Details

simplify9.5m

Calls

4953 calls:

Slowest
1.7s
(* (* (* (* (+ (+ (* x y) (* z t)) (* a b)) (+ (+ (* x y) (* z t)) (* a b))) (* (+ (+ (* x y) (* z t)) (* a b)) (+ (+ (* x y) (* z t)) (* a b)))) (* (+ (+ (* x y) (* z t)) (* a b)) (+ (+ (* x y) (* z t)) (* a b)))) (* (* (+ (+ (* x y) (* z t)) (* a b)) (+ (+ (* x y) (* z t)) (* a b))) (+ (+ (* x y) (* z t)) (* a b))))
1.2s
(* (/ (* (* (sin b) (sin b)) (sin b)) (* (* (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))) (* (* (+ (* (cos a) (cos b)) (* (sin a) (sin b))) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))))
1.2s
(sqrt (- (pow (* b b) 3) (pow (* (* 4 a) c) 3)))
1.1s
(sqrt (- (pow (* b b) 3) (pow (* (* 4 a) c) 3)))
1.1s
(* (* (* (* (+ (+ (* x y) (* z t)) (* a b)) (+ (+ (* x y) (* z t)) (* a b))) (+ (+ (* x y) (* z t)) (* a b))) (* (* (+ (+ (* x y) (* z t)) (* a b)) (+ (+ (* x y) (* z t)) (* a b))) (+ (+ (* x y) (* z t)) (* a b)))) (* (* (+ (+ (* x y) (* z t)) (* a b)) (+ (+ (* x y) (* z t)) (* a b))) (+ (+ (* x y) (* z t)) (* a b))))

sample3.4m

Algorithm
58×intervals
Results
1.5m327065×body80valid
37.6s200643×body80nan
28.6s21187×body1280valid
12.6s11106×body640valid
6.0s5384×body2560valid
4.2s5029×body320valid
1.6s2503×body160valid
1.1s16512×pre80true
268.0ms226×body5120valid

prune2.5m

series41.6s

Calls

334 calls:

Slowest
3.4s
(* (* (+ (+ (* x y) (* z t)) (* a b)) (+ (+ (* x y) (* z t)) (* a b))) (+ (+ (* x y) (* z t)) (* a b)))
1.1s
(cbrt (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
553.0ms
(/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (* (cbrt (* (+ (* (+ y a) y) b) y)) (* (cbrt (+ (* (+ y a) y) b)) (cbrt y))) (cbrt (* (+ (* (+ y a) y) b) y))) c) y) i))
535.0ms
(/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (* (cbrt (* (+ (* (+ y a) y) b) y)) (cbrt (* (+ (* (+ y a) y) b) y))) (cbrt (* (+ (* (+ y a) y) b) y))) c) y) i))
445.0ms
(exp (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))

regimes28.9s

Accuracy

Total 33.5b remaining (25%)

10.8b-19.2%Linear.Matrix:det44 from linear-1.19.1.3
4.4b17.1%Hakyll.Web.Tags:renderTagCloud from hakyll-4.7.2.3
3.6b0%Linear.Matrix:det33 from linear-1.19.1.3
2.4b9.4%cos(2*x)/(cos^2(x)*sin^2(x))
2.0b67.9%Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1

bsearch7.3s

rewrite6.7s

Algorithm
100×rewrite-expression-head
Calls

334 calls:

Slowest
294.0ms
(/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (* (cbrt (* (+ (* (+ y a) y) b) y)) (* (cbrt (+ (* (+ y a) y) b)) (cbrt y))) (cbrt (* (+ (* (+ y a) y) b) y))) c) y) i))
262.0ms
(+ (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (- (log z) t))) (* (- a 0.5) (log t)))
238.0ms
(/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (* (cbrt (* (+ (* (+ y a) y) b) y)) (cbrt (* (+ (* (+ y a) y) b) y))) (cbrt (* (+ (* (+ y a) y) b) y))) c) y) i))
179.0ms
(- (+ (- (* (* (* x 18.0) y) (* z t)) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i))
161.0ms
(- (+ (- (* (* (* x 18.0) y) (* z t)) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i))
Rules
1169×add-sqr-sqrt
1152×*-un-lft-identity
1091×add-cube-cbrt
801×times-frac
639×add-exp-log
627×pow1
564×add-cbrt-cube
497×add-log-exp
334×insert-posit16
301×associate-*r*
262×flip3-- flip--
240×associate-/r*
230×associate-*l*
217×associate-*r/
216×frac-times
199×associate-*l/
196×associate-/l*
189×cbrt-div
171×associate-/r/
167×flip-+ flip3-+
153×div-inv
145×cbrt-prod
138×sqrt-prod
122×sub-neg
109×pow-prod-down
108×exp-prod
107×prod-exp
106×sin-mult
102×*-commutative
96×distribute-lft-neg-in distribute-rgt-neg-in
95×sqrt-div
85×cbrt-unprod
79×associate-/l/
76×cos-mult
75×distribute-rgt-in distribute-lft-in
65×frac-2neg clear-num
58×pow1/3 log-pow
57×pow-prod-up
56×sum-log
52×div-exp
49×frac-sub
46×pow-unpow
45×log-prod cbrt-undiv
39×pow1/2
38×exp-diff
37×diff-log
36×rec-exp associate-+l-
35×div-sub frac-add
33×pow-flip
32×inv-pow neg-mul-1 tan-quot
31×+-commutative
29×rem-sqrt-square log-div
28×associate-+l+
27×difference-of-squares
26×pow-plus
25×distribute-lft-out exp-sum
23×associate-+r+
22×neg-sub0
21×sub-div
17×pow2 pow-sub
15×associate-+r- distribute-lft-out-- associate--l+ distribute-frac-neg
13×un-div-inv rem-exp-log
10×distribute-neg-frac
9×unpow-prod-up associate--l- unpow-prod-down
8×pow-to-exp
7×rem-log-exp
6×difference-of-sqr-1 cos-2
5×pow3 exp-neg
4×sum-cubes
3×pow-exp pow-neg pow-pow rem-cbrt-cube pow-div
2×log-rec sqrt-unprod tan-sum unpow2 cos-sum
1×distribute-rgt-out-- cube-unmult sub0-neg rem-square-sqrt distribute-rgt1-in

localize4.3s

end1.0ms