Details

Time bar (total: 17.5s)

sample117.0ms

Algorithm
intervals
Results
27.0ms107×body80nan
22.0ms37×body2560valid
20.0ms198×body80valid
9.0ms19×body1280valid
5.0ms13×body640valid
2.0ms9×body320valid
1.0ms2×body5120valid
1.0ms4×body160valid

simplify111.0ms

Counts
1 → 1
Iterations
IterNodes
done139
7139
6137
5132
4127
3106
261
128
014

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b
(- (* b b) (* 4.0 (* a c)))
1.1b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-cbrt-cube add-exp-log
7×times-frac add-cube-cbrt associate-/l*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-rgt-neg-in diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp cbrt-unprod div-inv
Counts
4 → 77
Calls
4 calls:
52.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
7.0ms
(- (* b b) (* 4.0 (* a c)))
42.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series430.0ms

Counts
4 → 12
Calls
4 calls:
156.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
52.0ms
(- (* b b) (* 4.0 (* a c)))
106.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
116.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.9s

Counts
89 → 89
Iterations
IterNodes
done5006
34673
21246
1402
0155

prune633.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.4b
(- (* b b) (* 4.0 (* a c)))
1.1b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
67×times-frac
48×add-sqr-sqrt
47×*-un-lft-identity
27×add-cube-cbrt
25×add-exp-log
13×associate-/r* add-cbrt-cube
12×div-exp
10×distribute-lft-out-- add-log-exp difference-of-squares
9×associate-/r/
8×sqrt-prod
7×flip3-- flip--
6×pow1
5×cbrt-undiv distribute-rgt-neg-in div-inv
3×rec-exp diff-log 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 neg-log cbrt-unprod pow-flip inv-pow
Counts
4 → 125
Calls
4 calls:
67.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
13.0ms
(- (* b b) (* 4.0 (* a c)))
19.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series468.0ms

Counts
4 → 12
Calls
4 calls:
184.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
83.0ms
(- (* b b) (* 4.0 (* a c)))
103.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
99.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.1s

Counts
137 → 137
Iterations
IterNodes
done5004
21822
1572
0226

prune856.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 c) a)))) (* 2.0 a))
0.4b
(- (* b b) (* (* 4.0 c) a))
1.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 c) a))))
20.7b
(sqrt (- (* b b) (* (* 4.0 c) a)))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-cbrt-cube add-exp-log
7×times-frac add-cube-cbrt associate-/l*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-rgt-neg-in diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp cbrt-unprod div-inv
Counts
4 → 77
Calls
4 calls:
68.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 c) a)))) (* 2.0 a))
12.0ms
(- (* b b) (* (* 4.0 c) a))
25.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 c) a))))
7.0ms
(sqrt (- (* b b) (* (* 4.0 c) a)))

series437.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 c) a)))) (* 2.0 a))
77.0ms
(- (* b b) (* (* 4.0 c) a))
123.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 c) a))))
90.0ms
(sqrt (- (* b b) (* (* 4.0 c) a)))

simplify1.4s

Counts
89 → 89
Iterations
IterNodes
done5000
21320
1408
0157

prune537.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.9b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (/ 1 2.0) a) (- (- b) (sqrt (- (* b b) (* (* 4.0 c) a)))))
0.4b
(- (* b b) (* (* 4.0 c) a))
1.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 c) a))))
20.7b
(sqrt (- (* b b) (* (* 4.0 c) a)))

rewrite201.0ms

Algorithm
rewrite-expression-head
Rules
71×times-frac
62×add-sqr-sqrt
50×*-un-lft-identity
43×associate-*l*
41×add-cube-cbrt
19×add-exp-log
13×add-cbrt-cube
10×add-log-exp
7×pow1 associate-*r*
6×div-exp
5×flip3-- prod-exp sqrt-prod flip--
4×sub-neg div-inv distribute-lft-out-- difference-of-squares unswap-sqr
3×cbrt-undiv diff-log cbrt-unprod
2×distribute-rgt-in frac-times distribute-rgt-neg-in distribute-lft-in sqrt-div associate-*r/
1×associate--l- neg-sub0 rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-down neg-log associate-*l/ *-commutative
Counts
4 → 125
Calls
4 calls:
148.0ms
(* (/ (/ 1 2.0) a) (- (- b) (sqrt (- (* b b) (* (* 4.0 c) a)))))
6.0ms
(- (* b b) (* (* 4.0 c) a))
30.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 c) a))))
7.0ms
(sqrt (- (* b b) (* (* 4.0 c) a)))

series449.0ms

Counts
4 → 12
Calls
4 calls:
175.0ms
(* (/ (/ 1 2.0) a) (- (- b) (sqrt (- (* b b) (* (* 4.0 c) a)))))
50.0ms
(- (* b b) (* (* 4.0 c) a))
118.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 c) a))))
106.0ms
(sqrt (- (* b b) (* (* 4.0 c) a)))

simplify1.7s

Counts
137 → 137
Iterations
IterNodes
done5002
21993
1673
0254

prune857.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.9b

regimes518.0ms

Accuracy

83.9% (4.6b remaining)

Error of 10.2b against oracle of 5.7b and baseline of 33.9b

bsearch163.0ms

Steps
ItersRangePoint
6
4.2942163002471454e+116
2.920461936675284e+117
2.865381670376961e+117
9
-2.9209995635511727e-62
-5.172501488366762e-68
-2.5694949190681246e-64

simplify5.0ms

Iterations
IterNodes
done35
135
027

end0.0ms

sample3.1s

Algorithm
intervals
Results
875.0ms906×body1280valid
628.0ms1038×body2560valid
515.0ms5913×body80valid
272.0ms2911×body80nan
209.0ms443×body640valid
98.0ms110×body5120valid
52.0ms241×body320valid
15.0ms105×body160valid