Details

Time bar (total: 16.3s)

sample89.0ms

Algorithm
intervals
Results
17.0ms204×body80valid
15.0ms29×body2560valid
13.0ms31×body1280valid
9.0ms106×body80nan
3.0ms9×body640valid
2.0ms9×body320valid
1.0ms2×body5120valid
0.0ms1×body160valid

simplify130.0ms

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

prune19.0ms

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)))

rewrite165.0ms

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:
85.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
7.0ms
(- (* b b) (* (* 3.0 a) c))
59.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
13.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series447.0ms

Counts
4 → 12
Calls
4 calls:
168.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
63.0ms
(- (* b b) (* (* 3.0 a) c))
115.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
101.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.4s

Counts
84 → 84
Iterations
IterNodes
done5001
21254
1392
0154

prune671.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.0b

localize38.0ms

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)))

rewrite191.0ms

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:
125.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0)
14.0ms
(- (* b b) (* (* 3.0 a) c))
40.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
8.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series410.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0)
61.0ms
(- (* b b) (* (* 3.0 a) c))
90.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
115.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.8s

Counts
96 → 96
Iterations
IterNodes
done5000
34335
21052
1369
0154

prune694.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 8.0b

localize34.0ms

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)))

rewrite118.0ms

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))
12.0ms
(- (* b b) (* (* 3.0 a) c))
44.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
13.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series495.0ms

Counts
4 → 12
Calls
4 calls:
222.0ms
(/ (* 3.0 a) (- (sqrt (- (* b b) (* (* 3.0 a) c))) b))
52.0ms
(- (* b b) (* (* 3.0 a) c))
134.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
87.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.3s

Counts
83 → 83
Iterations
IterNodes
done5004
21245
1376
0147

prune517.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 7.9b

localize37.0ms

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)))

rewrite188.0ms

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:
110.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (sqrt 3.0))
17.0ms
(- (* b b) (* (* 3.0 a) c))
48.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
7.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series518.0ms

Counts
4 → 12
Calls
4 calls:
193.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (sqrt 3.0))
87.0ms
(- (* b b) (* (* 3.0 a) c))
129.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
108.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.3s

Counts
117 → 117
Iterations
IterNodes
done5000
21250
1437
0180

prune630.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 7.9b

regimes1.0s

Accuracy

84% (4.6b remaining)

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

bsearch139.0ms

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

simplify5.0ms

Iterations
IterNodes
done32
132
027

end0.0ms

sample3.0s

Algorithm
intervals
Results
936.0ms5864×body80valid
473.0ms1059×body2560valid
383.0ms224×body320valid
374.0ms902×body1280valid
204.0ms2873×body80nan
104.0ms433×body640valid
89.0ms123×body5120valid
13.0ms111×body160valid