Details

Time bar (total: 38.6s)

sample165.0ms

Algorithm
intervals
Results
45.0ms130×body160valid
40.0ms294×body80nan
33.0ms550×pre80true
18.0ms126×body80valid

simplify107.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
107.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.2b

localize22.0ms

Local error

Found 4 expressions with local error:

27.0b
(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.2b
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
0.2b
(- (* b b) (* (* c a) 4))
0.1b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite168.0ms

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
Counts
4 → 76
Calls
4 calls:
Slowest
116.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
36.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
8.0ms
(- (* b b) (* (* c a) 4))
7.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series399.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
130.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
114.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
87.0ms
(sqrt (- (* b b) (* (* c a) 4)))
68.0ms
(- (* b b) (* (* c a) 4))

simplify5.2s

Counts
49 → 88
Calls
49 calls:
Slowest
558.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
351.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
281.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
281.0ms
(/ (* (* (- (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)))
258.0ms
(- b (* 2 (/ (* a c) b)))

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.2b

localize11.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

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

series0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

simplify0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

prune81.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 9.2b

localize21.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (* a c) b)
0.2b
(/ (* -2 (/ (* a c) b)) (* 2 a))

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/
Counts
2 → 53
Calls
2 calls:
Slowest
36.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
17.0ms
(/ (* a c) b)

series69.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
41.0ms
(/ (* a c) b)
28.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))

simplify11.7s

Counts
37 → 59
Calls
37 calls:
Slowest
1.7s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) 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 a) (* 2 a)) (* 2 a)))
1.3s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a 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)))
917.0ms
(/ (* (* (* -2 (/ (* a c) b)) (* -2 (/ (* a c) b))) (* -2 (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune632.0ms

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 9.1b

localize28.0ms

Local error

Found 2 expressions with local error:

0.3b
(* a (/ c b))
0.2b
(/ (* -2 (* a (/ c b))) (* 2 a))

rewrite47.0ms

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/
Counts
2 → 64
Calls
2 calls:
Slowest
31.0ms
(/ (* -2 (* a (/ c b))) (* 2 a))
9.0ms
(* a (/ c b))

series63.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
33.0ms
(/ (* -2 (* a (/ c b))) (* 2 a))
29.0ms
(* a (/ c b))

simplify12.0s

Counts
49 → 70
Calls
49 calls:
Slowest
1.4s
(/ (* (* (* -2 (* a (/ c b))) (* -2 (* a (/ c b)))) (* -2 (* a (/ c b)))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.4s
(/ (* (* (* -2 -2) -2) (* (* (* a a) a) (/ (* (* c c) c) (* (* b b) b)))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.2s
(/ (* (* (* -2 -2) -2) (* (* (* a a) a) (/ (* (* c c) c) (* (* b b) b)))) (* (* (* 2 2) 2) (* (* a a) a)))
1.1s
(/ (* (* (* -2 -2) -2) (* (* (* a a) a) (* (* (/ c b) (/ c b)) (/ c b)))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.1s
(/ (* (* (* -2 -2) -2) (* (* (* a (/ c b)) (* a (/ c b))) (* a (/ c b)))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune623.0ms

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 9.1b

regimes1.1s

Accuracy

46.4% (7.4b remaining)

Error of 16.3b against oracle of 8.9b and baseline of 22.6b

bsearch10.0ms

end0.0ms

sample5.0s

Algorithm
intervals
Results
1.3s4510×body160valid
1.1s8323×body80nan
1.1s16323×pre80true
547.0ms3490×body80valid