Details

Time bar (total: 48.4s)

sample559.0ms

Algorithm
intervals
Results
380.0ms491×pre80true
41.0ms130×body320valid
25.0ms235×body80nan
17.0ms81×body160valid
6.0ms12×body640valid
3.0ms33×body80valid

simplify177.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
176.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.9b

localize54.0ms

Local error

Found 4 expressions with local error:

24.3b
(- (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)))

rewrite191.0ms

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
123.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
36.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
15.0ms
(- (* b b) (* (* c a) 4))
14.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series471.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
174.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
120.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
119.0ms
(sqrt (- (* b b) (* (* c a) 4)))
57.0ms
(- (* b b) (* (* c a) 4))

simplify5.6s

Counts
49 → 88
Calls
49 calls:
Slowest
621.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
397.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
388.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
368.0ms
(/ (* (* (- (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)))
255.0ms
(- b (* 2 (/ (* a c) b)))

prune1.1s

Pruning

12 alts after pruning (12 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

prune68.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.5b

localize28.0ms

Local error

Found 2 expressions with local error:

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

rewrite47.0ms

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
31.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
15.0ms
(/ (* a c) b)

series61.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
38.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
23.0ms
(/ (* a c) b)

simplify11.1s

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)))
1.4s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.3s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 2) 2) (* (* a a) a)))
1.2s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
917.0ms
(/ (* (* (* -2 (/ (* a c) b)) (* -2 (/ (* a c) b))) (* -2 (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune570.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 2.5b

localize25.0ms

Local error

Found 3 expressions with local error:

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

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
109×times-frac
62×add-cbrt-cube add-exp-log
60×sqrt-prod
50×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
27×cbrt-undiv div-exp
17×prod-exp cbrt-unprod
13×associate-/r*
12×associate-/l*
10×div-inv
3×pow1 clear-num frac-2neg insert-posit16 add-log-exp
2×associate-/l/
1×associate-*r/
Counts
3 → 157
Calls
3 calls:
Slowest
42.0ms
(/ (* -2 (/ (/ (* a c) (sqrt b)) (sqrt b))) (* 2 a))
16.0ms
(/ (* a c) (sqrt b))
12.0ms
(/ (/ (* a c) (sqrt b)) (sqrt b))

series177.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
68.0ms
(/ (* a c) (sqrt b))
60.0ms
(/ (/ (* a c) (sqrt b)) (sqrt b))
49.0ms
(/ (* -2 (/ (/ (* a c) (sqrt b)) (sqrt b))) (* 2 a))

simplify19.8s

Counts
196 → 166
Calls
196 calls:
Slowest
1.8s
(/ (* (* (* -2 -2) -2) (/ (/ (* (* (* a a) a) (* (* c c) c)) (* (* (sqrt b) (sqrt b)) (sqrt b))) (* (* (sqrt b) (sqrt b)) (sqrt b)))) (* (* (* 2 2) 2) (* (* a a) a)))
1.5s
(/ (* (* (* -2 -2) -2) (/ (/ (* (* (* a a) a) (* (* c c) c)) (* (* (sqrt b) (sqrt b)) (sqrt b))) (* (* (sqrt b) (sqrt b)) (sqrt b)))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.4s
(/ (* (* (* -2 -2) -2) (/ (/ (* (* (* a c) (* a c)) (* a c)) (* (* (sqrt b) (sqrt b)) (sqrt b))) (* (* (sqrt b) (sqrt b)) (sqrt b)))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.3s
(/ (* (* (* -2 -2) -2) (/ (/ (* (* (* a c) (* a c)) (* a c)) (* (* (sqrt b) (sqrt b)) (sqrt b))) (* (* (sqrt b) (sqrt b)) (sqrt b)))) (* (* (* 2 2) 2) (* (* a a) a)))
1.0s
(/ (* (* (* -2 (/ (/ (* a c) (sqrt b)) (sqrt b))) (* -2 (/ (/ (* a c) (sqrt b)) (sqrt b)))) (* -2 (/ (/ (* a c) (sqrt b)) (sqrt b)))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune1.6s

Pruning

21 alts after pruning (19 fresh and 2 done)

Merged error: 2.5b

regimes420.0ms

Accuracy

0% (3.7b remaining)

Error of 6.4b against oracle of 2.7b and baseline of 6.4b

bsearch2.0ms

end0.0ms

sample6.2s

Algorithm
intervals
Results
2.0s3623×body320valid
1.3s2878×body160valid
1.1s8234×body80nan
950.0ms16234×pre80true
338.0ms545×body640valid
140.0ms954×body80valid