Details

Time bar (total: 1.3m)

sample479.0ms

Algorithm
intervals
Results
90.0ms102×body320valid
48.0ms277×body80nan
43.0ms533×pre80true
40.0ms115×body160valid
12.0ms17×body640valid
4.0ms22×body80valid

simplify318.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
317.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.2b

localize63.0ms

Local error

Found 4 expressions with local error:

30.4b
(- (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))
0.1b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite163.0ms

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
76.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
60.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
15.0ms
(sqrt (- (* b b) (* (* c a) 4)))
8.0ms
(- (* b b) (* (* c a) 4))

series492.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
155.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
142.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
113.0ms
(sqrt (- (* b b) (* (* c a) 4)))
81.0ms
(- (* b b) (* (* c a) 4))

simplify13.1s

Counts
105 → 88
Calls
105 calls:
Slowest
589.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
447.0ms
(sqrt (- (* b b) (* (* c a) 4)))
405.0ms
(/ (* (* (- (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)))
394.0ms
(- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4)))
386.0ms
(+ (* (* b b) (* b b)) (+ (* (* (* c a) 4) (* (* c a) 4)) (* (* b b) (* (* c a) 4))))

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.5b

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

prune58.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.5b

localize16.0ms

Local error

Found 2 expressions with local error:

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

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/
Counts
2 → 53
Calls
2 calls:
Slowest
21.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
17.0ms
(/ (* a c) b)

series57.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
33.0ms
(/ (* a c) b)
24.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))

simplify15.5s

Counts
65 → 59
Calls
65 calls:
Slowest
1.2s
(/ (* (* (* -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 a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 2 2) 2) (* (* a a) a)))
1.2s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 2) 2) (* (* a a) a)))
812.0ms
(/ (* (* (* -2 (/ (* a c) b)) (* -2 (/ (* a c) b))) (* -2 (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune620.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 2.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ a (sqrt b)) (/ c (sqrt b)))
0.3b
(/ a (sqrt b))
0.2b
(/ c (sqrt b))
0.2b
(/ (* -2 (* (/ a (sqrt b)) (/ c (sqrt b)))) (* 2 a))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
90×add-sqr-sqrt
85×times-frac
76×add-cbrt-cube add-exp-log
60×*-un-lft-identity add-cube-cbrt
48×sqrt-prod
28×prod-exp cbrt-unprod
26×cbrt-undiv div-exp
22×associate-*r* associate-*l*
13×associate-/r*
9×unswap-sqr
7×associate-/l*
6×pow1
5×associate-*r/ div-inv
4×insert-posit16 add-log-exp
3×clear-num frac-2neg associate-/l/
2×frac-times associate-*l/
1×pow-prod-down *-commutative
Counts
4 → 195
Calls
4 calls:
Slowest
44.0ms
(/ (* -2 (* (/ a (sqrt b)) (/ c (sqrt b)))) (* 2 a))
39.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))
5.0ms
(/ a (sqrt b))
5.0ms
(/ c (sqrt b))

series236.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
78.0ms
(/ c (sqrt b))
69.0ms
(/ a (sqrt b))
51.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))
37.0ms
(/ (* -2 (* (/ a (sqrt b)) (/ c (sqrt b)))) (* 2 a))

simplify36.3s

Counts
256 → 207
Calls
256 calls:
Slowest
1.9s
(/ (* (* (* -2 -2) -2) (* (* (* (/ a (sqrt b)) (/ a (sqrt b))) (/ a (sqrt b))) (* (* (/ c (sqrt b)) (/ c (sqrt b))) (/ c (sqrt b))))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.7s
(/ (* (* (* -2 -2) -2) (* (/ (* (* a a) a) (* (* (sqrt b) (sqrt b)) (sqrt b))) (* (* (/ c (sqrt b)) (/ c (sqrt b))) (/ c (sqrt b))))) (* (* (* 2 2) 2) (* (* a a) a)))
1.6s
(/ (* (* (* -2 (* (/ a (sqrt b)) (/ c (sqrt b)))) (* -2 (* (/ a (sqrt b)) (/ c (sqrt b))))) (* -2 (* (/ a (sqrt b)) (/ c (sqrt b))))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.6s
(/ (* (* (* -2 -2) -2) (* (* (* (/ a (sqrt b)) (/ a (sqrt b))) (/ a (sqrt b))) (* (* (/ c (sqrt b)) (/ c (sqrt b))) (/ c (sqrt b))))) (* (* (* 2 2) 2) (* (* a a) a)))
1.6s
(/ (* (* (* -2 -2) -2) (* (* (* (/ a (sqrt b)) (/ a (sqrt b))) (/ a (sqrt b))) (/ (* (* c c) c) (* (* (sqrt b) (sqrt b)) (sqrt b))))) (* (* (* 2 2) 2) (* (* a a) a)))

prune2.1s

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 2.4b

regimes504.0ms

Accuracy

0% (3.3b remaining)

Error of 6.0b against oracle of 2.7b and baseline of 6.0b

bsearch1.0ms

end0.0ms

sample6.8s

Algorithm
intervals
Results
1.8s3698×body320valid
1.3s2911×body160valid
1.2s8296×body80nan
1.1s16296×pre80true
764.0ms521×body640valid
151.0ms870×body80valid