Details

Time bar (total: 13.3s)

sample89.0ms

Algorithm
intervals
Results
19.0ms205×body80valid
16.0ms31×body2560valid
14.0ms31×body1280valid
7.0ms89×body80nan
4.0ms12×body640valid
3.0ms4×body5120valid
1.0ms5×body320valid
0.0ms2×body160valid

simplify169.0ms

Counts
1 → 1
Iterations
IterNodes
done156
6156
5152
4142
3115
264
128
014

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* b b) (* a (* 4.0 c)))
0.1b
(/ (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (* 2.0 a))
0.7b
(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
19.5b
(sqrt (- (* b b) (* a (* 4.0 c))))

rewrite152.0ms

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:
11.0ms
(- (* b b) (* a (* 4.0 c)))
87.0ms
(/ (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (* 2.0 a))
37.0ms
(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
14.0ms
(sqrt (- (* b b) (* a (* 4.0 c))))

series486.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(- (* b b) (* a (* 4.0 c)))
156.0ms
(/ (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (* 2.0 a))
139.0ms
(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
104.0ms
(sqrt (- (* b b) (* a (* 4.0 c))))

simplify767.0ms

Counts
89 → 89
Iterations
IterNodes
done5000
21644
1418
0157

prune502.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* b b) (* a (* 4.0 c)))
0.2b
(* (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (/ (/ 1 2.0) a))
0.7b
(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
19.5b
(sqrt (- (* b b) (* a (* 4.0 c))))

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
71×times-frac
62×add-sqr-sqrt
50×*-un-lft-identity
43×associate-*r*
41×add-cube-cbrt
19×add-exp-log
13×add-cbrt-cube
10×add-log-exp
7×pow1 associate-*l*
6×div-exp
5×flip3-- prod-exp sqrt-prod flip--
4×div-inv distribute-lft-out-- difference-of-squares unswap-sqr
3×cbrt-undiv diff-log cbrt-unprod
2×frac-times sub-neg distribute-rgt-neg-in sqrt-div associate-*l/
1×associate--l- neg-sub0 rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-down neg-log associate-*r/ *-commutative
Counts
4 → 121
Calls
4 calls:
9.0ms
(- (* b b) (* a (* 4.0 c)))
119.0ms
(* (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (/ (/ 1 2.0) a))
35.0ms
(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
8.0ms
(sqrt (- (* b b) (* a (* 4.0 c))))

series405.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(- (* b b) (* a (* 4.0 c)))
126.0ms
(* (- (- b) (sqrt (- (* b b) (* a (* 4.0 c))))) (/ (/ 1 2.0) a))
113.0ms
(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
95.0ms
(sqrt (- (* b b) (* a (* 4.0 c))))

simplify448.0ms

Counts
133 → 133
Iterations
IterNodes
done5001
1769
0268

prune774.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (* c a))
0.1b
(/ (/ (- (+ b (sqrt (- (* b b) (* 4.0 (* c a)))))) 2.0) a)
0.7b
(+ b (sqrt (- (* b b) (* 4.0 (* c a)))))
19.5b
(sqrt (- (* b b) (* 4.0 (* c a))))

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
264×times-frac
185×*-un-lft-identity
136×add-sqr-sqrt
135×add-cube-cbrt
48×distribute-lft-neg-in distribute-rgt-neg-in
40×associate-/l*
25×distribute-lft-out
14×add-cbrt-cube add-exp-log
12×neg-mul-1
10×pow1
6×add-log-exp
5×div-inv
3×cbrt-undiv associate-/r* div-exp associate-*l* pow-prod-down prod-exp sqrt-prod cbrt-unprod
2×sqrt-div div-sub distribute-frac-neg
1×neg-sub0 +-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 flip3-+ flip3-- pow1/2 associate-*r* *-commutative flip-+ flip-- associate-/l/
Counts
4 → 225
Calls
4 calls:
13.0ms
(* 4.0 (* c a))
120.0ms
(/ (/ (- (+ b (sqrt (- (* b b) (* 4.0 (* c a)))))) 2.0) a)
22.0ms
(+ b (sqrt (- (* b b) (* 4.0 (* c a)))))
7.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))

series416.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(* 4.0 (* c a))
127.0ms
(/ (/ (- (+ b (sqrt (- (* b b) (* 4.0 (* c a)))))) 2.0) a)
124.0ms
(+ b (sqrt (- (* b b) (* 4.0 (* c a)))))
132.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))

simplify1.8s

Counts
237 → 237
Iterations
IterNodes
done5001
24893
11052
0413

prune1.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.5b

localize62.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
19.5b
(sqrt (- (* b b) (* a (* 4.0 c))))
19.5b
(sqrt (- (* b b) (* a (* 4.0 c))))
19.5b
(sqrt (- (* b b) (* a (* 4.0 c))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×*-un-lft-identity
10×sqrt-prod
8×add-log-exp
7×pow1 add-cube-cbrt
6×sqrt-div
4×flip3-- add-cbrt-cube add-exp-log flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
2×diff-log distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg distribute-rgt-neg-in neg-log
Counts
4 → 63
Calls
4 calls:
20.0ms
(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
7.0ms
(sqrt (- (* b b) (* a (* 4.0 c))))
7.0ms
(sqrt (- (* b b) (* a (* 4.0 c))))
7.0ms
(sqrt (- (* b b) (* a (* 4.0 c))))

series443.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(- (- b) (sqrt (- (* b b) (* a (* 4.0 c)))))
107.0ms
(sqrt (- (* b b) (* a (* 4.0 c))))
128.0ms
(sqrt (- (* b b) (* a (* 4.0 c))))
100.0ms
(sqrt (- (* b b) (* a (* 4.0 c))))

simplify489.0ms

Counts
75 → 75
Iterations
IterNodes
done5000
2897
1217
087

prune994.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 3.5b

regimes419.0ms

Accuracy

85.8% (4.1b remaining)

Error of 9.4b against oracle of 5.3b and baseline of 34.1b

bsearch182.0ms

Steps
ItersRangePoint
8
2.072994944964499e+129
8.571507078369983e+131
3.087668654677018e+130
8
-8.904680992578465e-52
-2.849527055171251e-56
-4.356959927988237e-56

simplify9.0ms

Iterations
IterNodes
done41
241
138
028

end2.0ms

sample2.8s

Algorithm
intervals
Results
946.0ms1025×body2560valid
590.0ms5841×body80valid
342.0ms921×body1280valid
229.0ms2877×body80nan
152.0ms122×body5120valid
120.0ms457×body640valid
56.0ms245×body320valid
17.0ms116×body160valid