Details

simplify15.4m

Calls

8987 calls:

Slowest
2.1s
(/ (* (* (* 2 2) 2) (* (* c c) c)) (* (* (* (- (* a (/ c b)) b) 2) (* (- (* a (/ c b)) b) 2)) (* (- (* a (/ c b)) b) 2)))
1.9s
(/ (* (* (* 2 2) 2) (* (* c c) c)) (* (* (* (- (* a (/ c b)) b) 2) (* (- (* a (/ c b)) b) 2)) (* (- (* a (/ c b)) b) 2)))
1.7s
(/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos))) (* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos)))))
1.6s
(/ (/ (* (* (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)))
1.6s
(/ (/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* x x) x) (* (* sin sin) sin)) (* (* cos cos) cos))) (* (* (* (* x x) x) (* (* sin sin) sin)) (* (* cos cos) cos)))

sample3.2m

Algorithm
60×intervals
Results
1.4m335701×body80valid
31.8s208247×body80nan
29.1s21427×body1280valid
10.7s10978×body640valid
5.6s5270×body2560valid
3.5s5136×body320valid
1.6s16512×pre80true
1.1s2553×body160valid
161.0ms237×body5120valid

prune3.0m

series58.7s

Calls

345 calls:

Slowest
4.3s
(* (/ (cbrt (- y z)) (- (+ t 1.0) z)) (- a x))
1.1s
(cbrt (* (/ (- y z) (- (+ t 1.0) z)) (- a x)))
1.1s
(cbrt (* (/ (- y z) (- (+ t 1.0) z)) (- a x)))
1.0s
(cbrt (* (/ (- y z) (- (+ t 1.0) z)) (- a x)))
1.0s
(cbrt (* (/ (- y z) (- (+ t 1.0) z)) (- a x)))

regimes28.7s

Accuracy

Total 35.4b remaining (23.7%)

8.6b0.2%Linear.Matrix:det44 from linear-1.19.1.3
5.3b-9.8%Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2
3.8b4.3%Linear.Matrix:det33 from linear-1.19.1.3
3.4b88%The quadratic formula (r1)
2.5b0%cos(2*x)/(cos^2(x)*sin^2(x))

rewrite14.2s

Algorithm
102×rewrite-expression-head
Calls

345 calls:

Slowest
1.2s
(/ (- (* (cos a) (* (cos b) (* (* (cos b) (cos a)) (* (cos b) (cos a))))) (* (* (sin a) (* (* (sin b) (sin a)) (* (sin b) (sin a)))) (sin b))) (+ (* (* (sin b) (sin a)) (+ (* (cos b) (cos a)) (* (sin b) (sin a)))) (* (* (cos b) (cos a)) (* (cos b) (cos a)))))
344.0ms
(* z (sqrt (+ t a)))
337.0ms
(* (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (/ 1 (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))
270.0ms
(* (sqrt (exp (/ (- (+ f n)) (- f n)))) (sqrt (exp (/ (- (+ f n)) (- f n)))))
269.0ms
(/ (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3)) (+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b))))))
Rules
4173×*-un-lft-identity
3139×add-sqr-sqrt
2803×times-frac
1981×add-cube-cbrt
1447×add-exp-log
1279×add-cbrt-cube
1223×pow1
1108×exp-prod
1006×sqrt-pow1
616×distribute-rgt-neg-in
603×pow-prod-down
534×associate-*r*
528×distribute-lft-neg-in
527×add-log-exp
520×associate-*l* distribute-lft-out--
486×prod-exp
445×cbrt-unprod
417×difference-of-squares
399×distribute-lft-out
348×cbrt-prod
346×flip3-- flip--
345×insert-posit16
289×associate-*r/
261×frac-times
245×associate-/r*
240×sqrt-prod
238×associate-/l*
230×div-exp
225×associate-*l/
196×pow-prod-up
192×pow-sqr
189×cbrt-div
174×cbrt-undiv
171×associate-/r/
147×cos-mult unswap-sqr
137×neg-mul-1
126×sub-neg
122×div-inv
119×sin-mult
118×*-commutative
114×distribute-rgt-in distribute-lft-in
112×flip-+ flip3-+
98×sqrt-div
97×pow-unpow frac-add
79×log-prod
75×frac-sub
72×pow1/3
62×associate-/l/
61×diff-log
59×frac-2neg clear-num
54×swap-sqr
50×pow1/2
43×sum-log
42×associate-+r+
35×1-exp rec-exp
33×log-pow
32×rem-sqrt-square
29×unpow-prod-down
28×div-sub
27×neg-sub0
26×sqr-pow
24×associate-+l+ associate--r+
21×+-commutative tan-quot
19×pow-plus
18×pow-exp
17×associate--l+ associate-+l-
16×sub-div
15×pow-flip distribute-frac-neg
13×neg-log pow-pow
12×associate--l- inv-pow log-div
11×exp-diff pow2 pow-to-exp
10×distribute-neg-frac
9×unpow-prod-up exp-neg
8×rem-exp-log
6×cube-div
5×exp-sum cos-2 e-exp-1 pow-sub
4×rem-cube-cbrt difference-cubes un-div-inv
3×sqrt-unprod
2×cube-prod associate-+r- unpow3 cos-sum tan-sum unpow2 distribute-rgt-out-- rem-square-sqrt remove-posit16 cube-mult distribute-neg-in
1×distribute-lft-neg-out pow-neg difference-of-sqr-1 exp-to-pow unpow1/3 rem-log-exp

localize6.1s

bsearch4.3s

end1.0ms