Details

Time bar (total: 48.1s)

sample403.0ms

Algorithm
intervals
Results
81.0ms90×body160valid
56.0ms115×body320valid
42.0ms262×body80nan
40.0ms518×pre80true
11.0ms18×body640valid
5.0ms33×body80valid

simplify212.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
211.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune60.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.3b

localize52.0ms

Local error

Found 4 expressions with local error:

26.2b
(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.1b
(- (* b b) (* (* c a) 4))
0.1b
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
0.0b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite241.0ms

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
Counts
4 → 76
Calls
4 calls:
Slowest
101.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
85.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
13.0ms
(sqrt (- (* b b) (* (* c a) 4)))
8.0ms
(- (* b b) (* (* c a) 4))

series710.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
255.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
220.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
124.0ms
(sqrt (- (* b b) (* (* c a) 4)))
105.0ms
(- (* b b) (* (* c a) 4))

simplify5.4s

Counts
49 → 88
Calls
49 calls:
Slowest
648.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
418.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
355.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
289.0ms
(/ (* (* (- (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)))
248.0ms
(- b (* 2 (/ (* a c) b)))

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.6b

localize5.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0
Calls
0 calls:
Slowest

series0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

simplify0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

prune44.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.6b

localize29.0ms

Local error

Found 2 expressions with local error:

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

rewrite28.0ms

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/
Counts
2 → 53
Calls
2 calls:
Slowest
17.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
11.0ms
(/ (* a c) b)

series72.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
37.0ms
(/ (* a c) b)
34.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))

simplify11.6s

Counts
37 → 59
Calls
37 calls:
Slowest
1.4s
(/ (* (* (* -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)))
1.2s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.2s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 2) 2) (* (* a a) a)))
893.0ms
(/ (* (* (* -2 (/ (* a c) b)) (* -2 (/ (* a c) b))) (* -2 (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune583.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 2.5b

localize31.0ms

Local error

Found 2 expressions with local error:

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

rewrite121.0ms

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*
Counts
2 → 85
Calls
2 calls:
Slowest
101.0ms
(* (* -2 (/ (* a c) b)) (/ 1 (* 2 a)))
17.0ms
(/ (* a c) b)

series55.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
33.0ms
(* (* -2 (/ (* a c) b)) (/ 1 (* 2 a)))
21.0ms
(/ (* a c) b)

simplify19.7s

Counts
72 → 91
Calls
72 calls:
Slowest
1.3s
(* (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (/ (* (* 1 1) 1) (* (* (* 2 2) 2) (* (* a a) a))))
1.2s
(* (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (/ (* (* 1 1) 1) (* (* (* 2 2) 2) (* (* a a) a))))
956.0ms
(* (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (/ (* (* 1 1) 1) (* (* (* 2 a) (* 2 a)) (* 2 a))))
919.0ms
(* (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (/ (* (* 1 1) 1) (* (* (* 2 a) (* 2 a)) (* 2 a))))
768.0ms
(* (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (/ 1 (* 2 a)) (/ 1 (* 2 a))) (/ 1 (* 2 a))))

prune744.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 2.5b

regimes315.0ms

Accuracy

0% (3.3b remaining)

Error of 5.9b against oracle of 2.6b and baseline of 5.9b

bsearch1.0ms

end0.0ms

sample6.6s

Algorithm
intervals
Results
1.7s3681×body320valid
1.4s16277×pre80true
1.3s8277×body80nan
964.0ms2934×body160valid
771.0ms524×body640valid
116.0ms861×body80valid