Details

Time bar (total: 50.0s)

sample190.0ms

Algorithm
intervals
Results
51.0ms156×body160valid
39.0ms262×body80nan
36.0ms518×pre80true
27.0ms34×body320valid
11.0ms66×body80valid

simplify160.0ms

Calls
1 calls:
Slowest
160.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.7b

localize44.0ms

Local error

Found 4 expressions with local error:

39.3b
(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.2b
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
0.1b
(- (* b b) (* (* c a) 4))
0.1b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite162.0ms

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
99.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
45.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
9.0ms
(- (* b b) (* (* c a) 4))
8.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series404.0ms

Calls
4 calls:
Slowest
131.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
101.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
97.0ms
(sqrt (- (* b b) (* (* c a) 4)))
76.0ms
(- (* b b) (* (* c a) 4))

simplify6.0s

Calls
49 calls:
Slowest
567.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
427.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
334.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
296.0ms
(/ (* (* (- (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)))
279.0ms
(/ (exp (* b b)) (exp (* (* c a) 4)))

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.6b

localize11.0ms

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

prune98.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 4.6b

localize29.0ms

Local error

Found 2 expressions with local error:

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

rewrite39.0ms

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
28.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
10.0ms
(/ (* a c) b)

series65.0ms

Calls
2 calls:
Slowest
38.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
27.0ms
(/ (* a c) b)

simplify12.6s

Calls
37 calls:
Slowest
1.5s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 2) 2) (* (* a a) a)))
1.5s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 2 2) 2) (* (* a a) a)))
1.4s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.4s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.3s
(/ (* (* (* -2 (/ (* a c) b)) (* -2 (/ (* a c) b))) (* -2 (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune551.0ms

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 4.6b

localize26.0ms

Local error

Found 2 expressions with local error:

0.4b
(* (* -2 (/ (* a c) b)) (/ 1 (* 2 a)))
0.3b
(/ (* a c) b)

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
125×add-exp-log
69×prod-exp
61×add-cbrt-cube
32×div-exp
29×cbrt-unprod
16×cbrt-undiv
8×rec-exp 1-exp
7×pow1 associate-*r*
6×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
3×associate-/r* pow-prod-down associate-*r/
2×insert-posit16 div-inv add-log-exp
1×frac-times clear-num frac-2neg associate-*l* associate-*l/ un-div-inv *-commutative associate-/l*
Calls
2 calls:
Slowest
81.0ms
(* (* -2 (/ (* a c) b)) (/ 1 (* 2 a)))
11.0ms
(/ (* a c) b)

series70.0ms

Calls
2 calls:
Slowest
38.0ms
(/ (* a c) b)
32.0ms
(* (* -2 (/ (* a c) b)) (/ 1 (* 2 a)))

simplify21.7s

Calls
72 calls:
Slowest
1.2s
(* (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (/ (* (* 1 1) 1) (* (* (* 2 2) 2) (* (* a a) a))))
1.0s
(* (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (/ (* (* 1 1) 1) (* (* (* 2 a) (* 2 a)) (* 2 a))))
917.0ms
(* (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (/ (* (* 1 1) 1) (* (* (* 2 2) 2) (* (* a a) a))))
905.0ms
(* (* (* (* -2 (/ (* a c) b)) (* -2 (/ (* a c) b))) (* -2 (/ (* a c) b))) (/ (* (* 1 1) 1) (* (* (* 2 a) (* 2 a)) (* 2 a))))
885.0ms
(* (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (/ (* (* 1 1) 1) (* (* (* 2 a) (* 2 a)) (* 2 a))))

prune734.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 4.6b

regimes563.0ms

Accuracy

6.2% (6.4b remaining)

Error of 11.5b against oracle of 5.2b and baseline of 12.0b

bsearch38.0ms

end0.0ms

sample5.3s

Algorithm
intervals
Results
1.5s8248×body80nan
1.4s4865×body160valid
1.0s16248×pre80true
660.0ms1348×body320valid
372.0ms1787×body80valid