Details

Time bar (total: 35.9s)

sample116.0ms

Algorithm
intervals
Results
19.0ms35×body2560valid
17.0ms188×body80valid
12.0ms28×body1280valid
9.0ms5×body5120valid
7.0ms85×body80nan
5.0ms14×body640valid
3.0ms10×body320valid
1.0ms4×body160valid

simplify282.0ms

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

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
0.8b
(- (* b b) (* (* 3.0 a) c))
1.6b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
21.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite588.0ms

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:
160.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
10.0ms
(- (* b b) (* (* 3.0 a) c))
399.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
13.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series632.0ms

Counts
4 → 12
Calls
4 calls:
208.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
110.0ms
(- (* b b) (* (* 3.0 a) c))
176.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
137.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.9s

Counts
88 → 88
Iterations
IterNodes
done5000
21257
1398
0158

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.8b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
0.8b
(- (* b b) (* (* 3.0 a) c))
1.6b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
21.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite114.0ms

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:
21.0ms
(* (* 3.0 a) c)
14.0ms
(- (* b b) (* (* 3.0 a) c))
64.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
12.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series429.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* (* 3.0 a) c)
81.0ms
(- (* b b) (* (* 3.0 a) c))
159.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
150.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify6.9s

Counts
76 → 76
Iterations
IterNodes
done5003
33583
2916
1298
0124

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.8b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 c) a)
0.8b
(- (* b b) (* (* 3.0 c) a))
1.6b
(- (sqrt (- (* b b) (* (* 3.0 c) a))) b)
21.2b
(sqrt (- (* b b) (* (* 3.0 c) a)))

rewrite137.0ms

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:
27.0ms
(* (* 3.0 c) a)
16.0ms
(- (* b b) (* (* 3.0 c) a))
77.0ms
(- (sqrt (- (* b b) (* (* 3.0 c) a))) b)
14.0ms
(sqrt (- (* b b) (* (* 3.0 c) a)))

series390.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* (* 3.0 c) a)
100.0ms
(- (* b b) (* (* 3.0 c) a))
136.0ms
(- (sqrt (- (* b b) (* (* 3.0 c) a))) b)
127.0ms
(sqrt (- (* b b) (* (* 3.0 c) a)))

simplify8.4s

Counts
76 → 76
Iterations
IterNodes
done5000
34000
2982
1299
0125

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.8b

localize98.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 3.0) (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) a))
0.8b
(- (* b b) (* (* 3.0 a) c))
1.6b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
21.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite338.0ms

Algorithm
rewrite-expression-head
Rules
56×add-sqr-sqrt
34×times-frac
32×*-un-lft-identity
26×add-exp-log
22×associate-*r* add-cube-cbrt
16×add-cbrt-cube
13×associate-*l*
8×div-exp prod-exp add-log-exp difference-of-squares
7×pow1 sqrt-prod
6×unswap-sqr
4×cbrt-undiv cbrt-unprod insert-posit16 distribute-lft-out--
3×flip3-- flip--
2×rec-exp sub-neg sqrt-div diff-log 1-exp div-inv
1×frac-times rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 111
Calls
4 calls:
199.0ms
(* (/ 1 3.0) (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) a))
19.0ms
(- (* b b) (* (* 3.0 a) c))
91.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
21.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series592.0ms

Counts
4 → 12
Calls
4 calls:
209.0ms
(* (/ 1 3.0) (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) a))
89.0ms
(- (* b b) (* (* 3.0 a) c))
151.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
142.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify4.1s

Counts
123 → 123
Iterations
IterNodes
done5001
22021
1610
0224

prune1.4s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.8b

regimes1.7s

Accuracy

83.6% (4.8b remaining)

Error of 10.3b against oracle of 5.5b and baseline of 34.7b

bsearch176.0ms

Steps
ItersRangePoint
6
1.5727591416233446e-143
1.789606490082599e-142
1.744031351412433e-142
8
-1.3198903247987554e+155
-1.1250773400730914e+152
-1.2705286994550075e+152

simplify19.0ms

Iterations
IterNodes
done32
132
027

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.0s1082×body2560valid
484.0ms5801×body80valid
337.0ms933×body1280valid
227.0ms2987×body80nan
198.0ms490×body640valid
100.0ms123×body160valid
53.0ms107×body5120valid
46.0ms245×body320valid