Details

simplify30.7m

Calls

15290 calls:

Slowest
3.3s
(/ (* (* (* (/ 1 sin) (/ (cos (* 2 x)) (* x cos))) (* (/ 1 sin) (/ (cos (* 2 x)) (* x cos)))) (* (/ 1 sin) (/ (cos (* 2 x)) (* x cos)))) (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos))))
3.2s
(/ (/ (* (/ (* (* 1 1) 1) (* (* sin sin) sin)) (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x)))) (* (* (* x x) x) (* (* cos cos) cos))) (* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos))))
3.0s
(/ (/ (* (* (* (/ 1 sin) (cos (* 2 x))) (* (/ 1 sin) (cos (* 2 x)))) (* (/ 1 sin) (cos (* 2 x)))) (* (* (* x cos) (* x cos)) (* x cos))) (* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos))))
3.0s
(/ (* (/ (* (* 1 1) 1) (* (* sin sin) sin)) (/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* x x) x) (* (* cos cos) cos)))) (* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos))))
2.9s
(/ (* (* (* (/ 1 sin) (/ 1 sin)) (/ 1 sin)) (/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* x cos) (* x cos)) (* x cos)))) (* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos))))

prune3.7m

series3.0m

Calls

324 calls:

Slowest
2.1m
(* (fma (- (cbrt x)) (* (cbrt x) (cbrt x)) (* (cbrt x) (* (cbrt x) (* (* (sqrt (cbrt (* (cbrt x) (cbrt x)))) (sqrt (cbrt (* (cbrt x) (cbrt x))))) (cbrt (cbrt x)))))) (/ (- y z) (- (+ t 1.0) z)))
941.0ms
(fma j (- (* t c) (* y i)) (- (* (* (- (* z y) (* t a)) (* (cbrt x) (cbrt x))) (cbrt x)) (* (- (* z c) (* i a)) b)))
901.0ms
(fma (- (cbrt x)) (* (cbrt x) (cbrt x)) (* (cbrt x) (* (cbrt x) (* (* (sqrt (cbrt (* (cbrt x) (cbrt x)))) (sqrt (cbrt (* (cbrt x) (cbrt x))))) (cbrt (cbrt x))))))
884.0ms
(fma (- (cbrt x)) (* (cbrt x) (cbrt x)) (* (cbrt x) (* (cbrt x) (cbrt x))))
859.0ms
(fma j (- (* t c) (* y i)) (- (* (- (* z y) (* t a)) x) (* (- (* z c) (* i a)) b)))

sample2.6m

Algorithm
59×intervals
Results
50.8s264236×body80valid
33.2s209020×body80nan
28.2s21438×body1280valid
10.8s10867×body640valid
6.7s5455×body2560valid
4.5s5172×body320valid
1.0s2570×body160valid
1.0s16512×pre80true
208.0ms219×body5120valid

regimes18.2s

Accuracy

Total 26.0b remaining (16.6%)

5.0b82.6%NMSE problem 3.2.1
4.8b1.9%Linear.Matrix:det33 from linear-1.19.1.3
3.3b26.1%Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1
2.3b0%cos(2*x)/(cos^2(x)*sin^2(x))
1.9b0%Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1

rewrite11.2s

Algorithm
99×rewrite-expression-head
Calls

328 calls:

Slowest
482.0ms
(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
305.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z))))) (tan a))
291.0ms
(* (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0)) (- b c))
207.0ms
(* x (/ (* (* (* (cbrt (cbrt y)) (cbrt (cbrt y))) (cbrt (cbrt y))) (cbrt y)) (* (cbrt z) (cbrt z))))
199.0ms
(/ y (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))
Rules
8406×times-frac
7897×*-un-lft-identity
7286×add-sqr-sqrt
5789×add-cube-cbrt
2702×prod-diff
1830×add-exp-log
1543×cbrt-prod
1433×add-cbrt-cube
1120×pow1
1043×sqrt-prod
978×distribute-rgt-neg-in
909×distribute-lft-neg-in
777×associate-*r*
641×prod-exp
619×associate-*l*
502×cbrt-unprod
501×distribute-lft-out--
490×difference-of-squares
485×fma-neg
477×distribute-lft-out
472×add-log-exp
454×div-inv
432×div-exp
361×swap-sqr
334×associate-/l*
331×pow-prod-down
327×expm1-log1p-u log1p-expm1-u insert-posit16
304×associate-/r*
294×cbrt-undiv
287×exp-prod
265×neg-mul-1
216×log-pow
190×sqrt-pow1
188×unswap-sqr
179×flip3-- flip--
159×associate-/r/
108×distribute-rgt-in distribute-lft-in
104×pow-prod-up
96×*-commutative associate-*l/
93×associate-+r+
85×associate--r+
74×pow1/3
73×sub-neg
70×pow-sqr
68×frac-2neg clear-num associate-*r/
66×associate-/l/
64×frac-sub
60×1-exp
58×frac-times
56×cbrt-div rec-exp diff-log
55×flip-+ flip3-+
51×log-prod
49×exp-sum fma-def
45×pow-plus
42×tan-quot pow1/2
38×fma-udef
34×sqrt-div
33×pow2 unpow-prod-down frac-add
32×div-sub
28×sin-mult
26×associate-+l+
25×pow-flip
23×cos-mult
22×sum-log rem-sqrt-square
18×inv-pow distribute-rgt-out--
17×neg-sub0
16×pow-unpow sub-div
14×distribute-neg-frac rem-exp-log
13×distribute-frac-neg
11×sqr-pow
10×exp-diff +-commutative
9×pow-exp associate--l+ un-div-inv
7×pow-pow
6×pow-to-exp log-div
5×unpow-prod-up exp-neg
4×associate--l- associate-+r- associate-+l- cos-2
3×rem-log-exp distribute-rgt-out
2×remove-posit16 neg-log difference-of-sqr-1 sqrt-unprod tan-sum unpow2 cos-sum e-exp-1
1×quot-tan unpow1/2 log-rec rem-square-sqrt associate--r-

localize5.4s

bsearch1.4s

end1.0ms