Details

simplify39.7m

Calls

17816 calls:

Slowest
1.4s
(/ (/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* x x) x) (* (* cos cos) cos)) (* (* sin sin) sin))) (* (* (* (* x x) x) (* (* cos cos) cos)) (* (* sin sin) sin)))
1.3s
(/ (/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* x cos) (* x cos)) (* x cos)) (* (* sin sin) sin))) (* (* (* (* x cos) sin) (* (* x cos) sin)) (* (* x cos) sin)))
1.3s
(/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* (* x cos) (* x cos)) (* x cos)) (* (* sin sin) sin)) (* (* (* (* x cos) sin) (* (* x cos) sin)) (* (* x cos) sin))))
1.3s
(/ (/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* x cos) (* x cos)) (* x cos)) (* (* sin sin) sin))) (* (* (* (* x x) x) (* (* cos cos) cos)) (* (* sin sin) sin)))
1.3s
(/ (/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* x x) x) (* (* cos cos) cos)) (* (* sin sin) sin))) (* (* (* (* x cos) (* x cos)) (* x cos)) (* (* sin sin) sin)))

sample3.7m

Algorithm
60×intervals
Results
1.8m335826×body80valid
32.6s206243×body80nan
25.2s21621×body1280valid
11.5s11009×body640valid
6.4s5289×body2560valid
4.5s5018×body320valid
1.9s2464×body160valid
942.0ms16512×pre80true
298.0ms228×body5120valid

prune3.6m

series48.1s

Calls

327 calls:

Slowest
735.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
709.0ms
(fma (/ (+ (tan y) (tan z)) (- (* 1 1) (* (tan y) (* (tan z) (* (tan y) (tan z)))))) (+ 1 (* (tan y) (tan z))) (- (tan a)))
701.0ms
(* (/ (- y z) (- (+ 1.0 t) z)) (- a x))
626.0ms
(cbrt (fma -4 (* c a) (* b b)))
584.0ms
(fma (/ 1 (/ (* (cbrt t) (cbrt t)) (* (cbrt z) (cbrt z)))) (/ (sqrt (+ a t)) (/ (cbrt t) (cbrt z))) (* (- c b) (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0))))

regimes32.0s

Accuracy

Total 36.5b remaining (23.1%)

Threshold costs 6.9b (4.4%)

11.3b-8.9%Linear.Matrix:det44 from linear-1.19.1.3
5.4b-5.1%Hakyll.Web.Tags:renderTagCloud from hakyll-4.7.2.3
4.3b13.1%Linear.Matrix:det33 from linear-1.19.1.3
2.5b0%cos(2*x)/(cos^2(x)*sin^2(x))
1.9b57.4%Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1

rewrite16.0s

Algorithm
99×rewrite-expression-head
Calls

327 calls:

Slowest
1.0s
(/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (* (cbrt (+ (* (+ y a) y) b)) (* (cbrt (* (cbrt (+ (* (+ y a) y) b)) (cbrt (+ (* (+ y a) y) b)))) (cbrt (cbrt (+ (* (+ y a) y) b))))) (* (cbrt (+ (* (+ y a) y) b)) y)) c) y) i))
841.0ms
(* (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (/ 1 y))
810.0ms
(* (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (/ 1 y))
769.0ms
(* (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (/ 1 y))
437.0ms
(/ (+ (* (+ (* (+ (* (* (cbrt (* (+ (* x y) z) y)) (cbrt (* (+ (* x y) z) y))) (cbrt (* (+ (* x y) z) y))) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
Rules
7480×times-frac
6723×*-un-lft-identity
6002×add-sqr-sqrt
5028×add-cube-cbrt
2335×prod-diff
1336×add-exp-log
1198×add-cbrt-cube
1067×pow1
507×distribute-lft-out
504×sqrt-prod
479×associate-*r*
465×div-inv
460×add-log-exp
423×prod-exp
403×distribute-lft-out--
400×distribute-rgt-neg-in
390×cbrt-unprod
376×distribute-lft-neg-in
358×associate-*l*
353×difference-of-squares
346×pow-prod-down
336×associate-/r*
328×log1p-expm1-u
327×expm1-log1p-u insert-posit16
301×fma-neg
291×associate-/l*
285×cbrt-prod
246×div-exp
219×flip3-- flip--
210×fma-def
188×associate-/r/
183×cbrt-undiv
145×frac-times
136×associate-*l/
129×associate-*r/
116×distribute-rgt-in neg-mul-1 distribute-lft-in
110×tan-quot
107×*-commutative
102×associate-+l+
101×unswap-sqr
82×sub-neg
81×log-pow
79×associate-+r+ flip-+ flip3-+
64×log-prod pow1/3
62×cbrt-div
60×frac-2neg clear-num
56×exp-sum
53×sin-mult
48×associate-/l/ diff-log
45×exp-prod
36×sqrt-pow1 1-exp rec-exp pow1/2
34×pow-unpow
33×swap-sqr
29×sum-log frac-sub rem-sqrt-square
25×pow-prod-up pow-sqr
22×associate--r+ distribute-neg-frac
21×associate--l+ fma-udef frac-add
20×sqrt-div
18×exp-diff div-sub
17×rem-exp-log
16×cos-mult distribute-neg-in
14×unpow-prod-down
12×+-commutative associate-+l-
11×unpow-prod-up pow-plus
10×pow-flip pow-pow log-div
9×neg-sub0 sub-div inv-pow
8×associate--l-
6×pow-exp pow2 neg-log un-div-inv
5×sqr-pow pow-to-exp
4×difference-of-sqr-1 expm1-def
3×associate-+r- distribute-frac-neg cos-2
2×pow3 tan-sum cos-sum rem-log-exp rem-cbrt-cube
1×expm1-log1p expm1-udef distribute-lft-neg-out difference-of-sqr--1 pow-neg log1p-expm1 log1p-udef sqrt-unprod sqr-sin exp-neg unpow2 pow-sub

localize6.3s

bsearch5.6s

end1.0ms