Details

simplify6.5m

Calls

4994 calls:

Slowest
939.0ms
(* (- (* (* x y2) (* x y2)) (* (* z y3) (* z y3))) (- (* (* y0 c) (* y0 c)) (* (* y1 a) (* y1 a))))
902.0ms
(/ (sqrt (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))) (sqrt (+ (* (cos a) (cos b)) (* (sin a) (sin b)))))
870.0ms
(* (* (* (* a a) (* a a)) (* a a)) (* (* (+ 1 a) (+ 1 a)) (+ 1 a)))
867.0ms
(/ 1 (sqrt (fma (fma (+ y a) y b) (* y y) (fma y c i))))
778.0ms
(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))

sample2.9m

Algorithm
59×intervals
Results
1.4m328228×body80valid
28.1s21654×body1280valid
22.7s152936×body80nan
11.5s10930×body640valid
6.6s5267×body2560valid
3.6s5145×body320valid
1.5s2550×body160valid
1.1s16512×pre80true
271.0ms222×body5120valid

prune2.4m

series32.7s

Calls

347 calls:

Slowest
564.0ms
(fma (- (* z y) (* t a)) x (- (* (- (* t c) (* y i)) j) (* (- (* z c) (* i a)) b)))
526.0ms
(pow (pow (exp (sqrt (fma x x -1))) (sqrt (sqrt (fma x x -1)))) (sqrt (sqrt (fma x x -1))))
457.0ms
(cos (+ a b))
440.0ms
(sqrt (fma c (* a -4) (* b b)))
435.0ms
(/ (fma (fma (+ y a) y b) (* y y) (fma y c i)) (fma y (fma (* y y) (fma y x z) (fma y 27464.7644705 230661.510616)) t))

regimes23.1s

Accuracy

Total 34.8b remaining (20.4%)

8.1b-9.6%Linear.Matrix:det44 from linear-1.19.1.3
4.8b82.8%NMSE problem 3.2.1
4.2b8.3%Linear.Matrix:det33 from linear-1.19.1.3
3.5b37.4%Hakyll.Web.Tags:renderTagCloud from hakyll-4.7.2.3
2.5b0%cos(2*x)/(cos^2(x)*sin^2(x))

localize3.4s

bsearch2.5s

rewrite2.3s

Algorithm
104×rewrite-expression-head
Calls

347 calls:

Slowest
53.0ms
(/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
46.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
38.0ms
(/ (sin b) (/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))))
34.0ms
(cbrt (/ (/ (- (- n) f) (- f n)) (* (* (cbrt (/ (- f n) (+ n f))) (cbrt (/ (- f n) (+ n f)))) (* (cbrt (/ (- f n) (+ n f))) (/ (- f n) (+ n f))))))
30.0ms
(/ (* r (sin b)) (cos (+ a b)))
Rules
1302×*-un-lft-identity
1279×add-sqr-sqrt
1210×add-cube-cbrt
671×add-exp-log
616×add-cbrt-cube
606×times-frac
581×pow1
420×prod-diff
418×add-log-exp
347×expm1-log1p-u
347×log1p-expm1-u
338×associate-*r*
267×associate-*l*
237×cbrt-prod
230×flip3--
230×flip--
208×sqrt-prod
207×div-inv
203×associate-/r*
162×associate-/r/
152×frac-times
148×associate-*l/
136×associate-/l*
134×associate-*r/
129×fma-neg
121×cbrt-div
114×prod-exp
106×*-commutative
101×cbrt-unprod
99×distribute-rgt-in
99×distribute-lft-in
91×pow-prod-down
90×sub-neg
87×flip-+
87×flip3-+
77×associate-+r+
74×sqrt-div
71×div-exp
69×frac-sub
66×cbrt-undiv
64×frac-2neg
64×clear-num
58×pow1/3
58×sin-mult
53×cos-mult
50×tan-quot
49×associate-/l/
49×fma-udef
46×fma-def
37×exp-prod
37×neg-mul-1
36×difference-of-squares
35×pow1/2
33×associate--r+
32×sub-div
31×distribute-lft-out
31×unpow-prod-down
29×rem-sqrt-square
28×pow-unpow
26×diff-log
24×distribute-lft-neg-in
24×distribute-rgt-neg-in
21×pow-pow
21×pow-prod-up
19×log-prod
19×distribute-lft-out--
19×rec-exp
19×div-sub
18×pow-to-exp
18×log-pow
14×pow-flip
14×+-commutative
13×associate-+l+
13×neg-sub0
13×exp-sum
13×inv-pow
12×pow-exp
12×pow-plus
11×associate--l+
10×log-div
10×pow2
10×frac-add
9×sum-log
8×associate-+l-
7×associate--l-
7×rem-exp-log
5×un-div-inv
5×unpow2
4×exp-diff
4×associate-+r-
4×cube-prod
4×cube-div
4×cos-2
3×rem-cube-cbrt
3×distribute-frac-neg
3×pow-sub
3×pow-neg
2×unpow3
2×sqrt-unprod
2×tan-sum
2×distribute-neg-frac
2×cos-sum
2×rem-log-exp
2×cube-mult
2×associate--r-
1×unpow-prod-up
1×distribute-lft-neg-out
1×difference-of-sqr-1
1×distribute-rgt-out--
1×unpow1/3
1×rem-square-sqrt

end1.0ms