Details

Time bar (total: 16.6s)

sample155.0ms

Algorithm
intervals
Results
42.0ms152×body160valid
40.0ms231×body80nan
28.0ms487×pre80true
18.0ms45×body320valid
8.0ms59×body80valid

simplify122.0ms

Calls
1 calls:
Slowest
122.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.5b

localize21.0ms

Local error

Found 4 expressions with local error:

39.5b
(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.2b
(- (* b b) (* (* c a) 4))
0.2b
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
0.1b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite53.0ms

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
35.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
13.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
2.0ms
(- (* b b) (* (* c a) 4))
2.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series200.0ms

Calls
4 calls:
Slowest
70.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
55.0ms
(sqrt (- (* b b) (* (* c a) 4)))
49.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
24.0ms
(- (* b b) (* (* c a) 4))

simplify3.7s

Calls
32 calls:
Slowest
614.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
478.0ms
(sqrt (- (pow (* b b) 3) (pow (* (* c a) 4) 3)))
319.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
263.0ms
(- b (* 2 (/ (* a c) b)))
214.0ms
(/ (* (* (- (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)))

prune865.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.5b

localize10.0ms

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

prune53.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 5.5b

localize20.0ms

Local error

Found 2 expressions with local error:

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

rewrite15.0ms

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
9.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
5.0ms
(/ (* a c) b)

series43.0ms

Calls
2 calls:
Slowest
24.0ms
(/ (* a c) b)
18.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))

simplify1.2s

Calls
11 calls:
Slowest
801.0ms
(/ (* (* (* -2 (/ (* a c) b)) (* -2 (/ (* a c) b))) (* -2 (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
162.0ms
(/ (/ (* a c) b) a)
126.0ms
(- (log (* -2 (/ (* a c) b))) (log (* 2 a)))
26.0ms
(* -1 (/ c b))
25.0ms
(/ (* a c) b)

prune397.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 5.5b

localize16.0ms

Local error

Found 2 expressions with local error:

0.3b
(* (* a c) (/ 1 b))
0.2b
(/ (* -2 (* (* a c) (/ 1 b))) (* 2 a))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
6×add-cbrt-cube add-exp-log
4×pow1 associate-*r* associate-*r/
3×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
2×un-div-inv insert-posit16 div-inv add-log-exp associate-/l/
1×cbrt-undiv clear-num associate-/r* frac-2neg times-frac div-exp associate-*l* pow-prod-down prod-exp *-commutative cbrt-unprod associate-/l*
Calls
2 calls:
Slowest
8.0ms
(/ (* -2 (* (* a c) (/ 1 b))) (* 2 a))
8.0ms
(* (* a c) (/ 1 b))

series28.0ms

Calls
2 calls:
Slowest
15.0ms
(/ (* -2 (* (* a c) (/ 1 b))) (* 2 a))
13.0ms
(* (* a c) (/ 1 b))

simplify2.7s

Calls
19 calls:
Slowest
1.3s
(/ (* (* (* -2 (* (* a c) (/ 1 b))) (* -2 (* (* a c) (/ 1 b)))) (* -2 (* (* a c) (/ 1 b)))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
610.0ms
(* (* (* (* a c) (* a c)) (* a c)) (* (* (/ 1 b) (/ 1 b)) (/ 1 b)))
336.0ms
(/ (* (* a c) (/ 1 b)) a)
189.0ms
(- (log (* -2 (* (* a c) (/ 1 b)))) (log (* 2 a)))
82.0ms
(+ (log (* a c)) (log (/ 1 b)))

prune388.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 5.4b

regimes425.0ms

Accuracy

12.7% (5.9b remaining)

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

bsearch42.0ms

end0.0ms

sample6.0s

Algorithm
intervals
Results
2.3s4813×body160valid
1.3s8219×body80nan
1.0s16219×pre80true
754.0ms1398×body320valid
340.0ms1789×body80valid