Details

Time bar (total: 15.0s)

sample142.0ms

Algorithm
intervals
Results
37.0ms42×body2560valid
29.0ms23×body1280valid
24.0ms176×body80valid
12.0ms98×body80nan
11.0ms23×body640valid
4.0ms10×body320valid
3.0ms3×body5120valid
1.0ms4×body160valid

simplify198.0ms

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: 33.5b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
0.6b
(- (* b b) (* 4 (* a c)))
0.7b
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
21.9b
(sqrt (- (* b b) (* 4 (* a c))))

rewrite106.0ms

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:
50.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
14.0ms
(- (* b b) (* 4 (* a c)))
27.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
13.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series400.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
49.0ms
(- (* b b) (* 4 (* a c)))
132.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
89.0ms
(sqrt (- (* b b) (* 4 (* a c))))

simplify1.1s

Counts
93 → 93
Iterations
IterNodes
done2006
32006
21254
1400
0154

prune576.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.3b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
0.6b
(- (* b b) (* 4 (* a c)))
0.7b
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
21.9b
(sqrt (- (* b b) (* 4 (* a c))))

rewrite88.0ms

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:
40.0ms
(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
17.0ms
(- (* b b) (* 4 (* a c)))
20.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
7.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series436.0ms

Counts
4 → 12
Calls
4 calls:
152.0ms
(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
58.0ms
(- (* b b) (* 4 (* a c)))
111.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
115.0ms
(sqrt (- (* b b) (* 4 (* a c))))

simplify1.6s

Counts
141 → 141
Iterations
IterNodes
done2002
32002
21799
1571
0229

prune592.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* -4 a) c)
0.6b
(+ (* b b) (* (* -4 a) c))
0.7b
(- (- b) (sqrt (+ (* b b) (* (* -4 a) c))))
21.9b
(sqrt (+ (* b b) (* (* -4 a) c)))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1 *-un-lft-identity add-log-exp
9×add-cbrt-cube add-exp-log
6×add-cube-cbrt
4×sqrt-prod insert-posit16
3×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×flip3-+ sqrt-div diff-log flip-+ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 +-commutative rem-sqrt-square sum-log sub-neg distribute-rgt-neg-in sqrt-pow1 flip3-- pow1/2 associate-*l* neg-log *-commutative flip--
Counts
4 → 66
Calls
4 calls:
29.0ms
(* (* -4 a) c)
18.0ms
(+ (* b b) (* (* -4 a) c))
19.0ms
(- (- b) (sqrt (+ (* b b) (* (* -4 a) c))))
6.0ms
(sqrt (+ (* b b) (* (* -4 a) c)))

series273.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* (* -4 a) c)
64.0ms
(+ (* b b) (* (* -4 a) c))
98.0ms
(- (- b) (sqrt (+ (* b b) (* (* -4 a) c))))
90.0ms
(sqrt (+ (* b b) (* (* -4 a) c)))

simplify1.3s

Counts
78 → 78
Iterations
IterNodes
done2004
32004
21104
1331
0130

prune428.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.3b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* -4 a) c)
0.6b
(+ (* b b) (* (* -4 a) c))
0.7b
(- (- b) (sqrt (+ (* b b) (* (* -4 a) c))))
21.9b
(sqrt (+ (* b b) (* (* -4 a) c)))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1 *-un-lft-identity add-log-exp
9×add-cbrt-cube add-exp-log
6×add-cube-cbrt
4×sqrt-prod insert-posit16
3×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×flip3-+ sqrt-div diff-log flip-+ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 +-commutative rem-sqrt-square sum-log sub-neg distribute-rgt-neg-in sqrt-pow1 flip3-- pow1/2 associate-*l* neg-log *-commutative flip--
Counts
4 → 66
Calls
4 calls:
15.0ms
(* (* -4 a) c)
23.0ms
(+ (* b b) (* (* -4 a) c))
30.0ms
(- (- b) (sqrt (+ (* b b) (* (* -4 a) c))))
12.0ms
(sqrt (+ (* b b) (* (* -4 a) c)))

series335.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(* (* -4 a) c)
90.0ms
(+ (* b b) (* (* -4 a) c))
123.0ms
(- (- b) (sqrt (+ (* b b) (* (* -4 a) c))))
88.0ms
(sqrt (+ (* b b) (* (* -4 a) c)))

simplify1.1s

Counts
78 → 78
Iterations
IterNodes
done2004
32004
21104
1331
0130

prune371.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.3b

regimes606.0ms

Accuracy

83.1% (4.7b remaining)

Error of 10.4b against oracle of 5.8b and baseline of 33.4b

bsearch171.0ms

Steps
ItersRangePoint
7
6.52945691119865e+99
1.3360629297740576e+102
6.384705165981893e+101
9
-3.929467862544791e-84
-4.77908653107304e-89
-5.961198324014865e-88

simplify10.0ms

Iterations
IterNodes
done32
132
027

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.4s1077×body2560valid
920.0ms5862×body80valid
682.0ms903×body1280valid
419.0ms117×body160valid
381.0ms2940×body80nan
308.0ms471×body640valid
221.0ms109×body5120valid
86.0ms219×body320valid