Details

Time bar (total: 47.8s)

sample96.0ms

Algorithm
intervals
Results
27.0ms138×body160valid
21.0ms274×body80nan
20.0ms530×pre80true
10.0ms118×body80valid

simplify175.0ms

Calls
1 calls:
Slowest
175.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize45.0ms

Local error

Found 4 expressions with local error:

26.9b
(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.3b
(- (* b b) (* (* c a) 4))
0.2b
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
0.1b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite154.0ms

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
83.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
55.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
8.0ms
(- (* b b) (* (* c a) 4))
7.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series431.0ms

Calls
4 calls:
Slowest
129.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
129.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
98.0ms
(sqrt (- (* b b) (* (* c a) 4)))
74.0ms
(- (* b b) (* (* c a) 4))

simplify5.6s

Calls
49 calls:
Slowest
603.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
361.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
329.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
277.0ms
(/ (* (* (- (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)))
274.0ms
(- b (* 2 (/ (* a c) b)))

prune1.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.7b

localize6.0ms

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

prune61.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 8.7b

localize33.0ms

Local error

Found 2 expressions with local error:

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

rewrite51.0ms

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
36.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
14.0ms
(/ (* a c) b)

series60.0ms

Calls
2 calls:
Slowest
39.0ms
(/ (* a c) b)
22.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))

simplify11.7s

Calls
37 calls:
Slowest
1.4s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 2) 2) (* (* a a) a)))
1.4s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a 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 a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
839.0ms
(/ (* (* (* -2 (/ (* a c) b)) (* -2 (/ (* a c) b))) (* -2 (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune530.0ms

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 8.6b

localize28.0ms

Local error

Found 1 expressions with local error:

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

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
37×add-cbrt-cube add-exp-log
18×prod-exp cbrt-unprod
9×cbrt-undiv div-exp
1×add-sqr-sqrt pow1 clear-num associate-/r* frac-2neg *-un-lft-identity times-frac add-cube-cbrt insert-posit16 div-inv associate-/l* add-log-exp
Calls
1 calls:
Slowest
50.0ms
(/ (* -2 (* a c)) (* (* 2 a) b))

series21.0ms

Calls
1 calls:
Slowest
21.0ms
(/ (* -2 (* a c)) (* (* 2 a) b))

simplify21.7s

Calls
23 calls:
Slowest
2.9s
(/ (* (* (* -2 (* a c)) (* -2 (* a c))) (* -2 (* a c))) (* (* (* (* 2 a) b) (* (* 2 a) b)) (* (* 2 a) b)))
2.5s
(/ (* (* (* -2 -2) -2) (* (* (* a c) (* a c)) (* a c))) (* (* (* (* 2 a) b) (* (* 2 a) b)) (* (* 2 a) b)))
2.4s
(/ (* (* (* -2 -2) -2) (* (* (* a a) a) (* (* c c) c))) (* (* (* (* 2 a) b) (* (* 2 a) b)) (* (* 2 a) b)))
2.1s
(/ (* (* (* -2 -2) -2) (* (* (* a a) a) (* (* c c) c))) (* (* (* (* 2 a) (* 2 a)) (* 2 a)) (* (* b b) b)))
2.1s
(/ (* (* (* -2 -2) -2) (* (* (* a c) (* a c)) (* a c))) (* (* (* (* 2 a) (* 2 a)) (* 2 a)) (* (* b b) b)))

prune331.0ms

Pruning

28 alts after pruning (26 fresh and 2 done)

Merged error: 8.6b

regimes765.0ms

Accuracy

47.8% (7.2b remaining)

Error of 16.2b against oracle of 9.0b and baseline of 22.7b

bsearch10.0ms

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.3s8707×body80nan
1.2s4495×body160valid
1.0s16707×pre80true
820.0ms3505×body80valid