Details

Time bar (total: 54.4s)

sample56.0ms

Algorithm
intervals
Results
12.0ms40×body2560valid
9.0ms183×body80valid
8.0ms35×body1280valid
4.0ms79×body80nan
3.0ms16×body640valid
1.0ms2×body5120valid
0.0ms5×body160valid
0.0ms2×body320valid

simplify81.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b
(- (* b b) (* (* 4.0 a) c))
1.3b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite121.0ms

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:
82.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
6.0ms
(- (* b b) (* (* 4.0 a) c))
18.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series437.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
71.0ms
(- (* b b) (* (* 4.0 a) c))
120.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
121.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify804.0ms

Counts
82 → 82
Iterations
IterNodes
done5001
21926
1421
0154

prune411.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.7b

localize22.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.6b
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
7.8b
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite198.0ms

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:
28.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
100.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
51.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
7.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series736.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
221.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
287.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
118.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts
166 → 166
Iterations
IterNodes
done5000
23736
1659
0254

prune856.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.6b

localize76.0ms

Local error

Found 4 expressions with local error:

3.6b
(/ (/ (/ (/ (* 4.0 a) (/ (cbrt (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) c)) (cbrt (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))) (cbrt (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
24.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.2b
(sqrt (- (* b b) (* 4.0 (* a c))))
24.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite3.8s

Algorithm
rewrite-expression-head
Rules
32486×times-frac
15464×add-sqr-sqrt
15461×*-un-lft-identity
15204×cbrt-prod
6773×add-cube-cbrt
4344×distribute-lft-out-- difference-of-squares
3966×associate-/l*
2181×sqrt-prod
2172×distribute-rgt-neg-in
423×div-inv
244×associate-/r/
77×add-exp-log
51×add-cbrt-cube
48×cbrt-undiv div-exp
44×cbrt-div
25×flip3-- flip--
11×prod-exp cbrt-unprod
7×pow1
6×sqrt-div
4×add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×clear-num associate-/r* frac-2neg associate-/l/
Counts
4 → 8017
Calls
4 calls:
1.6s
(/ (/ (/ (/ (* 4.0 a) (/ (cbrt (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) c)) (cbrt (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))) (cbrt (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
7.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series722.0ms

Counts
4 → 12
Calls
4 calls:
379.0ms
(/ (/ (/ (/ (* 4.0 a) (/ (cbrt (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) c)) (cbrt (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))) (cbrt (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
103.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
98.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
141.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.7s

Counts
8029 → 8029
Iterations
IterNodes
done5511
05511

prune35.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 3.6b

localize69.0ms

Local error

Found 4 expressions with local error:

24.2b
(sqrt (- (* b b) (* 4.0 (* a c))))
24.2b
(sqrt (- (* b b) (* 4.0 (* a c))))
24.2b
(sqrt (- (* b b) (* 4.0 (* a c))))
24.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 *-un-lft-identity sqrt-div add-cube-cbrt
4×rem-sqrt-square sqrt-pow1 flip3-- add-cbrt-cube pow1/2 add-exp-log flip-- add-log-exp
Counts
4 → 60
Calls
4 calls:
6.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
6.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
6.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
6.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series293.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.1s

Counts
72 → 72
Iterations
IterNodes
done5000
33085
2530
1136
051

prune664.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 3.6b

regimes341.0ms

Accuracy

92.1% (2.1b remaining)

Error of 7.5b against oracle of 5.4b and baseline of 31.3b

bsearch231.0ms

Steps
ItersRangePoint
9
2.1340360609407003e+79
6.102484722804822e+84
1.1328213746323388e+81
6
-4.703140979328633e-287
-4.631372015676109e-288
-4.7180785979542405e-288
9
-3.845605078781637e+76
-1.2146338677939432e+68
-7.943482039519134e+75

simplify6.0ms

Iterations
IterNodes
done64
164
053

end0.0ms

sample2.3s

Algorithm
intervals
Results
944.0ms5779×body80valid
357.0ms1094×body2560valid
238.0ms931×body1280valid
184.0ms2886×body80nan
98.0ms226×body320valid
80.0ms448×body640valid
33.0ms93×body5120valid
11.0ms125×body160valid