (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.2b
(- (* b_2 b_2) (* a c))
1.1b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite289.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
25×*-un-lft-identity
24×associate-*r*
20×times-frac
16×add-cube-cbrt
13×add-exp-log
9×add-cbrt-cube
8×add-log-exp difference-of-squares
7×pow1 sqrt-prod
4×flip3-- prod-exp flip-- distribute-lft-out--
3×associate-*l* unswap-sqr
2×sub-neg sqrt-div diff-log div-exp associate-/r/ cbrt-unprod
1×cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-*r/ pow-prod-down un-div-inv *-commutative div-inv
Counts
4 → 89
Calls
4 calls:
184.0ms
(* c (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
9.0ms
(- (* b_2 b_2) (* a c))
70.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
19.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series570.0ms

Counts
4 → 12
Calls
4 calls:
275.0ms
(* c (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
67.0ms
(- (* b_2 b_2) (* a c))
111.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
116.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts
101 → 101
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01701564
13981354
29091212
320661208
done50001196

prune284.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.3b

regimes159.0ms

Accuracy

95.8% (1.0b remaining)

Error of 6.3b against oracle of 5.2b and baseline of 29.5b

bsearch187.0ms

Steps
ItersRangePoint
10
4.61796087672408e+142
1.3206820209921783e+153
1.1043857160155008e+144
4
1.096458200021764e-161
2.1348066422084948e-161
1.123334719424155e-161
9
-6.354265220965125e+156
-1.769171722317776e+149
-2.4466612317601678e+151

simplify4.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03357
13955
done3955

end0.0ms

sample2.9s

Algorithm
intervals
Results
880.0ms5724×body80valid
652.0ms1098×body2560valid
287.0ms959×body1280valid
258.0ms2913×body80nan
144.0ms456×body640valid
92.0ms119×body5120valid
42.0ms242×body320valid
13.0ms116×body160valid