Details

simplify47.0m

Calls

17237 calls:

Slowest
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) (/ (* (* (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))))
2.1s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (/ (* (* (* (* t (/ (sin k) (/ l t))) (* t (/ (sin k) (/ l t)))) (* t (/ (sin k) (/ l t)))) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (cos k) (cos k)) (cos k))))
2.0s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (* (* (* (* (sin k) (tan k)) (* (sin k) (tan k))) (* (sin k) (tan k))) (/ (* (* t t) t) (* (/ (* (* l l) l) (* (* t t) t)) (/ (* (* l l) l) (* (* t t) t))))))
2.0s
(/ (* (* (/ 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) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (cos k) (cos k)) (cos k))))
1.9s
(* (* (* h h) h) (* (/ (* (* 1 1) 1) (* (* l l) l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))))

prune4.6m

sample3.3m

Algorithm
53×intervals
Results
55.5s231092×body80valid
36.0s160852×body80nan
27.7s15467×body1280valid
20.1s8572×body10240exit
17.0s11903×body640valid
7.2s4942×body2560valid
6.1s2323×body5120valid
5.4s6027×body320valid
3.6s7357×body160valid
1.1s610×body1280nan
971.0ms635×body640nan
214.0ms357×body320nan
167.0ms217×body160nan

series1.4m

Calls

387 calls:

Slowest
1.7s
(* (* (* (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
(* (* (* (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)) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))))
1.6s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.6s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.5s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite24.1s

Algorithm
101×rewrite-expression-head
Calls

387 calls:

Slowest
4.1s
(* (/ c0 (* w 2)) (+ (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))
1.3s
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
958.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
Rules
48507×times-frac
21098×add-sqr-sqrt
20231×*-un-lft-identity
19351×add-cube-cbrt
13515×cbrt-prod
9650×add-exp-log
5970×associate-*l*
4302×prod-exp
3777×add-cbrt-cube
3691×div-exp
2805×sqrt-prod
2361×div-inv
1599×cbrt-undiv
1230×associate-/l*
1204×pow1
1180×associate-/r/
1178×associate-*r*
1117×cbrt-unprod
938×difference-of-squares
740×prod-diff
734×pow-exp
677×associate-/r*
547×1-exp
440×add-log-exp
414×unpow-prod-down
413×rec-exp
387×expm1-log1p-u insert-posit16 log1p-expm1-u
340×pow-unpow
336×log-prod exp-sum
327×pow-prod-down
307×distribute-rgt-in distribute-lft-in
296×associate-*r/
277×unswap-sqr
270×associate-*l/
263×swap-sqr
226×frac-times
206×pow-to-exp
197×flip-- flip3--
185×distribute-rgt-neg-in
181×distribute-lft-neg-in
175×distribute-lft-out--
121×*-commutative
111×sqr-pow
102×frac-2neg clear-num
97×fma-neg
94×distribute-lft-out
89×pow-prod-up
72×pow1/3
61×pow-sqr
58×exp-prod
57×sqrt-div
48×pow-plus
47×sqrt-pow1 cos-sum
45×sub-neg
44×tan-quot
40×pow-pow
38×pow2 rem-sqrt-square
37×fma-def pow1/2 fma-udef
34×unpow2
31×associate-/l/
22×associate--r+ associate--l+
21×flip-+ flip3-+
19×frac-sub neg-mul-1 diff-log
16×frac-add
12×difference-of-sqr-1 div-sub
11×pow-flip
sum-log +-commutative inv-pow
cbrt-div pow-sub
un-div-inv
neg-sub0 neg-log hypot-udef
asin-acos acos-asin
associate-+r+ distribute-frac-neg sub-div associate--l- sqr-sin distribute-neg-frac cos-diff associate--r- sin-mult expm1-def
associate-+l+ expm1-log1p expm1-udef remove-posit16 exp-diff sin-sum associate-+r- sqrt-undiv exp-neg rem-exp-log

regimes15.9s

Accuracy

Total 41.4b remaining (30.1%)

10.5b-4.1%Henrywood and Agarwal, Equation (13)
8.1b36.1%Toniolo and Linder, Equation (13)
5.5b-40.3%Maksimov and Kolovsky, Equation (3)
5.4b77%Toniolo and Linder, Equation (7)
4.6b0%Henrywood and Agarwal, Equation (12)

localize5.5s

bsearch2.7s

end1.0ms