Details

Time bar (total: 17.6s)

sample64.0ms

Algorithm
intervals
Results
15.0ms37×body2560valid
13.0ms191×body80valid
10.0ms30×body1280valid
6.0ms103×body80nan
4.0ms16×body640valid
1.0ms6×body320valid
1.0ms6×body160valid

simplify90.0ms

Counts
1 → 1
Iterations
IterNodes
done93
793
692
590
482
366
240
121
012

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
0.4b
(- (* b b) (* (* 3 a) c))
1.6b
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
21.3b
(sqrt (- (* b b) (* (* 3 a) c)))

rewrite212.0ms

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-- insert-posit16 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 → 76
Calls
4 calls:
125.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
17.0ms
(- (* b b) (* (* 3 a) c))
58.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
9.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

series400.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
52.0ms
(- (* b b) (* (* 3 a) c))
121.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
90.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.1s

Counts
88 → 88
Iterations
IterNodes
done5013
21265
1396
0157

prune440.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.8b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (* 3 a))
0.4b
(- (* b b) (* (* 3 a) c))
1.6b
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
21.3b
(sqrt (- (* b b) (* (* 3 a) c)))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
15×add-exp-log
12×add-sqr-sqrt
9×*-un-lft-identity add-cbrt-cube
8×pow1 add-log-exp
7×add-cube-cbrt
4×div-exp sqrt-prod insert-posit16
3×times-frac flip3-- prod-exp flip-- associate-/l*
2×cbrt-undiv rec-exp sub-neg sqrt-div diff-log 1-exp pow-flip difference-of-squares
1×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 pow-prod-down cbrt-unprod div-inv distribute-lft-out-- inv-pow
Counts
4 → 74
Calls
4 calls:
13.0ms
(/ 1 (* 3 a))
8.0ms
(- (* b b) (* (* 3 a) c))
61.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
9.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

series272.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(/ 1 (* 3 a))
56.0ms
(- (* b b) (* (* 3 a) c))
100.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
91.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

simplify2.4s

Counts
86 → 86
Iterations
IterNodes
done5000
33410
2920
1326
0140

prune409.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.8b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3 a) c)
0.4b
(- (* b b) (* (* 3 a) c))
1.6b
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
21.3b
(sqrt (- (* b b) (* (* 3 a) c)))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1
9×add-cbrt-cube add-exp-log
8×*-un-lft-identity add-log-exp
6×add-cube-cbrt
4×sqrt-prod insert-posit16
3×flip3-- associate-*r* pow-prod-down prod-exp cbrt-unprod flip--
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative distribute-lft-out--
Counts
4 → 64
Calls
4 calls:
35.0ms
(* (* 3 a) c)
15.0ms
(- (* b b) (* (* 3 a) c))
61.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
15.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

series290.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* (* 3 a) c)
68.0ms
(- (* b b) (* (* 3 a) c))
89.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
100.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

simplify2.8s

Counts
76 → 76
Iterations
IterNodes
done5001
33518
2910
1297
0123

prune352.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.8b

localize58.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt c)
0.6b
(cbrt c)
1.6b
(- (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
21.3b
(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
9×*-un-lft-identity
7×add-cube-cbrt
6×cbrt-prod add-log-exp
5×pow1
4×add-cbrt-cube add-exp-log sqrt-prod insert-posit16
2×flip3-- pow1/3 sqrt-div flip-- difference-of-squares
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 56
Calls
4 calls:
1.0ms
(cbrt c)
1.0ms
(cbrt c)
54.0ms
(- (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
25.0ms
(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))

series826.0ms

Counts
4 → 12
Calls
4 calls:
261.0ms
(cbrt c)
280.0ms
(cbrt c)
130.0ms
(- (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
154.0ms
(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))

simplify3.2s

Counts
68 → 68
Iterations
IterNodes
done5001
33212
2736
1238
0106

prune378.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.8b

regimes820.0ms

Accuracy

80.6% (5.3b remaining)

Error of 10.9b against oracle of 5.6b and baseline of 33.1b

bsearch238.0ms

Steps
ItersRangePoint
7
3.2723221096518622e-21
8.349665184990521e-19
5.3117642643391765e-20
7
5.034617224646791e-70
8.084342686052032e-69
2.9864531425864206e-69
1
1.8923753200636452e-106
2.0232344302868159e-106
1.990519652731023e-106
6
-1.816545290760657e+37
-4.00557630224217e+36
-1.6519381339788066e+37

simplify16.0ms

Iterations
IterNodes
done52
152
040

end0.0ms

sample2.9s

Algorithm
intervals
Results
661.0ms5915×body80valid
632.0ms1068×body2560valid
412.0ms240×body320valid
351.0ms837×body1280valid
214.0ms3076×body80nan
164.0ms463×body640valid
69.0ms123×body5120valid
59.0ms124×body160valid