Details

Time bar (total: 17.3s)

sample133.0ms

Algorithm
intervals
Results
37.0ms37×body2560valid
29.0ms194×body80valid
19.0ms28×body1280valid
11.0ms86×body80nan
11.0ms18×body640valid
6.0ms5×body5120valid
2.0ms4×body320valid
1.0ms3×body160valid

simplify143.0ms

Counts
1 → 1
Iterations
IterNodes
done134
7134
6132
5129
4126
3103
262
128
014

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
0.9b
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
1.0b
(- (* b b) (* 4 (* a c)))
25.0b
(sqrt (- (* b b) (* 4 (* a c))))

rewrite88.0ms

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-- insert-posit16 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 → 81
Calls
4 calls:
53.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
18.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
8.0ms
(- (* b b) (* 4 (* a c)))
7.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series418.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
107.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
65.0ms
(- (* b b) (* 4 (* a c)))
91.0ms
(sqrt (- (* b b) (* 4 (* a c))))

simplify1.3s

Counts
93 → 93
Iterations
IterNodes
done2002
32002
21255
1400
0154

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.6b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* a (* c 4))))) (* 2 a))
0.9b
(- (- b) (sqrt (- (* b b) (* a (* c 4)))))
1.0b
(- (* b b) (* a (* c 4)))
25.0b
(sqrt (- (* b b) (* a (* c 4))))

rewrite118.0ms

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-- insert-posit16 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 → 81
Calls
4 calls:
55.0ms
(/ (- (- b) (sqrt (- (* b b) (* a (* c 4))))) (* 2 a))
30.0ms
(- (- b) (sqrt (- (* b b) (* a (* c 4)))))
16.0ms
(- (* b b) (* a (* c 4)))
15.0ms
(sqrt (- (* b b) (* a (* c 4))))

series364.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(/ (- (- b) (sqrt (- (* b b) (* a (* c 4))))) (* 2 a))
86.0ms
(- (- b) (sqrt (- (* b b) (* a (* c 4)))))
62.0ms
(- (* b b) (* a (* c 4)))
97.0ms
(sqrt (- (* b b) (* a (* c 4))))

simplify1.2s

Counts
93 → 93
Iterations
IterNodes
done2005
32005
21291
1401
0156

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.6b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* a (* c 4))))) (/ 1/2 a))
0.9b
(- (- b) (sqrt (- (* b b) (* a (* c 4)))))
1.0b
(- (* b b) (* a (* c 4)))
25.0b
(sqrt (- (* b b) (* a (* c 4))))

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
21×*-un-lft-identity
13×associate-*r* add-cube-cbrt
10×times-frac add-log-exp
9×add-cbrt-cube add-exp-log
7×pow1 associate-*l*
5×flip3-- sqrt-prod flip--
4×insert-posit16 distribute-lft-out-- difference-of-squares
3×diff-log
2×frac-times sub-neg distribute-rgt-neg-in sqrt-div associate-*l/ prod-exp cbrt-unprod unswap-sqr
1×associate--l- neg-sub0 cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp pow-prod-down neg-log associate-*r/ *-commutative div-inv
Counts
4 → 89
Calls
4 calls:
101.0ms
(* (- (- b) (sqrt (- (* b b) (* a (* c 4))))) (/ 1/2 a))
26.0ms
(- (- b) (sqrt (- (* b b) (* a (* c 4)))))
8.0ms
(- (* b b) (* a (* c 4)))
7.0ms
(sqrt (- (* b b) (* a (* c 4))))

series354.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(* (- (- b) (sqrt (- (* b b) (* a (* c 4))))) (/ 1/2 a))
91.0ms
(- (- b) (sqrt (- (* b b) (* a (* c 4)))))
52.0ms
(- (* b b) (* a (* c 4)))
115.0ms
(sqrt (- (* b b) (* a (* c 4))))

simplify958.0ms

Counts
101 → 101
Iterations
IterNodes
done2005
32005
21611
1454
0179

prune1.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
0.9b
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
1.0b
(- (* b b) (* 4 (* a c)))
25.0b
(sqrt (- (* b b) (* 4 (* a c))))

rewrite91.0ms

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
4×insert-posit16
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 → 129
Calls
4 calls:
47.0ms
(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
22.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
8.0ms
(- (* b b) (* 4 (* a c)))
11.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series344.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
91.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
48.0ms
(- (* b b) (* 4 (* a c)))
83.0ms
(sqrt (- (* b b) (* 4 (* a c))))

simplify1.2s

Counts
141 → 141
Iterations
IterNodes
done2002
32002
21729
1571
0229

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.6b

regimes465.0ms

Accuracy

83.7% (4.5b remaining)

Error of 9.8b against oracle of 5.3b and baseline of 33.2b

bsearch282.0ms

Steps
ItersRangePoint
9
1.1500868835104234e+100
1.1016243770318365e+105
2.5703497435733685e+102
10
-1.094129558870314e-56
-1.2317994276347943e-74
-1.8774910265390396e-73

simplify7.0ms

Iterations
IterNodes
done29
129
025

end0.0ms

sample5.0s

Algorithm
intervals
Results
2.1s1095×body2560valid
922.0ms5820×body80valid
750.0ms948×body1280valid
402.0ms2996×body80nan
274.0ms445×body640valid
88.0ms98×body5120valid
87.0ms225×body320valid
59.0ms116×body160valid