Details

Time bar (total: 3.0m)

sample285.0ms

Algorithm
intervals
Results
65.0ms298×body80nan
45.0ms112×body320valid
34.0ms554×pre80true
23.0ms93×body160valid
9.0ms17×body640valid
4.0ms34×body80valid

simplify180.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
180.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.7b

localize39.0ms

Local error

Found 4 expressions with local error:

28.6b
(- (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)))

rewrite170.0ms

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
88.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
51.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
15.0ms
(sqrt (- (* b b) (* (* c a) 4)))
13.0ms
(- (* b b) (* (* c a) 4))

series481.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
160.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
134.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
107.0ms
(sqrt (- (* b b) (* (* c a) 4)))
80.0ms
(- (* b b) (* (* c a) 4))

simplify5.4s

Counts
49 → 88
Calls
49 calls:
Slowest
629.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
382.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
307.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
294.0ms
(/ (* (* (- (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)))
284.0ms
(- b (* 2 (/ (* a c) b)))

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.9b

localize12.0ms

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

prune79.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.9b

localize29.0ms

Local error

Found 2 expressions with local error:

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

rewrite30.0ms

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
19.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
10.0ms
(/ (* a c) b)

series66.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
34.0ms
(/ (* a c) b)
32.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))

simplify12.1s

Counts
37 → 59
Calls
37 calls:
Slowest
1.4s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) 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 (/ (* a c) b)) (* -2 (/ (* a c) b))) (* -2 (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.3s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune558.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 2.8b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- (* (* (/ a (* a (/ b c))) (/ a (* a (/ b c)))) (/ a (* a (/ b c))))))
0.4b
(* (/ a (* a (/ b c))) (/ a (* a (/ b c))))
0.3b
(* (* (/ a (* a (/ b c))) (/ a (* a (/ b c)))) (/ a (* a (/ b c))))
0.3b
(* a (/ b c))

rewrite300.0ms

Algorithm
rewrite-expression-head
Rules
583×add-cbrt-cube add-exp-log
264×prod-exp cbrt-unprod
229×cbrt-undiv div-exp
32×pow1
31×add-sqr-sqrt
29×associate-*r*
25×times-frac
23×*-un-lft-identity add-cube-cbrt
13×associate-*r/
12×associate-*l*
11×frac-times associate-*l/
8×swap-sqr
7×cbrt-div pow-plus pow-prod-up distribute-neg-frac
6×cbrt-prod div-inv
5×pow-prod-down associate-/r/
4×insert-posit16 add-log-exp unswap-sqr
3×pow2 pow-sqr *-commutative
1×distribute-lft-neg-in neg-mul-1 distribute-rgt-neg-in pow1/3 pow3
Counts
4 → 302
Calls
4 calls:
Slowest
207.0ms
(* (* (/ a (* a (/ b c))) (/ a (* a (/ b c)))) (/ a (* a (/ b c))))
56.0ms
(* (/ a (* a (/ b c))) (/ a (* a (/ b c))))
14.0ms
(* a (/ b c))
6.0ms
(cbrt (- (* (* (/ a (* a (/ b c))) (/ a (* a (/ b c)))) (/ a (* a (/ b c))))))

series288.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
99.0ms
(cbrt (- (* (* (/ a (* a (/ b c))) (/ a (* a (/ b c)))) (/ a (* a (/ b c))))))
89.0ms
(* (* (/ a (* a (/ b c))) (/ a (* a (/ b c)))) (/ a (* a (/ b c))))
68.0ms
(* (/ a (* a (/ b c))) (/ a (* a (/ b c))))
32.0ms
(* a (/ b c))

simplify2.5m

Counts
293 → 314
Calls
293 calls:
Slowest
3.1s
(* (* (/ (* (* a a) a) (* (* (* a a) a) (* (* (/ b c) (/ b c)) (/ b c)))) (/ (* (* a a) a) (* (* (* a (/ b c)) (* a (/ b c))) (* a (/ b c))))) (/ (* (* a a) a) (* (* (* a a) a) (* (* (/ b c) (/ b c)) (/ b c)))))
3.0s
(* (* (/ (* (* a a) a) (* (* (* a (/ b c)) (* a (/ b c))) (* a (/ b c)))) (/ (* (* a a) a) (* (* (* a a) a) (* (* (/ b c) (/ b c)) (/ b c))))) (/ (* (* a a) a) (* (* (* a (/ b c)) (* a (/ b c))) (* a (/ b c)))))
2.6s
(* (* (/ (* (* a a) a) (* (* (* a a) a) (* (* (/ b c) (/ b c)) (/ b c)))) (/ (* (* a a) a) (* (* (* a (/ b c)) (* a (/ b c))) (* a (/ b c))))) (/ (* (* a a) a) (* (* (* a (/ b c)) (* a (/ b c))) (* a (/ b c)))))
2.5s
(* (* (/ (* (* a a) a) (* (* (* a a) a) (* (* (/ b c) (/ b c)) (/ b c)))) (/ (* (* a a) a) (* (* (* a a) a) (* (* (/ b c) (/ b c)) (/ b c))))) (/ (* (* a a) a) (* (* (* a (/ b c)) (* a (/ b c))) (* a (/ b c)))))
2.5s
(* (* (/ (* (* a a) a) (* (* (* a a) a) (* (* (/ b c) (/ b c)) (/ b c)))) (* (* (/ a (* a (/ b c))) (/ a (* a (/ b c)))) (/ a (* a (/ b c))))) (/ (* (* a a) a) (* (* (* a (/ b c)) (* a (/ b c))) (* a (/ b c)))))

prune2.8s

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 2.8b

regimes573.0ms

Accuracy

0% (3.5b remaining)

Error of 6.3b against oracle of 2.7b and baseline of 6.3b

bsearch2.0ms

end0.0ms

sample6.1s

Algorithm
intervals
Results
1.5s3616×body320valid
1.4s16229×pre80true
1.0s8229×body80nan
838.0ms2990×body160valid
303.0ms458×body640valid
112.0ms936×body80valid