Details

Time bar (total: 14.9s)

sample197.0ms

Algorithm
intervals
Results
46.0ms138×body160valid
46.0ms301×body80nan
41.0ms118×body80valid
38.0ms557×pre80true

simplify117.0ms

Calls
1 calls:
Slowest
117.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize38.0ms

Local error

Found 4 expressions with local error:

28.1b
(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.3b
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
0.2b
(- (* b b) (* (* c a) 4))
0.1b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log add-log-exp
4×pow1 flip3-- insert-posit16 flip--
3×times-frac sqrt-prod associate-/l*
2×sub-neg sqrt-div associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num associate-/r* frac-2neg pow1/2 diff-log div-sub div-exp div-inv
Calls
4 calls:
Slowest
49.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
25.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
5.0ms
(sqrt (- (* b b) (* (* c a) 4)))
5.0ms
(- (* b b) (* (* c a) 4))

series244.0ms

Calls
4 calls:
Slowest
75.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
75.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
59.0ms
(sqrt (- (* b b) (* (* c a) 4)))
35.0ms
(- (* b b) (* (* c a) 4))

simplify3.7s

Calls
32 calls:
Slowest
552.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
498.0ms
(sqrt (- (pow (* b b) 3) (pow (* (* c a) 4) 3)))
307.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
266.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
247.0ms
(/ (* (* (- (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)))

prune844.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 9.2b

localize8.0ms

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

prune65.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 9.2b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
4×add-cbrt-cube add-exp-log
2×add-sqr-sqrt pow1 clear-num frac-2neg *-un-lft-identity add-cube-cbrt insert-posit16 div-inv associate-/l* add-log-exp
1×cbrt-undiv associate-/r* times-frac div-exp associate-*r/ associate-/l/
Calls
2 calls:
Slowest
7.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
3.0ms
(/ (* a c) b)

series27.0ms

Calls
2 calls:
Slowest
14.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
13.0ms
(/ (* a c) b)

simplify1.1s

Calls
11 calls:
Slowest
751.0ms
(/ (* (* (* -2 (/ (* a c) b)) (* -2 (/ (* a c) b))) (* -2 (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
146.0ms
(/ (/ (* a c) b) a)
115.0ms
(- (log (* -2 (/ (* a c) b))) (log (* 2 a)))
20.0ms
(* -1 (/ c b))
20.0ms
(* -1 (/ c b))

prune377.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 9.1b

localize7.0ms

Local error

Found 1 expressions with local error:

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

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
3×add-cbrt-cube add-exp-log
1×add-sqr-sqrt pow1 cbrt-undiv clear-num associate-/r* frac-2neg *-un-lft-identity times-frac div-exp add-cube-cbrt insert-posit16 div-inv associate-/l* add-log-exp
Calls
1 calls:
Slowest
10.0ms
(/ (* -2 (* a c)) (* (* 2 a) b))

series26.0ms

Calls
1 calls:
Slowest
25.0ms
(/ (* -2 (* a c)) (* (* 2 a) b))

simplify2.3s

Calls
7 calls:
Slowest
2.0s
(/ (* (* (* -2 (* a c)) (* -2 (* a c))) (* -2 (* a c))) (* (* (* (* 2 a) b) (* (* 2 a) b)) (* (* 2 a) b)))
144.0ms
(- (log (* -2 (* a c))) (log (* (* 2 a) b)))
27.0ms
(* -1 (/ c b))
26.0ms
(* -1 (/ c b))
18.0ms
(* -1 (/ c b))

prune186.0ms

Pruning

26 alts after pruning (24 fresh and 2 done)

Merged error: 9.1b

regimes617.0ms

Accuracy

46.9% (7.2b remaining)

Error of 16.4b against oracle of 9.2b and baseline of 22.7b

bsearch17.0ms

end0.0ms

sample5.0s

Algorithm
intervals
Results
1.9s4458×body160valid
1.2s8687×body80nan
883.0ms16687×pre80true
539.0ms3542×body80valid