Details

Time bar (total: 18.5s)

sample160.0ms

Algorithm
intervals
Results
16.0ms30×body2560valid
16.0ms191×body80valid
12.0ms28×body1280valid
9.0ms22×body640valid
6.0ms80×body80nan
2.0ms4×body5120valid
1.0ms5×body320valid
0.0ms2×body160valid

simplify117.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
01013
11813
23213
34113
44413
done4413

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.5b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.6b
(- (* b_2 b_2) (* a c))
22.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite223.0ms

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:
113.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
64.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
18.0ms
(- (* b_2 b_2) (* a c))
21.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series382.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
107.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
56.0ms
(- (* b_2 b_2) (* a c))
107.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.3s

Counts
103 → 103
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01561821
13661727
210051611
327701595
done50011593

prune428.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b_2 b_2) (* a c))
2.5b
(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
8.0b
(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite253.0ms

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:
17.0ms
(- (* b_2 b_2) (* a c))
128.0ms
(/ (/ (* 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))
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series717.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* b_2 b_2) (* a c))
301.0ms
(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
279.0ms
(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
89.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts
136 → 136
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02372999
15862794
219382466
done50012460

prune529.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.0b

localize12.0ms

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)
0.6b
(- (* b_2 b_2) (* a c))
22.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite191.0ms

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:
86.0ms
(/ (/ c 1) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
71.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms
(- (* b_2 b_2) (* a c))
15.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series537.0ms

Counts
4 → 12
Calls
4 calls:
269.0ms
(/ (/ c 1) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
123.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
45.0ms
(- (* b_2 b_2) (* a c))
99.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.5s

Counts
169 → 169
Iterations

Useful iterations: done (2.5s)

IterNodesCost
02623935
15913277
211393153
325163149
done50003137

prune370.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ c 1) (- (sqrt (- (pow b_2 2) (* a c))) b_2))
0.6b
(- (sqrt (- (pow b_2 2) (* a c))) b_2)
0.6b
(- (pow b_2 2) (* a c))
22.1b
(sqrt (- (pow b_2 2) (* a c)))

rewrite277.0ms

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:
95.0ms
(/ (/ c 1) (- (sqrt (- (pow b_2 2) (* a c))) b_2))
130.0ms
(- (sqrt (- (pow b_2 2) (* a c))) b_2)
21.0ms
(- (pow b_2 2) (* a c))
14.0ms
(sqrt (- (pow b_2 2) (* a c)))

series542.0ms

Counts
4 → 12
Calls
4 calls:
274.0ms
(/ (/ c 1) (- (sqrt (- (pow b_2 2) (* a c))) b_2))
120.0ms
(- (sqrt (- (pow b_2 2) (* a c))) b_2)
57.0ms
(- (pow b_2 2) (* a c))
91.0ms
(sqrt (- (pow b_2 2) (* a c)))

simplify2.3s

Counts
169 → 169
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02613935
15873269
211163157
324653149
done50003137

prune380.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.0b

regimes461.0ms

Accuracy

95.9% (1.0b remaining)

Error of 6.6b against oracle of 5.7b and baseline of 29.7b

bsearch143.0ms

Steps
ItersRangePoint
0
2.0836136179885362e+135
2.1675125417143413e+135
2.1255630798514387e+135
7
-3.810451831161374e-279
-3.825977761355635e-281
-3.897979690537011e-281
8
-3.0008378519073826e+120
-1.7813274366303991e+117
-5.602441184943773e+118

simplify10.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
03555
14153
done4153

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.1s2885×body80nan
679.0ms5781×body80valid
632.0ms1103×body2560valid
411.0ms917×body1280valid
117.0ms431×body640valid
65.0ms118×body5120valid
49.0ms231×body320valid
14.0ms108×body160valid