Details

simplify24.2m

Calls

11141 calls:

Slowest
2.0s
(/ (* (* (/ 1 (/ (* (* cos sin) x) 1)) (/ 1 (/ (* (* cos sin) x) 1))) (/ 1 (/ (* (* cos sin) x) 1))) (/ (* (* (* (* cos sin) x) (* (* cos sin) x)) (* (* cos sin) x)) (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x)))))
1.7s
(/ (* (* 1 1) 1) (/ (* (* (* (* (* cos cos) cos) (* (* sin sin) sin)) (* (* x x) x)) (* (* (* (* cos sin) x) (* (* cos sin) x)) (* (* cos sin) x))) (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x)))))
1.6s
(/ (* (* (/ 1 (/ (* (* cos sin) x) 1)) (/ 1 (/ (* (* cos sin) x) 1))) (/ 1 (/ (* (* cos sin) x) 1))) (/ (* (* (* (* cos sin) (* cos sin)) (* cos sin)) (* (* x x) x)) (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x)))))
1.6s
(/ (* (* (/ 1 (/ (* (* cos sin) x) 1)) (/ 1 (/ (* (* cos sin) x) 1))) (/ 1 (/ (* (* cos sin) x) 1))) (/ (* (* (* (* cos cos) cos) (* (* sin sin) sin)) (* (* x x) x)) (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x)))))
1.6s
(/ (/ (* (* 1 1) 1) (* (* (/ (* (* cos sin) x) 1) (/ (* (* cos sin) x) 1)) (/ (* (* cos sin) x) 1))) (/ (* (* (* (* cos sin) x) (* (* cos sin) x)) (* (* cos sin) x)) (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x)))))

sample3.8m

Algorithm
60×intervals
Results
1.8m334270×body80valid
33.5s210588×body80nan
27.9s21411×body1280valid
10.5s10957×body640valid
7.1s5324×body2560valid
3.6s5139×body320valid
1.4s2616×body160valid
1.3s16512×pre80true
205.0ms212×body5120valid

prune3.3m

series1.0m

Calls

353 calls:

Slowest
5.7s
(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
5.0s
(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
694.0ms
(/ (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i) (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t))
663.0ms
(* (/ (- y z) (- (+ t 1.0) z)) (- a x))
654.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

regimes32.2s

Accuracy

Total 29.6b remaining (20.5%)

10.7b-15.3%Linear.Matrix:det44 from linear-1.19.1.3
3.7b0%Linear.Matrix:det33 from linear-1.19.1.3
3.1b37.7%Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1
2.3b16.1%cos(2*x)/(cos^2(x)*sin^2(x))
1.1b0%Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2

rewrite16.8s

Algorithm
103×rewrite-expression-head
Calls

353 calls:

Slowest
2.2s
(* (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))) (* (* (cbrt (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))) (cbrt (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))) (cbrt (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))))
501.0ms
(* (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))) (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))
468.0ms
(* (* (* x 18.0) y) z)
453.0ms
(/ 1 (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t))
420.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
Rules
4735×times-frac
4039×*-un-lft-identity
3998×add-sqr-sqrt
2903×add-cube-cbrt
2472×add-exp-log
1516×add-cbrt-cube
1249×pow1
862×prod-exp
786×div-exp
777×associate-*r*
548×add-log-exp
520×cbrt-unprod
507×associate-*l*
415×frac-times
412×pow-prod-down
362×sqrt-div
353×associate-/r* insert-posit16
326×flip3-- flip-- associate-*l/
318×cbrt-undiv div-inv
313×flip-+ flip3-+
311×difference-of-squares
305×distribute-rgt-neg-in
295×cbrt-div distribute-lft-out--
294×associate-/l*
291×distribute-lft-neg-in
286×associate-*r/
283×sqrt-prod
249×cbrt-prod
238×distribute-lft-out
224×frac-sub
213×associate-/r/
192×1-exp
179×log-prod
176×swap-sqr
168×unswap-sqr
147×rec-exp
121×sub-neg
114×*-commutative
93×neg-mul-1
86×pow-prod-up
84×distribute-rgt-in distribute-lft-in
73×unpow-prod-down
69×associate-/l/
65×frac-2neg clear-num
59×sqrt-pow1 diff-log
58×pow1/3
55×pow1/2
54×exp-prod
50×sum-log
45×pow-sqr
44×pow-flip inv-pow tan-quot
42×log-pow
39×pow-unpow
38×rem-sqrt-square
37×associate--l+
35×exp-sum
32×difference-of-sqr-1
31×sin-mult
29×associate--r+ frac-add
28×cos-mult
26×log-div
25×associate-+l+
24×associate-+r+
22×pow-plus
21×un-div-inv rem-exp-log
20×sqr-pow
19×+-commutative
18×neg-sub0 distribute-neg-in
17×sub-div
16×unpow-prod-up
15×pow-pow
14×associate-+l-
12×pow-exp pow2 pow-to-exp div-sub
11×exp-diff distribute-neg-frac
9×pow-neg neg-log
8×distribute-lft-neg-out associate--l- pow-sub
6×pow3 rem-log-exp
3×distribute-frac-neg unsub-neg
2×distribute-lft1-in associate-+r- cos-2 sqrt-unprod cos-sum tan-sum rem-cbrt-cube associate--r- pow-div distribute-rgt-out
1×sub0-neg sqrt-pow2 exp-neg rem-square-sqrt remove-posit16 unpow1/3

localize6.5s

bsearch4.6s

end1.0ms