Details

simplify18.6m

Calls

10028 calls:

Slowest
3.2s
(/ (/ (* (* (* (/ 1 sin) (cos (* 2 x))) (* (/ 1 sin) (cos (* 2 x)))) (* (/ 1 sin) (cos (* 2 x)))) (* (* (* x cos) (* x cos)) (* x cos))) (* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos))))
3.2s
(/ (* (/ (* (* 1 1) 1) (* (* sin sin) sin)) (/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* x cos) (* x cos)) (* x cos)))) (* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos))))
3.1s
(/ (/ (* (* (* (/ 1 sin) (/ 1 sin)) (/ 1 sin)) (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x)))) (* (* (* x x) x) (* (* cos cos) cos))) (* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos))))
3.0s
(/ (* (* (* (/ 1 sin) (/ 1 sin)) (/ 1 sin)) (/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* x cos) (* x cos)) (* x cos)))) (* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos))))
2.9s
(/ (* (* (* (- (* a (/ c b)) b) (- (* a (/ c b)) b)) (- (* a (/ c b)) b)) (* (* 2 2) 2)) (* (* (* 2 a) (* 2 a)) (* 2 a)))

sample3.5m

Algorithm
60×intervals
Results
1.6m335738×body80valid
32.3s209020×body80nan
30.1s21438×body1280valid
12.1s10867×body640valid
6.7s5455×body2560valid
4.5s5172×body320valid
1.5s2570×body160valid
1.3s16512×pre80true
281.0ms219×body5120valid

prune3.2m

series53.9s

Calls

345 calls:

Slowest
726.0ms
(* (/ (/ (- y z) (* (cbrt (- (+ t 1.0) z)) (cbrt (- (+ t 1.0) z)))) (cbrt (- (+ t 1.0) z))) (- a x))
652.0ms
(/ (+ (* (+ (* (* (+ (* (+ (* x y) z) y) 27464.7644705) (* (cbrt y) (cbrt y))) (cbrt y)) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
604.0ms
(* (/ (- y z) (- (+ t 1.0) z)) (- a x))
582.0ms
(cbrt (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (cbrt y)))
570.0ms
(/ (* 2 a) (- (sqrt (- (* b b) (* (* c a) 4))) b))

regimes29.9s

Accuracy

Total 37.4b remaining (24.7%)

8.8b-25.4%Linear.Matrix:det44 from linear-1.19.1.3
4.3b84.7%The quadratic formula (r1)
3.6b2%Linear.Matrix:det33 from linear-1.19.1.3
3.0b0%Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2
2.6b40.7%Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1

rewrite15.1s

Algorithm
101×rewrite-expression-head
Calls

345 calls:

Slowest
607.0ms
(* (- (/ y (- (+ t 1.0) z)) (/ z (- (+ t 1.0) z))) (- a x))
345.0ms
(* (/ (* (cbrt (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t)) (cbrt (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t))) 1) (/ (cbrt (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t)) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))
319.0ms
(/ (+ (* (+ (* (* (+ (* (+ (* x y) z) y) 27464.7644705) (* (cbrt y) (cbrt y))) (cbrt y)) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
316.0ms
(* (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (/ 1 (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))
256.0ms
(+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (+ (- (log z) t) (* (- a 0.5) (log t)))))
Rules
4101×*-un-lft-identity
3816×add-sqr-sqrt
3712×times-frac
2463×add-cube-cbrt
1934×add-exp-log
1740×cbrt-prod
1504×add-cbrt-cube
1059×pow1
926×associate-*l*
817×associate-*r*
694×prod-exp
647×distribute-rgt-neg-in
563×distribute-lft-neg-in
554×add-log-exp
528×cbrt-unprod
454×div-exp
442×distribute-lft-out--
423×sqrt-prod
391×swap-sqr
380×flip3-- flip--
377×frac-times
352×difference-of-squares
350×sqrt-div
346×associate-*r/
344×insert-posit16
328×pow-prod-down
317×cbrt-undiv
295×distribute-lft-out
280×associate-/r*
279×associate-*l/
266×cbrt-div
253×unswap-sqr
235×associate-/l*
224×associate-/r/
172×div-inv
153×neg-mul-1
150×flip-+ flip3-+
146×div-sub
142×neg-sub0
134×distribute-frac-neg
130×pow-neg
129×pow-sub
127×sub-neg
121×frac-sub
116×distribute-rgt-in distribute-lft-in
112×*-commutative
108×tan-quot
99×pow-prod-up
98×log-prod
96×pow1/3 unpow-prod-down
95×frac-add
81×pow-unpow
79×sqrt-pow1 pow1/2 pow-sqr
69×associate-/l/ diff-log
64×frac-2neg clear-num exp-prod
58×1-exp
56×sum-log
50×associate-+r+
48×rec-exp
43×sqr-pow
39×associate-+l+ exp-sum
35×log-pow
34×pow-plus
28×pow2
27×log-div
26×associate--l+ sin-mult
23×rem-exp-log rem-sqrt-square
22×cos-mult
21×+-commutative associate-+l-
20×pow-flip associate--r+
19×exp-diff
17×sub-div
16×pow-pow
14×pow-exp inv-pow
13×pow-to-exp
10×distribute-neg-frac
neg-log
associate-+r- sqrt-unprod
associate--l- distribute-rgt-out--
un-div-inv
cos-2 distribute-neg-in
unpow2 rem-square-sqrt
unpow-prod-up difference-of-sqr-1 tan-sum cos-sum rem-log-exp
remove-posit16 unpow1/2 exp-to-pow exp-neg associate--r- distribute-rgt-out

localize5.9s

bsearch5.8s

end1.0ms