Details

Time bar (total: 1.1m)

sample159.0ms

Algorithm
intervals
Results
38.0ms304×body80nan
38.0ms135×body160valid
33.0ms560×pre80true
21.0ms121×body80valid

simplify205.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
204.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.9b

localize20.0ms

Local error

Found 4 expressions with local error:

26.8b
(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.3b
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
0.2b
(- (* b b) (* (* c a) 4))
0.1b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite137.0ms

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))
34.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
7.0ms
(sqrt (- (* b b) (* (* c a) 4)))
7.0ms
(- (* b b) (* (* c a) 4))

series448.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
136.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
131.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
104.0ms
(sqrt (- (* b b) (* (* c a) 4)))
77.0ms
(- (* b b) (* (* c a) 4))

simplify12.7s

Counts
105 → 88
Calls
105 calls:
Slowest
641.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
472.0ms
(+ (* (* b b) (* b b)) (+ (* (* (* c a) 4) (* (* c a) 4)) (* (* b b) (* (* c a) 4))))
416.0ms
(- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4)))
388.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
388.0ms
(sqrt (+ (* (* b b) (* b b)) (+ (* (* (* c a) 4) (* (* c a) 4)) (* (* b b) (* (* c a) 4)))))

prune1.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.2b

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

prune76.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 10.2b

localize35.0ms

Local error

Found 2 expressions with local error:

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

rewrite27.0ms

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))
10.0ms
(/ (* a c) b)

series59.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
34.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
25.0ms
(/ (* a c) b)

simplify16.0s

Counts
65 → 59
Calls
65 calls:
Slowest
1.3s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.3s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) 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 2) 2) (* (* a a) a)))
962.0ms
(/ (* (* (* -2 (/ (* a c) b)) (* -2 (/ (* a c) b))) (* -2 (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune635.0ms

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 10.1b

localize18.0ms

Local error

Found 3 expressions with local error:

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

rewrite73.0ms

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
35.0ms
(/ (* -2 (/ (/ (* a c) (sqrt b)) (sqrt b))) (* 2 a))
22.0ms
(/ (/ (* a c) (sqrt b)) (sqrt b))
13.0ms
(/ (* a c) (sqrt b))

series219.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
77.0ms
(/ (/ (* a c) (sqrt b)) (sqrt b))
72.0ms
(/ (* -2 (/ (/ (* a c) (sqrt b)) (sqrt b))) (* 2 a))
70.0ms
(/ (* a c) (sqrt b))

simplify27.3s

Counts
236 → 166
Calls
236 calls:
Slowest
2.0s
(/ (* (* (* -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)))
1.4s
(/ (* (* (* -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)))
1.4s
(/ (* (* (* -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)))
1.3s
(/ (* (* (* -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 -2) -2) (/ (* (* (/ (* a c) (sqrt b)) (/ (* a c) (sqrt b))) (/ (* a c) (sqrt b))) (* (* (sqrt b) (sqrt b)) (sqrt b)))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune1.6s

Pruning

32 alts after pruning (31 fresh and 1 done)

Merged error: 10.1b

regimes726.0ms

Accuracy

42.5% (7.5b remaining)

Error of 16.8b against oracle of 9.3b and baseline of 22.4b

bsearch21.0ms

end0.0ms

sample5.4s

Algorithm
intervals
Results
1.8s4540×body160valid
1.4s16420×pre80true
1.2s8420×body80nan
510.0ms3460×body80valid