Details

Time bar (total: 25.8s)

sample81.0ms

Algorithm
intervals
Results
48.0ms271×body80valid
14.0ms106×body80nan

simplify253.0ms

Calls
1 calls:
Slowest
253.0ms
(if (>= b 0) (/ (* 2 c) (- (- b) (sqrt (- (* b b) (* (* 4 a) c))))) (/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a)))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.8b

localize156.0ms

Local error

Found 4 expressions with local error:

26.1b
(sqrt (- (* b b) (* (* 4 a) c)))
26.1b
(sqrt (- (* b b) (* (* 4 a) c)))
1.1b
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
0.6b
(- (* b b) (* (* 4 a) c))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt *-un-lft-identity add-log-exp
6×add-cube-cbrt sqrt-prod
4×pow1 add-cbrt-cube sqrt-div add-exp-log insert-posit16
3×flip3-- flip--
2×rem-sqrt-square pow1/2
1×neg-sub0 +-commutative sum-log sub-neg flip3-+ diff-log associate-+l- flip-+ distribute-lft-out
Calls
4 calls:
Slowest
7.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
5.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
3.0ms
(- (* b b) (* (* 4 a) c))
2.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series196.0ms

Calls
4 calls:
Slowest
66.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
52.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
42.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
36.0ms
(- (* b b) (* (* 4 a) c))

simplify3.4s

Calls
27 calls:
Slowest
596.0ms
(sqrt (- (pow (* b b) 3) (pow (* (* 4 a) c) 3)))
551.0ms
(sqrt (- (pow (* b b) 3) (pow (* (* 4 a) c) 3)))
294.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* 4 a) c) (* (* 4 a) c))))
240.0ms
(- b (* 2 (/ (* a c) b)))
239.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* 4 a) c) (* (* 4 a) c))))

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.8b

localize115.0ms

Local error

Found 4 expressions with local error:

26.1b
(sqrt (- (* b b) (* (* 4 a) c)))
26.1b
(sqrt (- (* b b) (* (* 4 a) c)))
26.1b
(sqrt (- (* b b) (* (* 4 a) c)))
8.1b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
7×*-un-lft-identity add-cube-cbrt
6×sqrt-div add-log-exp
4×pow1 flip3-- add-cbrt-cube add-exp-log insert-posit16 flip--
3×rem-sqrt-square pow1/2
1×associate--l- neg-sub0 sub-neg diff-log difference-of-squares
Calls
4 calls:
Slowest
4.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
3.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
2.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
2.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series214.0ms

Calls
4 calls:
Slowest
64.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
61.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
49.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
39.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify4.5s

Calls
33 calls:
Slowest
602.0ms
(sqrt (- (pow (* b b) 3) (pow (* (* 4 a) c) 3)))
567.0ms
(sqrt (- (pow (* b b) 3) (pow (* (* 4 a) c) 3)))
515.0ms
(sqrt (- (pow (* b b) 3) (pow (* (* 4 a) c) 3)))
294.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* 4 a) c) (* (* 4 a) c))))
274.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* 4 a) c) (* (* 4 a) c))))

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.2b

localize146.0ms

Local error

Found 4 expressions with local error:

26.1b
(sqrt (- (* b b) (* (* 4 a) c)))
4.5b
(* a (/ c b))
2.8b
(/ (* 2 c) (* (- (* a (/ c b)) b) 2))
1.1b
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
8×*-un-lft-identity
7×add-sqr-sqrt
6×add-cbrt-cube add-exp-log add-cube-cbrt add-log-exp
4×pow1 associate-*r* insert-posit16
3×sqrt-prod
2×flip3-- sqrt-div associate-*l/ associate-/r/ div-inv flip--
1×neg-sub0 cbrt-undiv +-commutative rem-sqrt-square clear-num associate-/r* sum-log frac-2neg flip3-+ times-frac pow1/2 div-exp associate-*r/ *-commutative associate-+l- flip-+ distribute-lft-out associate-/l*
Calls
4 calls:
Slowest
13.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
12.0ms
(/ (* 2 c) (* (- (* a (/ c b)) b) 2))
4.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
2.0ms
(* a (/ c b))

series166.0ms

Calls
4 calls:
Slowest
57.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
56.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
38.0ms
(/ (* 2 c) (* (- (* a (/ c b)) b) 2))
16.0ms
(* a (/ c b))

simplify3.5s

Calls
30 calls:
Slowest
682.0ms
(- b (* 2 (/ (* a c) b)))
585.0ms
(/ (* (* (* 2 c) (* 2 c)) (* 2 c)) (* (* (* (- (* a (/ c b)) b) 2) (* (- (* a (/ c b)) b) 2)) (* (- (* a (/ c b)) b) 2)))
528.0ms
(sqrt (- (pow (* b b) 3) (pow (* (* 4 a) c) 3)))
261.0ms
(- (log (* 2 c)) (log (* (- (* a (/ c b)) b) 2)))
256.0ms
(+ (* (* a (/ c b)) (* a (/ c b))) (+ (* b b) (* (* a (/ c b)) b)))

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.2b

localize137.0ms

Local error

Found 4 expressions with local error:

26.1b
(sqrt (- (* b b) (* (* 4 a) c)))
17.4b
(cbrt (* a (/ c b)))
17.4b
(cbrt (* a (/ c b)))
17.4b
(cbrt (* a (/ c b)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×*-un-lft-identity add-cube-cbrt
4×pow1 add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×cbrt-prod cbrt-div pow1/3 associate-*r/ sqrt-prod
2×sqrt-div
1×rem-sqrt-square flip3-- pow1/2 flip--
Calls
4 calls:
Slowest
5.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
1.0ms
(cbrt (* a (/ c b)))
1.0ms
(cbrt (* a (/ c b)))
1.0ms
(cbrt (* a (/ c b)))

series297.0ms

Calls
4 calls:
Slowest
87.0ms
(cbrt (* a (/ c b)))
84.0ms
(cbrt (* a (/ c b)))
76.0ms
(cbrt (* a (/ c b)))
49.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify3.8s

Calls
24 calls:
Slowest
545.0ms
(sqrt (- (pow (* b b) 3) (pow (* (* 4 a) c) 3)))
347.0ms
(exp (* 1/3 (- (log (/ 1 b)) (+ (log (/ 1 a)) (log (/ 1 c))))))
325.0ms
(* (exp (* 1/3 (- (log (/ -1 b)) (+ (log (/ -1 c)) (log (/ -1 a)))))) (cbrt -1))
318.0ms
(* (exp (* 1/3 (- (log (/ -1 b)) (+ (log (/ -1 c)) (log (/ -1 a)))))) (cbrt -1))
306.0ms
(exp (* 1/3 (- (log (/ 1 b)) (+ (log (/ 1 a)) (log (/ 1 c))))))

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.2b

regimes462.0ms

Accuracy

93.9% (0.9b remaining)

Error of 6.3b against oracle of 5.4b and baseline of 20.6b

bsearch252.0ms

end0.0ms

sample3.3s

Algorithm
intervals
Results
2.4s8680×body80valid
596.0ms2865×body80nan