Details

simplify1.0hr

Calls

21491 calls:

Slowest
2.8s
(/ (/ (* (* (* (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))) (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2))))) (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2))))) (* (* (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))) (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2))))) (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))))) (* (* t t) t)) (/ (* (* (sin k) (sin k)) (sin k)) (/ (* (* l l) l) (* (* t t) t))))
2.7s
(/ (/ (* (* (* (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))) (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2))))) (* (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))) (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))))) (* (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))) (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))))) (* (* t t) t)) (/ (* (* (sin k) (sin k)) (sin k)) (* (* (/ l t) (/ l t)) (/ l t))))
2.7s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (/ (* (* (* (* t t) t) (/ (* (* (sin k) (sin k)) (sin k)) (/ (* (* l l) l) (* (* t t) t)))) (/ (* (* (sin k) (sin k)) (sin k)) (/ (* (* l l) l) (* (* t t) t)))) (* (* (cos k) (cos k)) (cos k))))
2.7s
(/ (* (* (* (* -1/2 (* (* (/ D d) (/ M 2)) (* (* (/ D d) (/ M 2)) h))) (* (sqrt (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h))))) (* (* -1/2 (* (* (/ D d) (/ M 2)) (* (* (/ D d) (/ M 2)) h))) (* (sqrt (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h)))))) (* (* -1/2 (* (* (/ D d) (/ M 2)) (* (* (/ D d) (/ M 2)) h))) (* (sqrt (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h)))))) (* (* l l) l))
2.7s
(/ (/ (* (* (* (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))) (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2))))) (* (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))) (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))))) (* (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))) (* (cbrt (cos k)) (cbrt (/ 2 (fma (/ k t) (/ k t) 2)))))) (* (* t t) t)) (/ (* (* (sin k) (sin k)) (sin k)) (/ (* (* l l) l) (* (* t t) t))))

prune5.4m

sample3.1m

Algorithm
53×intervals
Results
52.3s235280×body80valid
36.2s159282×body80nan
26.3s16530×body1280valid
19.9s8525×body10240exit
15.2s13002×body640valid
7.4s5006×body2560valid
5.4s2363×body5120valid
5.1s6400×body320valid
3.9s7594×body160valid
983.0ms614×body1280nan
447.0ms552×body640nan
172.0ms339×body320nan
58.0ms177×body160nan

series1.3m

Calls

404 calls:

Slowest
1.8s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
1.7s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.5s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.5s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
1.3s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (pow (/ d (cbrt l)) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

rewrite26.2s

Algorithm
106×rewrite-expression-head
Calls

404 calls:

Slowest
4.5s
(* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (/ (* (* -1/2 (* (* (/ D d) (/ M 2)) (* (* (/ D d) (/ M 2)) h))) (* (sqrt (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h))))) l))
1.6s
(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
1.5s
(/ (* (* -1/2 (* (* (/ D d) (/ M 2)) (* (* (/ D d) (/ M 2)) h))) (* (sqrt (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h))))) l)
979.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
915.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
Rules
44873×times-frac
22554×add-sqr-sqrt
20871×*-un-lft-identity
19656×add-cube-cbrt
8527×sqrt-prod
7563×add-exp-log
5453×add-cbrt-cube
3680×cbrt-prod
3361×prod-exp
2481×div-exp
2372×cbrt-unprod
1872×associate-*r*
1860×pow1
1822×div-inv
1734×cbrt-undiv
1291×prod-diff
1261×associate-/l*
973×associate-*l*
895×associate-/r*
840×associate-/r/
729×unpow-prod-down
664×difference-of-squares
598×unswap-sqr
503×pow-prod-down
455×add-log-exp
454×associate-*r/
404×expm1-log1p-u insert-posit16 log1p-expm1-u
345×associate-*l/
315×pow-exp
294×frac-times
268×pow-prod-up
224×sqr-pow
223×distribute-lft-out--
200×distribute-lft-out
196×distribute-rgt-neg-in
192×distribute-lft-neg-in
184×flip3-- flip--
174×1-exp rec-exp
165×distribute-rgt-in distribute-lft-in
164×pow-unpow
155×pow-sqr
154×pow-to-exp
150×pow-plus *-commutative
130×sqrt-div
113×frac-2neg clear-num
107×cbrt-div
101×fma-neg
95×pow2
90×swap-sqr
74×sqrt-pow1
73×associate-/l/
58×pow1/3
53×sub-neg
47×rem-sqrt-square
46×fma-udef
44×associate--r+
42×pow1/2
35×tan-quot
30×unpow2
29×flip-+ flip3-+
27×pow-flip associate--l+ cos-sum
24×pow-pow fma-def
23×frac-sub inv-pow
22×neg-mul-1
21×diff-log
19×div-sub
18×frac-add
13×pow-sub
12×un-div-inv
sum-log +-commutative
log-prod
pow3 distribute-neg-frac hypot-udef
neg-sub0 distribute-lft-neg-out neg-log difference-of-sqr-1 exp-prod acos-asin
exp-sum associate--l- asin-acos
sin-sum associate-+r- distribute-frac-neg log-pow associate--r-
associate-+l+ mul0 sub-div sqr-sin rem-log-exp rem-exp-log rem-cbrt-cube cos-diff sin-mult

regimes15.6s

Accuracy

Total 45.1b remaining (33.6%)

10.7b30%Henrywood and Agarwal, Equation (3)
9.1b12.2%Toniolo and Linder, Equation (13)
7.4b1.4%Henrywood and Agarwal, Equation (13)
5.7b24.9%Henrywood and Agarwal, Equation (12)
5.2b78%Toniolo and Linder, Equation (7)

localize5.9s

bsearch2.4s

end1.0ms