Details

Time bar (total: 38.9s)

sample149.0ms

Algorithm
intervals
Results
50.0ms498×pre80true
31.0ms144×body160valid
26.0ms242×body80nan
18.0ms52×body320valid
8.0ms60×body80valid

simplify152.0ms

Calls
1 calls:
Slowest
152.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.8b

localize45.0ms

Local error

Found 4 expressions with local error:

36.4b
(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.2b
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
0.1b
(- (* b b) (* (* c a) 4))
0.1b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×add-cube-cbrt
6×times-frac sqrt-prod associate-/l* difference-of-squares
5×pow1
4×flip3-- insert-posit16 flip--
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp cbrt-unprod div-inv
Calls
4 calls:
Slowest
100.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
32.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
9.0ms
(- (* b b) (* (* c a) 4))
7.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series389.0ms

Calls
4 calls:
Slowest
135.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
100.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
95.0ms
(sqrt (- (* b b) (* (* c a) 4)))
59.0ms
(- (* b b) (* (* c a) 4))

simplify5.4s

Calls
49 calls:
Slowest
576.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
410.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
367.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
303.0ms
(/ (* (* (- (sqrt (- (* b b) (* (* c a) 4))) b) (- (sqrt (- (* b b) (* (* c a) 4))) b)) (- (sqrt (- (* b b) (* (* c a) 4))) b)) (* (* (* 2 a) (* 2 a)) (* 2 a)))
238.0ms
(- b (* 2 (/ (* a c) b)))

prune970.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.5b

localize5.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Calls
0 calls:
Slowest

series0.0ms

Calls
0 calls:
Slowest

simplify0.0ms

Calls
0 calls:
Slowest

prune58.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 5.5b

localize20.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ (* -2 (/ (* a c) b)) (* 2 a))
0.3b
(/ (* a c) b)

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
39×add-cbrt-cube add-exp-log
14×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
4×add-sqr-sqrt associate-/r* *-un-lft-identity times-frac add-cube-cbrt
2×pow1 clear-num frac-2neg insert-posit16 div-inv associate-/l* add-log-exp
1×associate-*r/ associate-/l/
Calls
2 calls:
Slowest
35.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
17.0ms
(/ (* a c) b)

series68.0ms

Calls
2 calls:
Slowest
35.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
33.0ms
(/ (* a c) b)

simplify11.2s

Calls
37 calls:
Slowest
1.6s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.3s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 2) 2) (* (* a a) a)))
1.3s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 2 2) 2) (* (* a a) a)))
1.2s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
902.0ms
(/ (* (* (* -2 (/ (* a c) b)) (* -2 (/ (* a c) b))) (* -2 (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune495.0ms

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 5.5b

localize16.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ (* -2 (* a (/ c b))) (* 2 a))
0.3b
(* a (/ c b))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
39×add-cbrt-cube add-exp-log
16×prod-exp cbrt-unprod
15×add-sqr-sqrt
13×associate-*r*
11×cbrt-undiv times-frac div-exp
10×*-un-lft-identity add-cube-cbrt
4×pow1
3×associate-*l* associate-*r/
2×insert-posit16 div-inv add-log-exp unswap-sqr
1×clear-num associate-/r* frac-2neg pow-prod-down *-commutative associate-/l* associate-/l/
Calls
2 calls:
Slowest
24.0ms
(/ (* -2 (* a (/ c b))) (* 2 a))
9.0ms
(* a (/ c b))

series50.0ms

Calls
2 calls:
Slowest
28.0ms
(/ (* -2 (* a (/ c b))) (* 2 a))
23.0ms
(* a (/ c b))

simplify13.0s

Calls
49 calls:
Slowest
1.5s
(/ (* (* (* -2 (* a (/ c b))) (* -2 (* a (/ c b)))) (* -2 (* a (/ c b)))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.5s
(/ (* (* (* -2 -2) -2) (* (* (* a a) a) (/ (* (* c c) c) (* (* b b) b)))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.5s
(/ (* (* (* -2 -2) -2) (* (* (* a a) a) (/ (* (* c c) c) (* (* b b) b)))) (* (* (* 2 2) 2) (* (* a a) a)))
1.2s
(/ (* (* (* -2 -2) -2) (* (* (* a a) a) (* (* (/ c b) (/ c b)) (/ c b)))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.2s
(/ (* (* (* -2 -2) -2) (* (* (* a a) a) (* (* (/ c b) (/ c b)) (/ c b)))) (* (* (* 2 2) 2) (* (* a a) a)))

prune495.0ms

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 5.5b

regimes1.1s

Accuracy

7.2% (6.4b remaining)

Error of 11.5b against oracle of 5.1b and baseline of 12.0b

bsearch51.0ms

end0.0ms

sample5.0s

Algorithm
intervals
Results
1.7s4798×body160valid
1.1s8211×body80nan
928.0ms16211×pre80true
569.0ms1403×body320valid
231.0ms1799×body80valid