Details

prune10.4m

simplify5.4m

sample3.8m

Algorithm
59×intervals
Results
1.1m255973×body80valid
41.5s161035×body80nan
38.9s23923×body1280valid
21.5s16555×body640valid
20.1s8677×body10240exit
6.8s5732×body2560valid
6.6s8537×body320valid
6.1s2472×body5120valid
3.8s8593×body160valid
715.0ms607×body1280nan
628.0ms627×body640nan
551.0ms8256×pre80true
224.0ms350×body320nan
73.0ms197×body160nan

rewrite3.6m

Algorithm
115×rewrite-expression-head
Calls

454 calls:

Slowest
16.4s
(/ (/ (/ 1 (/ (/ k 1) l)) (/ (sin k) (/ 2 (/ (/ k l) (/ 1 t))))) (tan k))
616.0ms
(/ (* (* (* (* (fabs (/ (cbrt d) (cbrt l))) (sqrt (/ (cbrt d) (cbrt l)))) (sqrt (/ d h))) (/ M (/ 2 (/ D d)))) (* (/ M (/ 2 (/ D d))) h)) (* l 2))
337.0ms
(cbrt (* (* (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))) (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))))
325.0ms
(/ (* (* (* (fabs (/ (cbrt d) (cbrt l))) (sqrt (/ (cbrt d) (cbrt l)))) (sqrt (/ d h))) (* (/ M (/ 2 (/ D d))) (* (/ M (/ 2 (/ D d))) h))) (* l 2))
307.0ms
(* (exp (- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))) (cos (- (/ (* (+ m n) K) 2) M)))
Rules
7271137×times-frac
2640481×add-sqr-sqrt
2639489×*-un-lft-identity
2637893×add-cube-cbrt
217821×div-inv
213835×associate-/l*
14943×associate-/r/
9963×add-exp-log
9205×cbrt-prod
8987×sqrt-prod
8172×add-cbrt-cube
5589×associate-*r*
4609×div-exp
3278×cbrt-undiv
3260×prod-exp
3020×cbrt-unprod
1869×pow1
1702×difference-of-squares
1669×associate-/r*
1130×associate-*l*
809×sqrt-div
755×flip-+ flip3-+
581×pow-prod-down
579×add-log-exp
525×associate-*r/
454×insert-posit16
441×frac-times
419×unswap-sqr
371×associate-*l/
334×distribute-lft-out--
284×flip3-- flip--
228×1-exp
199×unpow-prod-down
192×rec-exp
184×exp-prod
170×*-commutative
159×cbrt-div
156×sqr-pow
153×pow-prod-up
139×swap-sqr
115×frac-2neg clear-num
114×sqrt-pow1
108×frac-add
104×distribute-rgt-in distribute-lft-in
98×distribute-lft-out
96×pow-sqr
93×pow-exp
91×associate-/l/
86×pow1/2
84×rem-sqrt-square
82×pow-plus
73×sub-neg
71×sin-mult
64×pow-unpow
60×pow2
49×difference-of-sqr-1 pow-to-exp
48×div-sub
37×sum-log
30×pow-sub
28×pow1/3
27×pow-flip
26×+-commutative diff-log
25×distribute-rgt-out-- log-pow
18×pow-pow
14×associate-+l+
13×tan-quot inv-pow
11×associate-+r+
10×rem-exp-log
log-prod exp-sum sqr-sin
exp-diff pow3
acos-asin
pow-div distribute-lft-neg-out asin-acos
frac-sub associate--r+ remove-posit16 cos-diff distribute-rgt-out distribute-rgt1-in
sqrt-undiv associate--l+ cos-sum unpow2 rem-cbrt-cube rem-log-exp
sub-div un-div-inv exp-to-pow

series1.3m

Calls

454 calls:

Slowest
2.4s
(sqrt (pow (* (* (- t (* (+ (* l 2) (* n (* (/ l Om) (- U U*)))) (/ l Om))) U) (* n 2)) 1))
1.9s
(sqrt (* (* U 2) (* n (- t (* (/ l Om) (- (* 2 l) (- (/ (* n (* U* l)) Om) (/ (* U (* n l)) Om))))))))
1.9s
(sqrt (* (* (* U 2) n) (- t (* (/ l Om) (- (* 2 l) (* (* (- n) (- U U*)) (/ l Om)))))))
1.8s
(sqrt (* (* U 2) (* n (- t (* (/ l Om) (- (* 2 l) (* (* (- n) (- U U*)) (/ l Om))))))))
1.6s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

regimes18.2s

Accuracy

Total 44.2b remaining (23%)

Threshold costs 4.6b (2.4%)

10.9b17.2%Toniolo and Linder, Equation (13)
8.2b6.1%Maksimov and Kolovsky, Equation (3)
5.5b0%Henrywood and Agarwal, Equation (13)
5.4b77.3%Toniolo and Linder, Equation (7)
4.8b7.2%Henrywood and Agarwal, Equation (12)

localize6.4s

bsearch4.2s

end1.0ms