Details

simplify42.3m

Calls

18304 calls:

Slowest
1.9s
(/ (* (* (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))))
1.7s
(/ (/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* x x) x) (* (* sin sin) sin)) (* (* cos cos) cos))) (* (* (* (* x sin) (* x sin)) (* x sin)) (* (* cos cos) cos)))
1.7s
(/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos))) (* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos)))))
1.7s
(/ (/ (* (* (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))) (* (* (* (* (* cos cos) cos) (* (* sin sin) sin)) (* (* x x) x)) (* (* (* (* cos sin) (* cos sin)) (* cos sin)) (* (* x x) x))))

prune4.2m

sample2.7m

Algorithm
59×intervals
Results
52.2s263067×body80valid
34.5s207099×body80nan
26.9s21222×body1280valid
13.0s10988×body640valid
7.2s5287×body2560valid
3.4s5016×body320valid
1.7s2636×body160valid
1.0s16512×pre80true
150.0ms190×body5120valid

series58.5s

Calls

338 calls:

Slowest
2.9s
(/ (fma (+ (tan y) (tan z)) (* (- (tan y) (tan z)) (fma (cos a) (fma (* (tan y) (tan z)) (* (tan y) (tan z)) (* (tan y) (tan z))) (cos a))) (- (* (* (- (tan y) (tan z)) (sin a)) (- 1 (* (* (tan y) (tan z)) (* (* (tan y) (tan z)) (* (tan y) (tan z)))))))) (* (* (- 1 (* (tan y) (tan z))) (cos a)) (* (- (tan y) (tan z)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z))))))))
2.2s
(/ (/ (fma (fma y (fma (+ y a) y b) c) y i) (cbrt (fma y (fma y (fma y (fma y x z) 27464.7644705) 230661.510616) t))) (cbrt (fma y (fma y (fma y (fma y x z) 27464.7644705) 230661.510616) t)))
1.9s
(fma (+ (tan y) (tan z)) (* (- (tan y) (tan z)) (fma (cos a) (fma (* (tan y) (tan z)) (* (tan y) (tan z)) (* (tan y) (tan z))) (cos a))) (- (* (* (- (tan y) (tan z)) (sin a)) (- 1 (* (* (tan y) (tan z)) (* (* (tan y) (tan z)) (* (tan y) (tan z))))))))
1.0s
(fma j (fma t c (- (* y i))) (- (* (- (* z y) (* t a)) x) (* (* (* (- (* z c) (* i a)) (cbrt b)) (cbrt b)) (cbrt b))))
965.0ms
(fma j (fma t c (- (* y i))) (- (* (- (* z y) (* t a)) x) (* (* (- (* z c) (* i a)) (* (cbrt b) (cbrt b))) (cbrt b))))

regimes16.3s

Accuracy

Total 22.9b remaining (18.6%)

5.2b-4.4%Linear.Matrix:det33 from linear-1.19.1.3
2.8b0%cos(2*x)/(cos^2(x)*sin^2(x))
2.7b38.1%Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1
1.7b70.4%Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1
1.6b0%fabs fraction 1

rewrite11.9s

Algorithm
101×rewrite-expression-head
Calls

342 calls:

Slowest
728.0ms
(/ (fma (+ (tan y) (tan z)) (* (- (tan y) (tan z)) (fma (cos a) (fma (* (tan y) (tan z)) (* (tan y) (tan z)) (* (tan y) (tan z))) (cos a))) (- (* (* (- (tan y) (tan z)) (sin a)) (- 1 (* (* (tan y) (tan z)) (* (* (tan y) (tan z)) (* (tan y) (tan z)))))))) (* (* (- 1 (* (tan y) (tan z))) (cos a)) (* (- (tan y) (tan z)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z))))))))
484.0ms
(/ x (/ y (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))
345.0ms
(* (* (+ (tan y) (tan z)) (cos a)) (* (* (+ (tan y) (tan z)) (cos a)) (* (+ (tan y) (tan z)) (cos a))))
279.0ms
(cbrt (* (* (+ (tan y) (tan z)) (cos a)) (* (* (+ (tan y) (tan z)) (cos a)) (* (+ (tan y) (tan z)) (cos a)))))
252.0ms
(* (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0)) (- b c))
Rules
11602×times-frac
9416×*-un-lft-identity
8079×add-sqr-sqrt
7118×add-cube-cbrt
3358×prod-diff
1686×add-exp-log
1584×pow1
1451×add-cbrt-cube
970×cbrt-prod
958×sqrt-prod
862×distribute-rgt-neg-in
800×distribute-lft-neg-in
689×distribute-lft-out
687×div-inv
629×prod-exp
585×pow-prod-down
577×cbrt-unprod
548×associate-*r*
522×associate-*l/
517×add-log-exp
513×fma-neg
447×associate-*l*
421×associate-/r*
409×distribute-lft-out--
385×associate-/l*
343×expm1-log1p-u
342×log1p-expm1-u insert-posit16
336×difference-of-squares
335×frac-times
326×tan-quot
296×div-exp
272×associate-/r/
232×neg-mul-1
230×exp-sum
225×flip-+ flip3-+
224×cbrt-undiv
203×flip-- flip3--
188×swap-sqr
175×cbrt-div
168×associate-*r/
135×frac-add
130×pow-prod-up
104×distribute-rgt-in distribute-lft-in
103×*-commutative
102×unswap-sqr
90×pow-sqr
81×sub-neg
80×fma-def
78×pow1/3
64×frac-2neg clear-num
63×frac-sub diff-log
55×log-prod
54×pow-plus
47×associate-/l/
44×associate--r+
43×associate-+r+
41×exp-prod
37×associate-+l+ associate--l+
36×fma-udef
34×1-exp rec-exp
32×pow2
31×sum-log
28×sqrt-div
25×log-pow sin-mult
24×sqrt-pow1 pow1/2
23×distribute-rgt-out-- rem-exp-log
22×rem-sqrt-square
20×div-sub
19×neg-sub0
18×cos-mult
12×unpow-prod-up exp-diff associate--l- neg-log +-commutative sub-div
11×distribute-frac-neg
9×pow-unpow distribute-neg-frac associate-+l- unpow-prod-down
8×pow-flip inv-pow
7×expm1-log1p expm1-udef un-div-inv
5×cos-2
4×pow-exp log-div
3×pow3 sqr-pow pow-pow pow-to-exp rem-cbrt-cube distribute-rgt-out
2×distribute-lft-neg-out cube-unmult cos-sum remove-posit16 tan-sum
1×associate-+r- distribute-rgt-neg-out log1p-expm1 difference-of-sqr-1 sqrt-unprod unpow2 sqr-neg e-exp-1 pow-sub log1p-udef

localize6.0s

bsearch2.3s

end1.0ms