Details

Time bar (total: 42.9s)

sample317.0ms

Algorithm
intervals
Results
50.0ms90×body160valid
45.0ms115×body320valid
32.0ms240×body80nan
30.0ms496×pre80true
9.0ms17×body640valid
5.0ms34×body80valid

simplify168.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
167.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.5b

localize30.0ms

Local error

Found 4 expressions with local error:

24.7b
(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.1b
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
0.1b
(- (* b b) (* (* c a) 4))
0.0b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite182.0ms

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
87.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
64.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
14.0ms
(- (* b b) (* (* c a) 4))
14.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series453.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
153.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
131.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
118.0ms
(sqrt (- (* b b) (* (* c a) 4)))
51.0ms
(- (* b b) (* (* c a) 4))

simplify5.7s

Counts
49 → 88
Calls
49 calls:
Slowest
610.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
406.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
344.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
326.0ms
(/ (* (* (- (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)))
268.0ms
(- b (* 2 (/ (* a c) b)))

prune989.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.5b

localize6.0ms

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

prune74.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.5b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite26.0ms

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))
8.0ms
(/ (* a c) b)

series64.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
42.0ms
(/ (* a c) b)
22.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))

simplify12.4s

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

prune499.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 2.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))
0.3b
(/ (* -2 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) (* 2 a))
0.2b
(/ (* a c) b)
0.2b
(/ (* a c) b)

rewrite173.0ms

Algorithm
rewrite-expression-head
Rules
37×add-cbrt-cube add-exp-log
34×sqrt-prod
32×add-sqr-sqrt
20×*-un-lft-identity add-cube-cbrt
19×pow1 times-frac
12×swap-sqr prod-exp cbrt-unprod
10×cbrt-undiv div-exp associate-*r* associate-*l*
8×sqrt-pow1 pow1/2 sqrt-div
7×associate-/r* div-inv
5×associate-*r/ pow-prod-up
4×insert-posit16 add-log-exp unswap-sqr
3×clear-num frac-2neg pow-prod-down pow-sqr associate-/l* associate-/l/
2×frac-times associate-*l/
1×pow2 rem-square-sqrt pow-plus sqrt-unprod *-commutative
Counts
4 → 138
Calls
4 calls:
Slowest
104.0ms
(/ (* -2 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) (* 2 a))
34.0ms
(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))
17.0ms
(/ (* a c) b)
15.0ms
(/ (* a c) b)

series191.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
86.0ms
(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))
54.0ms
(/ (* -2 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) (* 2 a))
29.0ms
(/ (* a c) b)
22.0ms
(/ (* a c) b)

simplify13.0s

Counts
133 → 150
Calls
133 calls:
Slowest
1.2s
(/ (* (* (* -2 -2) -2) (* (* (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))) (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.1s
(/ (* (* (* -2 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) (* -2 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))))) (* -2 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.0s
(/ (* (* (* -2 -2) -2) (* (* (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))) (sqrt (/ (* a c) b))) (* (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))) (sqrt (/ (* a c) b))))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.0s
(/ (* (* (* -2 -2) -2) (* (* (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))) (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))))) (* (* (* 2 2) 2) (* (* a a) a)))
978.0ms
(/ (* (* (* -2 -2) -2) (* (* (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))) (sqrt (/ (* a c) b))) (* (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))) (sqrt (/ (* a c) b))))) (* (* (* 2 2) 2) (* (* a a) a)))

prune1.5s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 2.5b

regimes409.0ms

Accuracy

0% (3.5b remaining)

Error of 6.2b against oracle of 2.7b and baseline of 6.2b

bsearch2.0ms

end0.0ms

sample6.7s

Algorithm
intervals
Results
1.7s3561×body320valid
1.5s16290×pre80true
1.3s8290×body80nan
1.3s3021×body160valid
350.0ms527×body640valid
119.0ms891×body80valid