Details

simplify21.7m

Calls

10830 calls:

Slowest
2.0s
(/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* (* x sin) (* x sin)) (* x sin)) (* (* cos cos) cos)) (* (* (* (* x sin) cos) (* (* x sin) cos)) (* (* x sin) cos))))
1.4s
(/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* (* x sin) (* x sin)) (* x sin)) (* (* cos cos) cos)) (* (* (* (* x x) x) (* (* sin sin) sin)) (* (* cos cos) cos))))
1.4s
(/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos))) (* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos)))))
1.4s
(/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos))) (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos)))))
1.3s
(/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos))) (* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos)))))

prune3.0m

sample2.6m

Algorithm
58×intervals
Results
51.8s256768×body80valid
35.6s206357×body80nan
26.7s20209×body1280valid
11.1s10701×body640valid
6.4s4291×body2560valid
3.7s4972×body320valid
1.8s2441×body160valid
1.2s16512×pre80true
134.0ms115×body5120valid

series1.1m

Calls

329 calls:

Slowest
3.7s
(fma (- (* y (* z (* x 18.0))) (* a 4.0)) t (- (* c b) (fma (* k j) 27.0 (* (* x 4.0) i))))
3.6s
(fma (- (* (* y z) (* x 18.0)) (* a 4.0)) t (- (* c b) (fma (* k j) 27.0 (* (* x 4.0) i))))
3.6s
(fma (- (* (* y z) (* x 18.0)) (* a 4.0)) t (- (* b c) (fma (* 27.0 k) j (* i (* 4.0 x)))))
3.5s
(fma (- (* (* y z) (* x 18.0)) (* a 4.0)) t (- (* c b) (fma k (* 27.0 j) (* (* x 4.0) i))))
1.1s
(fma j (- (* t c) (* y i)) (- (* (- (* z y) (* t a)) x) (* (* (* (- (* z c) (* i a)) (* (cbrt b) (cbrt b))) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (cbrt (cbrt b)))))

regimes15.6s

Accuracy

Total 26.2b remaining (21.6%)

5.4b0%Hakyll.Web.Tags:renderTagCloud from hakyll-4.7.2.3
4.8b0%Linear.Matrix:det33 from linear-1.19.1.3
2.3b44.3%Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1
2.2b-5%Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2
2.0b16.8%fabs fraction 1

rewrite8.3s

Algorithm
101×rewrite-expression-head
Calls

333 calls:

Slowest
478.0ms
(* (* (* (- (* z c) (* i a)) (* (cbrt b) (cbrt b))) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (cbrt (cbrt b)))
184.0ms
(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
157.0ms
(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
144.0ms
(* (* (* x sin) cos) (* (* x sin) cos))
128.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
Rules
14504×times-frac
10024×*-un-lft-identity
9868×add-sqr-sqrt
8916×add-cube-cbrt
4818×prod-diff
1653×sqrt-prod
1301×add-exp-log
1159×pow1
1083×add-cbrt-cube
803×div-inv
487×add-log-exp
439×prod-exp
425×associate-*l*
409×associate-*r*
395×distribute-rgt-neg-in
382×cbrt-unprod
377×distribute-lft-neg-in
372×cbrt-prod
365×pow-prod-down
333×expm1-log1p-u
332×log1p-expm1-u insert-posit16
307×difference-of-squares
305×distribute-lft-out--
294×exp-prod
276×associate-/r* fma-neg
273×distribute-lft-out
258×associate-/l*
219×div-exp
197×log-pow
189×associate--r+
162×distribute-rgt-in distribute-lft-in
151×flip3-- flip--
150×cbrt-undiv
116×unswap-sqr
115×exp-sum
111×neg-mul-1
107×associate-/r/
93×fma-def
88×associate-*l/
86×*-commutative
85×pow-unpow associate-+r+
84×log-prod
77×sub-neg
75×pow1/3
72×tan-quot
70×associate-*r/
66×pow-prod-up
61×frac-times
58×associate-+l+
56×frac-2neg clear-num unpow-prod-down fma-udef
53×diff-log
52×frac-sub pow-sqr
44×sqrt-div
41×cbrt-div
40×swap-sqr flip-+ flip3-+
38×1-exp
37×sqrt-pow1
36×associate-/l/
34×rec-exp
31×pow1/2
30×pow-plus
29×rem-sqrt-square
28×sum-log
26×associate--l+
24×pow-exp
22×sin-mult
20×neg-sub0 pow2
19×div-sub
18×pow-to-exp
17×+-commutative rem-exp-log
16×cos-mult
15×exp-diff sqr-pow
14×pow-pow log-div
12×associate-+l- distribute-frac-neg
11×pow-flip sub-div
10×neg-log difference-of-sqr-1 inv-pow
9×distribute-neg-frac
8×associate--l-
7×distribute-rgt-out-- rem-log-exp frac-add
5×un-div-inv
4×exp-neg unpow2
3×associate-+r- pow-neg
2×log1p-udef log-rec cos-sum tan-sum e-exp-1 pow-sub cos-2
1×expm1-log1p expm1-udef distribute-lft-neg-out unpow1/2 distribute-rgt-neg-out log1p-expm1 sqrt-unprod exp-to-pow remove-posit16 unsub-neg

localize5.9s

bsearch2.5s

end1.0ms