Details

simplify16.9m

Calls

9714 calls:

Slowest
1.7s
(/ (* (* (/ 1 (/ (* x cos) (/ (cos (* 2 x)) sin))) (/ 1 (/ (* x cos) (/ (cos (* 2 x)) sin)))) (/ 1 (/ (* x cos) (/ (cos (* 2 x)) sin)))) (* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos))))
1.6s
(/ (* (* (/ 1 (/ (* x cos) (/ (cos (* 2 x)) sin))) (/ 1 (/ (* x cos) (/ (cos (* 2 x)) sin)))) (/ 1 (/ (* x cos) (/ (cos (* 2 x)) sin)))) (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos))))
1.6s
(/ (/ (* (* (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))))
1.5s
(/ (/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos)))) (* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos))))
1.5s
(/ (* (* (/ 1 (/ (* x cos) (/ (cos (* 2 x)) sin))) (/ 1 (/ (* x cos) (/ (cos (* 2 x)) sin)))) (/ 1 (/ (* x cos) (/ (cos (* 2 x)) sin)))) (* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos))))

sample3.6m

Algorithm
60×intervals
Results
1.6m336046×body80valid
35.2s205049×body80nan
31.3s21438×body1280valid
11.5s11045×body640valid
6.3s5316×body2560valid
3.4s5100×body320valid
1.3s16512×pre80true
1.0s2428×body160valid
252.0ms236×body5120valid

prune3.3m

series1.1m

Calls

348 calls:

Slowest
5.1s
(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
5.0s
(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
1.1s
(cbrt (* (* (- y z) (/ 1 (- (+ t 1.0) z))) (- a x)))
1.1s
(cbrt (* (* (- y z) (/ 1 (- (+ t 1.0) z))) (- a x)))
958.0ms
(cbrt (* (* (- y z) (/ 1 (- (+ t 1.0) z))) (- a x)))

regimes33.3s

Accuracy

Total 35.8b remaining (23.3%)

9.4b-11.5%Linear.Matrix:det44 from linear-1.19.1.3
5.1b78.6%NMSE problem 3.2.1
4.0b-7.4%Linear.Matrix:det33 from linear-1.19.1.3
2.7b42.2%Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2
2.5b0%cos(2*x)/(cos^2(x)*sin^2(x))

rewrite17.5s

Algorithm
102×rewrite-expression-head
Calls

348 calls:

Slowest
780.0ms
(exp (+ x (- (/ (log (exp (+ (tan y) (tan z)))) (- 1 (* (tan y) (tan z)))) (tan a))))
569.0ms
(* (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))) (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))
513.0ms
(/ (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i) (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t))
506.0ms
(/ (+ (* (+ (* (* (cbrt (* (+ (* (+ (* x y) z) y) 27464.7644705) y)) (cbrt (* (+ (* (+ (* x y) z) y) 27464.7644705) y))) (cbrt (* (+ (* (+ (* x y) z) y) 27464.7644705) y))) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
468.0ms
(* (cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))) (cbrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))
Rules
3837×times-frac
3265×add-sqr-sqrt
3211×*-un-lft-identity
2542×add-cube-cbrt
1984×add-exp-log
1427×add-cbrt-cube
1215×pow1
642×prod-exp
582×associate-*r*
552×div-exp
536×add-log-exp
457×associate-*l*
433×cbrt-unprod
405×flip3-- flip--
378×associate-/r*
354×distribute-rgt-neg-in
348×insert-posit16
336×pow-prod-down
335×distribute-lft-neg-in
330×frac-times
328×associate-/l*
307×cbrt-div
295×cbrt-undiv
281×sqrt-prod
265×associate-*l/
222×div-inv
214×cbrt-prod
210×associate-*r/
182×difference-of-squares
177×distribute-lft-out--
164×exp-prod
152×distribute-lft-out
140×unswap-sqr
132×pow-prod-up
128×sub-neg
127×flip-+ flip3-+
121×associate-/r/
116×*-commutative
115×1-exp rec-exp
114×sqrt-div
106×distribute-rgt-in distribute-lft-in
104×neg-mul-1
99×log-pow
94×frac-sub
79×pow1/3
74×swap-sqr pow-sqr
71×log-prod frac-2neg clear-num
56×sqrt-pow1 pow-plus
54×associate-/l/
53×sum-log
51×diff-log
45×pow-flip inv-pow
38×pow1/2
36×pow2
34×sin-mult
33×associate-+r+ un-div-inv
31×rem-sqrt-square
28×cos-mult
24×associate--r+
23×+-commutative tan-quot
20×div-sub log-div
18×associate-+l+
17×exp-diff
16×sub-div
15×rem-exp-log
13×associate--l+ associate-+l-
12×neg-sub0 unpow-prod-down
11×exp-sum difference-of-sqr-1 frac-add
10×pow-unpow
8×distribute-neg-frac
7×distribute-frac-neg neg-log
6×cos-2 rem-log-exp
5×associate--l-
4×pow-exp associate-+r- sqr-pow pow-to-exp pow-pow
3×pow3 exp-neg
2×remove-posit16 sqrt-unprod tan-sum cos-sum unpow1/3
1×sub0-neg log-rec distribute-lft-neg-out exp-to-pow unpow2 rem-square-sqrt rem-cbrt-cube distribute-rgt-out

localize6.6s

bsearch4.5s

end1.0ms