Details

Time bar (total: 15.3s)

sample137.0ms

Algorithm
intervals
Results
39.0ms274×body80nan
34.0ms138×body160valid
28.0ms530×pre80true
15.0ms118×body80valid

simplify155.0ms

Calls
1 calls:
Slowest
155.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize21.0ms

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)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt
*-un-lft-identity add-cube-cbrt
add-cbrt-cube add-exp-log add-log-exp
pow1 flip3-- insert-posit16 flip--
times-frac sqrt-prod associate-/l*
sub-neg sqrt-div associate-/l/
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
28.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
12.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
2.0ms
(- (* b b) (* (* c a) 4))
2.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series422.0ms

Calls
4 calls:
Slowest
146.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
115.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
97.0ms
(sqrt (- (* b b) (* (* c a) 4)))
63.0ms
(- (* b b) (* (* c a) 4))

simplify3.9s

Calls
32 calls:
Slowest
579.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
525.0ms
(sqrt (- (pow (* b b) 3) (pow (* (* c a) 4) 3)))
286.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
282.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
250.0ms
(- b (* 2 (/ (* a c) b)))

prune700.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.7b

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

prune82.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 8.7b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
add-cbrt-cube add-exp-log
add-sqr-sqrt pow1 clear-num frac-2neg *-un-lft-identity add-cube-cbrt insert-posit16 div-inv associate-/l* add-log-exp
cbrt-undiv associate-/r* times-frac div-exp associate-*r/ associate-/l/
Calls
2 calls:
Slowest
4.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
2.0ms
(/ (* a c) b)

series64.0ms

Calls
2 calls:
Slowest
33.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
31.0ms
(/ (* a c) b)

simplify1.2s

Calls
11 calls:
Slowest
702.0ms
(/ (* (* (* -2 (/ (* a c) b)) (* -2 (/ (* a c) b))) (* -2 (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
170.0ms
(/ (/ (* a c) b) a)
160.0ms
(- (log (* -2 (/ (* a c) b))) (log (* 2 a)))
28.0ms
(* -2 (* a c))
26.0ms
(* -1 (/ c b))

prune406.0ms

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 8.7b

localize20.0ms

Local error

Found 3 expressions with local error:

0.3b
(/ (* -2 (/ 1 (/ b (* a c)))) (* 2 a))
0.3b
(/ b (* a c))
0.3b
(/ 1 (/ b (* a c)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
associate-/r* add-exp-log
add-cbrt-cube
add-sqr-sqrt pow1 *-un-lft-identity add-cube-cbrt div-inv
clear-num frac-2neg insert-posit16 add-log-exp
associate-/l/
cbrt-undiv rec-exp times-frac div-exp associate-*r/ associate-/r/ un-div-inv pow-flip associate-/l* inv-pow
Calls
3 calls:
Slowest
9.0ms
(/ (* -2 (/ 1 (/ b (* a c)))) (* 2 a))
2.0ms
(/ 1 (/ b (* a c)))
1.0ms
(/ b (* a c))

series91.0ms

Calls
3 calls:
Slowest
40.0ms
(/ 1 (/ b (* a c)))
26.0ms
(/ b (* a c))
25.0ms
(/ (* -2 (/ 1 (/ b (* a c)))) (* 2 a))

simplify1.7s

Calls
20 calls:
Slowest
745.0ms
(/ (* (* (* -2 (/ 1 (/ b (* a c)))) (* -2 (/ 1 (/ b (* a c))))) (* -2 (/ 1 (/ b (* a c))))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
456.0ms
(/ (/ 1 (/ b (* a c))) a)
183.0ms
(- (log (* -2 (/ 1 (/ b (* a c))))) (log (* 2 a)))
28.0ms
(* -1 (/ c b))
27.0ms
(/ 1 (* a c))

prune443.0ms

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 8.7b

regimes765.0ms

Accuracy

48% (7.1b remaining)

Error of 16.2b against oracle of 9.1b and baseline of 22.7b

bsearch16.0ms

end0.0ms

sample5.1s

Algorithm
intervals
Results
1.7s8707×body80nan
1.3s4495×body160valid
1.1s16707×pre80true
589.0ms3505×body80valid