Details

simplify22.5m

Calls

13337 calls:

Slowest
2.0s
(/ (* (/ (* (* (* 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)))
2.0s
(/ (* (* (* (/ 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))))))
1.8s
(/ (* (* (* (/ 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)))))
1.8s
(/ (* (* (* (/ 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)))))
1.7s
(* (/ (* (* (* (/ l t) (/ 2 k)) (* (/ l t) (/ 2 k))) (* (/ l t) (/ 2 k))) (* (* (/ (/ k 1) (/ l t)) (/ (/ k 1) (/ l t))) (/ (/ k 1) (/ l t)))) (* (* (/ t (* (sin k) (tan k))) (/ t (* (sin k) (tan k)))) (/ t (* (sin k) (tan k)))))

sample4.1m

Algorithm
55×intervals
Results
59.5s241818×body80valid
42.0s21914×body1280valid
41.6s159551×body80nan
22.0s16574×body640valid
19.7s8710×body10240exit
18.0s7255×body2560valid
14.0s3419×body5120valid
8.3s8043×body320valid
4.9s8363×body160valid
646.0ms600×body1280nan
476.0ms615×body640nan
198.0ms340×body320nan
65.0ms180×body160nan

prune3.4m

series52.8s

Calls

402 calls:

Slowest
1.2s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.0s
(* (* (/ (cbrt (/ 2 (sin k))) t) l) (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2)))
998.0ms
(sqrt (* (* (* (* 2 n) U) 1) (- t (fma (/ l Om) (* l 2) (- (* (/ U (/ Om l)) (/ n (/ Om l))) (* (/ U* (/ Om l)) (/ n (/ Om l))))))))
992.0ms
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
920.0ms
(* (* (* (fabs (/ (cbrt (/ -1 h)) (cbrt (/ -1 d)))) (sqrt (/ (cbrt (/ -1 h)) (cbrt (/ -1 d))))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) (/ 1 l))))

regimes15.3s

Accuracy

Total 44.2b remaining (28.3%)

8.6b11.1%Toniolo and Linder, Equation (13)
8.0b-5.5%Henrywood and Agarwal, Equation (13)
6.7b41.5%Toniolo and Linder, Equation (7)
4.2b40.8%Henrywood and Agarwal, Equation (12)
4.1b1.3%Toniolo and Linder, Equation (10-)

bsearch6.1s

rewrite5.6s

Algorithm
108×rewrite-expression-head
Calls

402 calls:

Slowest
341.0ms
(* (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))) (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (* (cbrt (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2))))) J))))
318.0ms
(cbrt (* (* (/ (* (* (/ M 2) (/ D d)) (* (* (/ M 2) (/ D d)) h)) l) (/ (* (* (/ M 2) (/ D d)) (* (* (/ M 2) (/ D d)) h)) l)) (/ (* (* (/ M 2) (/ D d)) (* (* (/ M 2) (/ D d)) h)) l)))
282.0ms
(+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)))
275.0ms
(+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)))
265.0ms
(+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)))
Rules
16054×times-frac
7796×add-sqr-sqrt
7771×*-un-lft-identity
7739×add-cube-cbrt
5168×sqrt-prod
3158×cbrt-prod
1889×div-inv
1081×associate-*r*
1036×add-exp-log
903×add-cbrt-cube
898×associate-/l*
636×pow1
465×associate-*r/
439×add-log-exp
433×associate-/r/
403×expm1-log1p-u log1p-expm1-u
402×insert-posit16
380×associate-/r*
341×associate-*l*
253×sqrt-div
215×div-exp
171×cbrt-undiv
170×prod-exp unpow-prod-up
169×flip3-- flip--
168×associate-*l/
164×frac-add
159×frac-times
144×cbrt-unprod
138×unpow-prod-down
135×flip-+ flip3-+
134×cbrt-div
130×*-commutative
126×sub-neg
106×frac-2neg clear-num
90×pow-prod-down
88×prod-diff
64×distribute-rgt-in distribute-lft-in
61×fma-def
56×pow1/2
52×associate-/l/
50×pow1/3
49×pow-to-exp
47×rem-sqrt-square
42×pow-unpow pow-sub
40×tan-quot
38×pow-exp
23×pow-prod-up fma-udef
18×frac-sub fma-neg
17×rec-exp pow-plus pow-pow
16×sum-log
15×pow2
14×difference-of-sqr-1 +-commutative log-pow
12×exp-prod
11×distribute-lft-out
10×difference-of-squares associate-+r+ associate--l+
log-prod
unpow2
pow-flip expm1-udef div-sub
distribute-lft-out-- inv-pow cos-sum
associate-+l+ expm1-log1p acos-asin
un-div-inv diff-log
pow-div distribute-lft-neg-in cos-mult pow3 distribute-rgt-neg-in hypot-udef asin-acos cos-diff
associate-+r- distribute-rgt-out-- sin-mult distribute-neg-frac rem-cbrt-cube expm1-def
neg-sub0 remove-posit16 distribute-frac-neg mul0 log1p-expm1 sqrt-unprod sub-div neg-mul-1 rem-log-exp rem-square-sqrt distribute-rgt-out log1p-udef

localize3.4s

end1.0ms