Details

Time bar (total: 52.6s)

sample147.0ms

Algorithm
intervals
Results
45.0ms544×pre80true
34.0ms150×body160valid
27.0ms288×body80nan
13.0ms43×body320valid
6.0ms63×body80valid

simplify141.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
140.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.3b

localize27.0ms

Local error

Found 4 expressions with local error:

37.9b
(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.2b
(- (* b b) (* (* c a) 4))
0.2b
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
0.1b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite149.0ms

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
68.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
58.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
14.0ms
(sqrt (- (* b b) (* (* c a) 4)))
7.0ms
(- (* b b) (* (* c a) 4))

series399.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
138.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
113.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
97.0ms
(sqrt (- (* b b) (* (* c a) 4)))
51.0ms
(- (* b b) (* (* c a) 4))

simplify12.8s

Counts
105 → 88
Calls
105 calls:
Slowest
570.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
437.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
435.0ms
(sqrt (+ (* (* b b) (* b b)) (+ (* (* (* c a) 4) (* (* c a) 4)) (* (* b b) (* (* c a) 4)))))
414.0ms
(+ (* (* b b) (* b b)) (+ (* (* (* c a) 4) (* (* c a) 4)) (* (* b b) (* (* c a) 4))))
385.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))

prune1.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 5.2b

localize10.0ms

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

prune81.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 5.2b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite35.0ms

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
26.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
8.0ms
(/ (* a c) b)

series58.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
33.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
25.0ms
(/ (* a c) b)

simplify15.8s

Counts
65 → 59
Calls
65 calls:
Slowest
1.4s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) 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 2) 2) (* (* a a) 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 c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
883.0ms
(/ (* (* (* -2 (/ (* a c) b)) (* -2 (/ (* a c) b))) (* -2 (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune535.0ms

Pruning

30 alts after pruning (29 fresh and 1 done)

Merged error: 5.1b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite49.0ms

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
39.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
8.0ms
(/ (* a c) b)

series68.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
34.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
33.0ms
(/ (* a c) b)

simplify15.2s

Counts
65 → 59
Calls
65 calls:
Slowest
1.6s
(/ (* (* (* -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)))
1.3s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.3s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 2 2) 2) (* (* a a) a)))
784.0ms
(/ (* (* (* -2 -2) -2) (* (* (/ (* a c) b) (/ (* a c) b)) (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune428.0ms

Pruning

29 alts after pruning (28 fresh and 1 done)

Merged error: 5.1b

regimes475.0ms

Accuracy

0% (6.6b remaining)

Error of 11.8b against oracle of 5.2b and baseline of 11.8b

bsearch2.0ms

end0.0ms

sample5.1s

Algorithm
intervals
Results
1.7s4893×body160valid
1.0s16340×pre80true
1.0s8340×body80nan
548.0ms1395×body320valid
289.0ms1712×body80valid