Details

simplify31.2m

Calls

14812 calls:

Slowest
1.7s
(/ (/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* x x) x) (* (* sin sin) 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 sin) (* x sin)) (* x sin)) (* (* cos cos) cos))) (* (* (* (* x sin) cos) (* (* x sin) cos)) (* (* x sin) cos)))
1.5s
(/ (* (* (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)))))
1.5s
(/ (* (* (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))))
1.4s
(/ (/ (* (* (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)))

prune3.7m

sample2.5m

Algorithm
57×intervals
Results
47.2s248333×body80valid
32.5s205379×body80nan
26.9s20501×body1280valid
10.2s10501×body640valid
6.4s4180×body2560valid
3.2s4898×body320valid
1.4s16512×pre80true
1.0s2430×body160valid
110.0ms130×body5120valid

series52.7s

Calls

314 calls:

Slowest
970.0ms
(fma (- (cbrt x)) (* (cbrt x) (cbrt x)) (* (cbrt x) (* (cbrt x) (cbrt x))))
944.0ms
(fma j (- (* t c) (* y i)) (- (* (- (* z y) (* t a)) x) (* (- (* z c) (* i a)) b)))
780.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (/ (- y z) (- (+ t 1.0) z)) (- a x)))
726.0ms
(* (/ (- y z) (- (+ t 1.0) z)) (- a x))
708.0ms
(fma (* (/ (cbrt z) (cbrt t)) (/ (cbrt z) (cbrt t))) (/ (sqrt (+ a t)) (/ (cbrt t) (cbrt z))) (- (* (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0)) (- b c))))

regimes16.7s

Accuracy

Total 22.6b remaining (18.2%)

5.4b-3.5%Linear.Matrix:det33 from linear-1.19.1.3
4.0b85.8%NMSE problem 3.2.1
2.5b0%cos(2*x)/(cos^2(x)*sin^2(x))
1.6b71.7%Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1
1.4b0%Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2

rewrite11.0s

Algorithm
97×rewrite-expression-head
Calls

318 calls:

Slowest
1.2s
(cbrt (* (* (* (* a a) (* a a)) (* a a)) (* (* (* a a) (* a a)) (* a a))))
324.0ms
(* (sqrt (exp (/ (- (+ f n)) (- f n)))) (sqrt (exp (/ (- (+ f n)) (- f n)))))
299.0ms
(exp (- (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (tan a)))
282.0ms
(/ (- (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))))))
247.0ms
(* (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0)) (- b c))
Rules
20289×times-frac
15105×*-un-lft-identity
13184×add-sqr-sqrt
11779×add-cube-cbrt
6387×prod-diff
2193×sqrt-prod
1402×pow1
1323×add-exp-log
1181×add-cbrt-cube
1130×exp-prod
1050×div-inv
1034×sqrt-pow1
880×distribute-lft-out
723×distribute-rgt-neg-in
638×distribute-lft-neg-in
607×pow-prod-down distribute-lft-out--
605×fma-neg
536×difference-of-squares
454×add-log-exp
428×prod-exp
398×associate-*r*
397×associate-/r*
393×associate-*l*
391×cbrt-unprod
318×expm1-log1p-u log1p-expm1-u insert-posit16
300×pow-prod-up
294×cbrt-prod
291×associate-/l*
252×pow-sqr
234×div-exp
202×associate-/r/
175×cbrt-undiv
174×neg-mul-1
165×flip3-- flip--
130×distribute-rgt-in distribute-lft-in
114×unswap-sqr
104×associate-+r+
103×associate-*l/
93×frac-times
91×pow-unpow
89×frac-add
86×*-commutative
81×associate-*r/
79×cos-mult
72×sub-neg sin-mult
68×pow-plus
66×associate--r+
64×swap-sqr log-pow
63×pow1/3
61×log-prod frac-sub frac-2neg clear-num
58×flip-+ fma-def flip3-+
57×pow1/2
52×diff-log
50×associate-+l+
48×pow2
43×cbrt-div
40×associate-/l/
38×fma-udef
36×unpow-prod-up
35×exp-sum
34×1-exp sqrt-div rec-exp
32×tan-quot
31×rem-sqrt-square
27×div-sub
25×sqr-pow
23×unpow-prod-down
22×sum-log
21×neg-sub0
16×pow-exp associate--l+
15×distribute-frac-neg
14×pow-flip distribute-neg-frac
12×+-commutative
11×exp-diff inv-pow rem-exp-log
10×associate--l- pow-pow
9×sub-div pow-to-exp
8×exp-neg associate-+l- log-div
6×neg-log distribute-rgt-out-- cube-div
5×e-exp-1 pow-sub cos-2
4×rem-cube-cbrt sqrt-unprod difference-cubes un-div-inv
3×rem-square-sqrt
2×quot-tan cube-prod associate-+r- pow3 unpow3 cos-sum tan-sum unpow2 remove-posit16 cube-mult distribute-neg-in
1×expm1-udef distribute-lft-neg-out expm1-log1p distribute-rgt-neg-out difference-of-sqr-1 exp-to-pow pow-neg rem-cbrt-cube rem-log-exp

localize5.4s

bsearch958.0ms

end1.0ms