Details

simplify13.5m

Calls

7354 calls:

Slowest
2.6s
(/ (* (* (* (/ 2 k) l) (* (/ 2 k) l)) (* (/ 2 k) l)) (* (* (* (* (/ (sin k) l) t) (* k (tan k))) (* (* (/ (sin k) l) t) (* k (tan k)))) (* (* (/ (sin k) l) t) (* k (tan k)))))
2.3s
(/ (* (* (* (/ 2 k) l) (* (/ 2 k) l)) (* (/ 2 k) l)) (* (* (* (/ (sin k) l) (/ (sin k) l)) (/ (sin k) l)) (* (* (* t (* k (tan k))) (* t (* k (tan k)))) (* t (* k (tan k))))))
2.1s
(/ (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* (/ l h) (/ l h)) (/ l h)))
2.1s
(/ (* (* (* (/ 2 k) l) (* (/ 2 k) l)) (* (/ 2 k) l)) (* (* (* (/ (sin k) l) (* t (* k (tan k)))) (* (/ (sin k) l) (* t (* k (tan k))))) (* (/ (sin k) l) (* t (* k (tan k))))))
1.9s
(/ (* (* (* (/ 2 k) l) (* (/ 2 k) l)) (* (/ 2 k) l)) (* (* (* (* (/ (sin k) l) t) (* (/ (sin k) l) t)) (* (/ (sin k) l) t)) (* (* (* k (tan k)) (* k (tan k))) (* k (tan k)))))

sample4.4m

Algorithm
56×intervals
Results
1.0m247501×body80valid
48.0s24106×body1280valid
40.8s160073×body80nan
27.9s18167×body640valid
19.9s8669×body10240exit
18.1s7306×body2560valid
14.1s3282×body5120valid
9.6s8998×body320valid
5.9s8854×body160valid
712.0ms348×body320nan
596.0ms612×body1280nan
560.0ms657×body640nan
102.0ms196×body160nan

prune2.6m

series1.1m

Calls

392 calls:

Slowest
2.8s
(sqrt (pow (* U (* (* (- (fma -2 (/ l (/ Om l)) t) (* (* n (/ l Om)) (* (/ l Om) (- U U*)))) n) 2)) 1))
2.5s
(sqrt (pow (* U (* (* (- (fma -2 (/ (* l l) Om) t) (* (* n (/ l Om)) (* (/ l Om) (- U U*)))) n) 2)) 1))
1.7s
(sqrt (pow (* U (* (* (fma (* (cbrt (fma -2 (/ l (/ Om l)) t)) (cbrt (fma -2 (/ l (/ Om l)) t))) (cbrt (fma -2 (/ l (/ Om l)) t)) (- (* (* n (/ l Om)) (* (/ l Om) (- U U*))))) n) 2)) 1))
1.6s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.4s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

regimes16.8s

Accuracy

Total 47.4b remaining (26.8%)

9.4b-19%Henrywood and Agarwal, Equation (13)
8.3b30.9%Toniolo and Linder, Equation (13)
6.1b73.7%Toniolo and Linder, Equation (7)
4.6b46.5%Henrywood and Agarwal, Equation (12)
3.9b68.1%Henrywood and Agarwal, Equation (3)

bsearch4.8s

rewrite3.5s

Algorithm
108×rewrite-expression-head
Calls

392 calls:

Slowest
251.0ms
(+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)))
96.0ms
(* (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))) (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) J))))
95.0ms
(/ (+ (* PI PI) (+ (* (* v (* PI v)) (* v (* PI v))) (* PI (* v (* PI v))))) (sqrt (fma (* v -6) v 2)))
73.0ms
(sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M)))
69.0ms
(* (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))) (* -2 (* (* (log1p (expm1 (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) J))))
Rules
2929×times-frac
2282×add-sqr-sqrt
2245×*-un-lft-identity
2222×add-cube-cbrt
988×add-exp-log
950×sqrt-prod
842×add-cbrt-cube
625×pow1
564×div-inv
501×associate-*l*
489×associate-/l*
426×add-log-exp
393×log1p-expm1-u
392×expm1-log1p-u insert-posit16
382×associate-/r*
337×associate-*r*
333×associate-/r/
191×associate-*r/
177×div-exp
171×prod-exp
150×cbrt-undiv
143×cbrt-prod
133×unpow-prod-down
127×associate-*l/
120×frac-2neg clear-num
118×*-commutative
116×cbrt-unprod
115×flip3-- flip--
101×prod-diff
97×frac-times
81×pow-prod-down
80×tan-quot
58×associate-/l/
57×sub-neg
56×sqrt-div
50×exp-prod
46×distribute-rgt-in distribute-lft-in
44×pow-exp pow-unpow pow-to-exp rem-sqrt-square
41×fma-udef
39×pow1/2
38×pow1/3 log-pow
35×cbrt-div flip-+ flip3-+
33×rec-exp unpow-prod-up
29×fma-neg
25×fma-def pow-prod-up
20×pow-plus
19×pow-pow
17×pow2
14×frac-add
12×log-prod frac-sub cube-unmult
11×pow-flip div-sub
10×inv-pow
distribute-lft-neg-in distribute-lft-out-- distribute-rgt-neg-in
sum-log associate--r+ diff-log
difference-of-squares associate--l+ asin-acos pow-sub
distribute-lft-out associate-+r- +-commutative un-div-inv distribute-neg-frac cos-sum
associate-+l+ unpow2
hypot-udef rem-exp-log
neg-sub0 exp-diff exp-sum pow3 distribute-frac-neg neg-mul-1 rem-log-exp cos-diff sin-mult
expm1-log1p expm1-udef associate-+r+ mul0 rem-cbrt-cube acos-asin
remove-posit16 sqrt-undiv sqrt-unprod sub-div sqr-sin associate--r-

localize2.9s

end1.0ms