Details

simplify50.3m

Calls

19297 calls:

Slowest
3.6s
(/ (/ (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* d d) d) (* (* 2 2) 2))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* d d) d) (* (* 2 2) 2)))) (* (* 2 2) 2)) (* (* l l) l))
3.4s
(/ (/ (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* d 2) (* d 2)) (* d 2))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* d 2) (* d 2)) (* d 2)))) (* (* 2 2) 2)) (* (* l l) l))
2.4s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (/ (* (* (* (* t t) t) (/ (* (* t t) t) (/ (* (* l l) l) (* (* (sin k) (sin k)) (sin k))))) (/ (* (* t t) t) (/ (* (* l l) l) (* (* (sin k) (sin k)) (sin k))))) (* (* (cos k) (cos k)) (cos k))))
2.2s
(/ (/ (* (* 2 2) 2) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2))) (/ (* (* (* (* t (/ t (/ l (sin k)))) (/ t (/ l (sin k)))) (* (* t (/ t (/ l (sin k)))) (/ t (/ l (sin k))))) (* (* t (/ t (/ l (sin k)))) (/ t (/ l (sin k))))) (* (* (cos k) (cos k)) (cos k))))
2.2s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (* (* (* (* (sin k) (sin k)) (sin k)) (* (* (tan k) (tan k)) (tan k))) (/ (* (* t t) t) (* (/ (* (* l l) l) (* (* t t) t)) (/ (* (* l l) l) (* (* t t) t))))))

prune5.0m

sample3.7m

Algorithm
57×intervals
Results
1.0m247068×body80valid
43.2s159531×body80nan
33.0s19088×body1280valid
20.3s8666×body10240exit
20.0s14732×body640valid
7.4s5764×body2560valid
7.2s7610×body320valid
4.9s2467×body5120valid
4.4s8157×body160valid
926.0ms641×body640nan
671.0ms646×body1280nan
446.0ms8256×pre80true
207.0ms333×body320nan
66.0ms190×body160nan

series1.4m

Calls

422 calls:

Slowest
1.9s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
1.9s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (pow (* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h) 1)))
1.9s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*)))))
1.8s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
1.7s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (/ (* (/ n (/ Om l)) (- U U*)) (/ Om l)))))

rewrite31.6s

Algorithm
112×rewrite-expression-head
Calls

422 calls:

Slowest
4.3s
(* (cbrt (/ NdChar (+ (* (* (cbrt (exp (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT))) (cbrt (exp (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT)))) (cbrt (exp (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT)))) 1))) (cbrt (/ NdChar (+ (* (* (cbrt (exp (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT))) (cbrt (exp (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT)))) (cbrt (exp (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT)))) 1))))
2.0s
(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
1.9s
(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
1.8s
(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
1.7s
(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
Rules
27111×times-frac
17319×*-un-lft-identity
15814×add-sqr-sqrt
13381×add-cube-cbrt
5498×add-exp-log
4832×sqrt-prod
3533×add-cbrt-cube
3380×prod-diff
2576×distribute-lft-out
2062×div-exp
1972×prod-exp
1411×pow1
1402×div-inv
1388×associate-*l*
1344×cbrt-undiv
1288×associate-/l*
1040×cbrt-unprod
974×associate-*r*
934×unpow-prod-down
927×associate-/r*
915×associate-/r/
634×cbrt-prod
500×add-log-exp
446×difference-of-squares
422×expm1-log1p-u insert-posit16 log1p-expm1-u
375×pow-prod-down
351×associate-*r/
345×sqr-pow
297×pow-exp distribute-rgt-in distribute-lft-in
270×unswap-sqr
239×distribute-lft-out--
228×associate-*l/
220×frac-times
170×flip3-- flip--
168×flip-+ flip3-+
166×1-exp
161×distribute-lft-neg-in distribute-rgt-neg-in
160×rec-exp
153×pow-unpow
127×pow-prod-up
124×*-commutative pow-to-exp
112×frac-2neg clear-num
108×sqrt-div
106×fma-neg
103×sqrt-pow1
91×swap-sqr
83×pow-sqr
80×fma-def
79×sub-neg
74×exp-prod
66×pow1/3
65×pow-plus
63×associate--l+
61×pow1/2
55×exp-sum
54×pow-flip
50×pow2
46×frac-sub
45×distribute-rgt-out--
43×fma-udef
42×associate-/l/
38×rem-sqrt-square
35×tan-quot
30×difference-of-sqr-1
28×log-prod cos-sum
23×pow-pow neg-mul-1
22×hypot-udef div-sub
20×sum-log cbrt-div diff-log
17×+-commutative inv-pow
16×associate-+r+
13×sqrt-unprod pow-sub
12×log-pow
10×distribute-neg-frac
frac-add
un-div-inv
unpow-prod-up neg-sub0 distribute-frac-neg
rem-log-exp unpow2
pow-div acos-asin cos-diff
rem-square-sqrt rem-exp-log
exp-diff associate-+r- sub-div asin-acos hypot-def sin-mult e-exp-1
mul0 pow3 sqrt-pow2 associate--r+ exp-neg rem-cbrt-cube expm1-def

regimes16.6s

Accuracy

Total 40.2b remaining (27.1%)

7.9b-4.7%Given's Rotation SVD example
7.5b25.7%Toniolo and Linder, Equation (13)
5.4b77%Toniolo and Linder, Equation (7)
5.4b25.1%Henrywood and Agarwal, Equation (13)
4.9b-22.7%Maksimov and Kolovsky, Equation (3)

localize5.9s

bsearch3.7s

end1.0ms