Details

Time bar (total: 40.1s)

sample144.0ms

Algorithm
intervals
Results
38.0ms161×body160valid
30.0ms291×body80nan
28.0ms547×pre80true
17.0ms38×body320valid
7.0ms57×body80valid

simplify148.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
148.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.6b

localize21.0ms

Local error

Found 4 expressions with local error:

38.5b
(- (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))
0.0b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite105.0ms

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
57.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
34.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
7.0ms
(sqrt (- (* b b) (* (* c a) 4)))
7.0ms
(- (* b b) (* (* c a) 4))

series434.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
157.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
125.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
76.0ms
(sqrt (- (* b b) (* (* c a) 4)))
75.0ms
(- (* b b) (* (* c a) 4))

simplify5.5s

Counts
49 → 88
Calls
49 calls:
Slowest
628.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
424.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
347.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
300.0ms
(- b (* 2 (/ (* a c) b)))
287.0ms
(/ (* (* (- (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)))

prune977.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 5.4b

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

prune62.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 5.4b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite45.0ms

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
27.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
17.0ms
(/ (* a c) b)

series69.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
35.0ms
(/ (* a c) b)
34.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))

simplify11.6s

Counts
37 → 59
Calls
37 calls:
Slowest
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 a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 2 2) 2) (* (* a a) 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 c) b) (/ (* a c) b)) (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.2s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune599.0ms

Pruning

30 alts after pruning (29 fresh and 1 done)

Merged error: 5.3b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite58.0ms

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
40.0ms
(/ (* -2 (* a (/ c b))) (* 2 a))
17.0ms
(* a (/ c b))

series74.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
42.0ms
(/ (* -2 (* a (/ c b))) (* 2 a))
32.0ms
(* a (/ c b))

simplify13.1s

Counts
49 → 70
Calls
49 calls:
Slowest
1.5s
(/ (* (* (* -2 (* a (/ c b))) (* -2 (* a (/ c b)))) (* -2 (* a (/ c b)))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.4s
(/ (* (* (* -2 -2) -2) (* (* (* a a) a) (/ (* (* c c) c) (* (* b b) b)))) (* (* (* 2 a) (* 2 a)) (* 2 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 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)))

prune563.0ms

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 5.3b

regimes523.0ms

Accuracy

13.4% (5.9b remaining)

Error of 11.1b against oracle of 5.2b and baseline of 12.0b

bsearch126.0ms

end0.0ms

sample5.9s

Algorithm
intervals
Results
1.8s4880×body160valid
1.6s16257×pre80true
1.3s8257×body80nan
548.0ms1342×body320valid
303.0ms1778×body80valid