Details

simplify19.1m

Calls

9741 calls:

Slowest
1.7s
(/ (sqrt (sin b)) (/ (* (cbrt (+ (* (sin b) (sin a)) (* (cos b) (cos a)))) (cbrt (+ (* (sin b) (sin a)) (* (cos b) (cos a))))) (/ (* (cbrt (+ (* (sin b) (sin a)) (* (cos b) (cos a)))) (cbrt (+ (* (sin b) (sin a)) (* (cos b) (cos a))))) 1)))
1.5s
(/ 1 (/ (* (cbrt y) (cbrt y)) (exp (- (* (log z) y) (* 1.0 (log a))))))
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)))))
1.4s
(/ (/ (* c a) -1/2) a)
1.4s
(/ (* (* (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))))

sample3.3m

Algorithm
60×intervals
Results
1.5m335380×body80valid
33.5s209224×body80nan
29.0s21120×body1280valid
12.2s11120×body640valid
6.8s5351×body2560valid
3.8s5200×body320valid
1.7s16512×pre80true
1.6s2545×body160valid
206.0ms236×body5120valid

prune3.3m

series55.8s

Calls

351 calls:

Slowest
735.0ms
(+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (- x (tan a)))
708.0ms
(* (* 1 (/ (- y z) (+ (- 1.0 z) t))) (- a x))
686.0ms
(* (* 1 (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (+ (- 1.0 z) t)) (cbrt (+ (- 1.0 z) t)))) (/ (cbrt (- y z)) (cbrt (+ (- 1.0 z) t))))) (- a x))
683.0ms
(exp (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (- x (tan a))))
681.0ms
(* (/ (- y z) (- (+ t 1.0) z)) (- a x))

regimes31.6s

Accuracy

Total 33.8b remaining (23%)

9.2b-3.6%Linear.Matrix:det44 from linear-1.19.1.3
5.1b0%Linear.Matrix:det33 from linear-1.19.1.3
3.8b-18.3%Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2
2.4b44.9%Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1
2.3b11.3%cos(2*x)/(cos^2(x)*sin^2(x))

rewrite16.3s

Algorithm
105×rewrite-expression-head
Calls

351 calls:

Slowest
2.3s
(* (* 1 (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (+ (- 1.0 z) t)) (cbrt (+ (- 1.0 z) t)))) (/ (cbrt (- y z)) (cbrt (+ (- 1.0 z) t))))) (- a x))
398.0ms
(* r (/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))))
339.0ms
(/ (* x (exp (+ (- (* (log z) y) (* 1.0 (log a))) (- (* t (log a)) b)))) y)
284.0ms
(/ (* (cbrt (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t)) (cbrt (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t))) (/ (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i) (cbrt (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t))))
255.0ms
(* (- (* 18.0 (* x (* z y))) (* a 4.0)) t)
Rules
3737×*-un-lft-identity
3600×add-sqr-sqrt
3529×times-frac
2413×add-cube-cbrt
1819×add-exp-log
1224×add-cbrt-cube
1173×pow1
735×prod-exp
606×add-log-exp
538×associate-*l*
515×associate-*r*
457×cbrt-unprod
416×div-exp
409×associate-/r*
404×distribute-lft-out--
403×pow-exp
397×pow-prod-down
392×difference-of-squares
377×cbrt-prod
349×distribute-rgt-neg-in insert-posit16
317×distribute-lft-neg-in
306×pow-unpow
296×flip3-- flip--
266×distribute-lft-out
258×unpow-prod-down
236×associate-/l*
234×associate-*r/
223×associate-/r/
192×unswap-sqr
185×cbrt-undiv
176×exp-prod
171×div-inv
169×frac-times sqrt-prod
155×flip-+ flip3-+
148×associate-*l/
138×frac-sub
135×e-exp-1
129×1-exp
125×sub-neg
114×cbrt-div
113×sin-mult
112×rec-exp *-commutative
110×distribute-rgt-in distribute-lft-in
107×cos-mult
102×sqrt-div
92×log-pow
91×neg-mul-1
81×log-prod
78×pow1/3
77×diff-log
69×sum-log pow-to-exp associate-/l/
59×frac-2neg clear-num
58×frac-add
56×sqr-pow
49×swap-sqr
44×pow-prod-up
43×pow-sqr
41×associate-+r+
38×neg-sub0
37×sub-div
35×sqrt-pow1 pow1/2 rem-exp-log
34×div-sub
33×rem-sqrt-square
29×distribute-frac-neg
26×exp-diff
25×tan-quot +-commutative associate-+l-
24×associate--r+
23×exp-sum
22×pow-pow
18×pow-plus
17×associate-+l+ neg-log
16×associate-+r- pow-neg
14×pow-flip pow-sub log-div
13×inv-pow
12×associate--l+ associate--l-
11×pow2
10×difference-of-sqr-1 distribute-neg-frac
8×un-div-inv
6×rem-log-exp
4×exp-neg unpow2
3×unpow-prod-up distribute-rgt-out--
2×log-rec cos-sum tan-sum remove-posit16 distribute-neg-in cos-2
1×distribute-lft-neg-out unpow1/2 sqrt-unprod distribute-rgt-out

localize6.2s

bsearch5.3s

end1.0ms