Details

Time bar (total: 17.3s)

sample56.0ms

Algorithm
intervals
Results
10.0ms204×body80valid
9.0ms29×body2560valid
7.0ms31×body1280valid
5.0ms106×body80nan
2.0ms9×body640valid
1.0ms9×body320valid
1.0ms2×body5120valid
0.0ms1×body160valid

simplify102.0ms

Counts
1 → 1
Iterations
IterNodes
done94
794
693
591
483
368
239
121
012

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize40.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
0.8b
(- (* b b) (* (* 3.0 a) c))
0.8b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
24.3b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×add-cube-cbrt
6×times-frac sqrt-prod associate-/l* difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp cbrt-unprod div-inv
Counts
4 → 72
Calls
4 calls:
90.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
6.0ms
(- (* b b) (* (* 3.0 a) c))
39.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
7.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series458.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
71.0ms
(- (* b b) (* (* 3.0 a) c))
133.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
119.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.6s

Counts
84 → 84
Iterations
IterNodes
done5001
21254
1392
0154

prune551.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0)
0.8b
(- (* b b) (* (* 3.0 a) c))
0.8b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
24.3b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite167.0ms

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×sqrt-prod add-log-exp
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×flip3-- flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 84
Calls
4 calls:
75.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0)
11.0ms
(- (* b b) (* (* 3.0 a) c))
65.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
14.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series404.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0)
68.0ms
(- (* b b) (* (* 3.0 a) c))
110.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
105.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.9s

Counts
96 → 96
Iterations
IterNodes
done5000
34335
21052
1369
0154

prune539.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 8.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (* 3.0 a) (- (sqrt (- (* b b) (* (* 3.0 a) c))) b))
0.8b
(- (* b b) (* (* 3.0 a) c))
0.8b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
24.3b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×add-cube-cbrt
6×associate-/r* times-frac sqrt-prod difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/r/
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 prod-exp cbrt-unprod div-inv associate-/l*
Counts
4 → 71
Calls
4 calls:
47.0ms
(/ (* 3.0 a) (- (sqrt (- (* b b) (* (* 3.0 a) c))) b))
11.0ms
(- (* b b) (* (* 3.0 a) c))
44.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
7.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series531.0ms

Counts
4 → 12
Calls
4 calls:
270.0ms
(/ (* 3.0 a) (- (sqrt (- (* b b) (* (* 3.0 a) c))) b))
67.0ms
(- (* b b) (* (* 3.0 a) c))
106.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
88.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.5s

Counts
83 → 83
Iterations
IterNodes
done5004
21245
1376
0147

prune595.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 7.9b

localize49.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (sqrt 3.0))
0.8b
(- (* b b) (* (* 3.0 a) c))
0.8b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
24.3b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
42×*-un-lft-identity
36×times-frac
32×sqrt-prod
26×add-cube-cbrt
16×difference-of-squares
8×distribute-lft-out-- add-log-exp
6×associate-/r* add-cbrt-cube add-exp-log associate-/l*
5×pow1
4×flip3-- flip--
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 105
Calls
4 calls:
83.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (sqrt 3.0))
9.0ms
(- (* b b) (* (* 3.0 a) c))
44.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
7.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series517.0ms

Counts
4 → 12
Calls
4 calls:
219.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (sqrt 3.0))
75.0ms
(- (* b b) (* (* 3.0 a) c))
128.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
95.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.4s

Counts
117 → 117
Iterations
IterNodes
done5000
21250
1437
0180

prune788.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 7.9b

regimes973.0ms

Accuracy

83.9% (4.6b remaining)

Error of 10.3b against oracle of 5.7b and baseline of 34.5b

bsearch128.0ms

Steps
ItersRangePoint
8
1.5119020269574885e-23
1.8921341643334238e-20
9.136492990928292e-23
6
-1.7989235910837076e+89
-1.4585470499056154e+88
-1.7633154797394035e+89

simplify9.0ms

Iterations
IterNodes
done32
132
027

end0.0ms

sample3.5s

Algorithm
intervals
Results
936.0ms5864×body80valid
924.0ms902×body1280valid
518.0ms1059×body2560valid
226.0ms2873×body80nan
152.0ms433×body640valid
59.0ms123×body5120valid
43.0ms224×body320valid
16.0ms111×body160valid