Details

Time bar (total: 15.2s)

sample108.0ms

Algorithm
intervals
Results
25.0ms43×body2560valid
15.0ms155×body80valid
12.0ms26×body1280valid
9.0ms94×body80nan
7.0ms19×body640valid
4.0ms12×body320valid
3.0ms5×body5120valid
1.0ms6×body160valid

simplify81.0ms

Counts
1 → 1
Iterations
IterNodes
done111
5111
4102
378
244
124
014

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.6b
(- (* b b) (* (* 4.0 a) c))
1.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-cbrt-cube add-exp-log
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-neg-in sqrt-prod
2×neg-sub0 cbrt-undiv sum-log flip3-+ flip3-- sqrt-div div-exp associate-+l- flip-+ flip-- associate-/l/
1×+-commutative rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
79.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
7.0ms
(- (* b b) (* (* 4.0 a) c))
20.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series586.0ms

Counts
4 → 12
Calls
4 calls:
213.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
83.0ms
(- (* b b) (* (* 4.0 a) c))
133.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
157.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
82 → 82
Iterations
IterNodes
done5001
21926
1421
0154

prune598.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.3b

localize61.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.2b
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
9.2b
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
21.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite250.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
84×add-sqr-sqrt
83×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-cbrt-cube add-exp-log
14×sqrt-prod
11×distribute-rgt-neg-in
8×associate-/r* add-log-exp
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×clear-num frac-2neg sqrt-div diff-log prod-exp cbrt-unprod
1×associate--l- neg-sub0 rem-sqrt-square sub-neg sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 154
Calls
4 calls:
22.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
101.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
105.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series807.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
251.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
334.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
102.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.7s

Counts
166 → 166
Iterations
IterNodes
done5000
23736
1659
0254

prune1.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.2b

localize17.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations
IterNodes
done0
00

prune54.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.2b

localize66.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* 4.0 (* a c)))
1.7b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.4b
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
21.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
25×add-cbrt-cube add-exp-log
10×add-sqr-sqrt add-log-exp
9×*-un-lft-identity prod-exp cbrt-unprod
6×cbrt-undiv div-exp
5×pow1 add-cube-cbrt
4×flip3-- sqrt-prod flip--
3×diff-log
2×sub-neg sqrt-div associate-*r/ associate-/r/ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square clear-num associate-/r* distribute-rgt-neg-in frac-2neg sqrt-pow1 times-frac pow1/2 neg-log div-inv associate-/l*
Counts
4 → 72
Calls
4 calls:
8.0ms
(- (* b b) (* 4.0 (* a c)))
27.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
53.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
15.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series537.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(- (* b b) (* 4.0 (* a c)))
140.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
204.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
117.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.9s

Counts
84 → 84
Iterations
IterNodes
done5002
23132
1483
0166

prune502.0ms

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 5.2b

regimes560.0ms

Accuracy

82.1% (4.8b remaining)

Error of 10.3b against oracle of 5.4b and baseline of 32.4b

bsearch245.0ms

Steps
ItersRangePoint
12
2.4919208328047006e-151
1.0529347607547997e-106
6.484072051994264e-107
8
-6.412561728939963e+28
-6.810701174428621e+25
-6.336287344206649e+28

simplify9.0ms

Iterations
IterNodes
done33
133
027

end0.0ms

sample3.6s

Algorithm
intervals
Results
783.0ms2942×body80nan
778.0ms957×body1280valid
662.0ms1104×body2560valid
588.0ms5735×body80valid
129.0ms461×body640valid
84.0ms226×body320valid
65.0ms119×body160valid
60.0ms106×body5120valid