Details

simplify39.3m

Calls

14078 calls:

Slowest
2.5s
(/ (* (* (/ 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))))
2.2s
(/ (/ (* (* 2 2) 2) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 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))))))
2.1s
(/ (* (* 53/8 53/8) 53/8) (* (/ (* (* PI PI) PI) (* (* (* v v) (* v v)) (* v v))) (/ (* (* (* (sqrt 2) t) (* (sqrt 2) t)) (* (sqrt 2) t)) (* (* (* v v) (* v v)) (* v v)))))
2.1s
(/ (* (* 53/8 53/8) 53/8) (* (/ (* (* PI PI) PI) (* (* (* v v) v) (* (* v v) v))) (/ (* (* (* (sqrt 2) t) (* (sqrt 2) t)) (* (sqrt 2) t)) (* (* (* v v) v) (* (* v v) v)))))
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))))))

prune4.1m

sample3.5m

Algorithm
54×intervals
Results
56.2s239551×body80valid
41.5s161835×body80nan
30.2s17610×body1280valid
19.8s8538×body10240exit
18.4s14312×body640valid
8.0s5001×body2560valid
7.1s2346×body5120valid
6.8s7203×body320valid
4.3s7915×body160valid
981.0ms615×body640nan
832.0ms585×body1280nan
269.0ms380×body320nan
71.0ms182×body160nan

series1.4m

Calls

390 calls:

Slowest
2.5s
(sqrt (* 2 (* U (* n (- (fma (* l (/ l Om)) -2 t) (* n (* (/ l Om) (+ (* (fma 1 U (- (* (cbrt U*) (* (cbrt U*) (cbrt U*))))) (/ l Om)) 0))))))))
2.4s
(sqrt (* 2 (* U (* n (- (fma (/ (* l l) Om) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*))))))))
2.3s
(sqrt (* 2 (* U (* n (- (fma (* l (/ l Om)) -2 t) (* n (* (/ l Om) (* (/ l Om) (- U U*)))))))))
2.2s
(sqrt (* 2 (* U (* n (- (fma (* l (/ l Om)) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*))))))))
1.9s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

rewrite27.1s

Algorithm
104×rewrite-expression-head
Calls

390 calls:

Slowest
5.1s
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))
3.9s
(* (/ 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)))
1.9s
(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
1.1s
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (sqrt (sqrt (cos (/ K 2)))) (* -2 (* J (pow (* (cos (* K 1/2)) (* (cos (* K 1/2)) (cos (* K 1/2)))) 1/4)))))
734.0ms
(+ (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))))
Rules
36788×times-frac
17457×add-sqr-sqrt
17076×*-un-lft-identity
16280×add-cube-cbrt
6989×add-exp-log
3728×sqrt-prod
3647×add-cbrt-cube
3614×cbrt-prod
3192×prod-exp
2213×div-exp
1577×div-inv
1401×pow1
1327×cbrt-undiv
1237×prod-diff
1203×cbrt-unprod
1015×associate-/l*
952×associate-*l*
796×associate-*r*
735×associate-/r*
724×associate-/r/
500×difference-of-squares
440×pow-exp
422×add-log-exp
403×pow-prod-down
391×expm1-log1p-u
390×insert-posit16 log1p-expm1-u
300×unpow-prod-down
298×pow-unpow
292×associate-*r/
287×unswap-sqr
229×associate-*l/
212×1-exp rec-exp
210×distribute-lft-out--
208×frac-times
205×distribute-rgt-in distribute-lft-in
202×exp-sum
174×pow-to-exp
160×pow1/3
155×swap-sqr
147×*-commutative
143×pow-prod-up
140×distribute-lft-out
116×exp-prod
104×distribute-lft-neg-in distribute-rgt-neg-in
101×sqrt-pow1
98×flip3-- flip--
97×pow-sqr
96×frac-2neg clear-num
88×sqr-pow
67×pow1/2 fma-udef
58×pow-plus
56×sub-neg
48×sqrt-div pow2
46×fma-neg
45×rem-sqrt-square
35×associate-/l/
33×associate--l+
31×tan-quot
29×pow-pow log-pow
25×fma-def cos-sum
22×flip-+ div-sub flip3-+
18×frac-add
16×unpow2
14×log-prod
12×neg-mul-1
10×pow-flip
pow-sub
sum-log +-commutative inv-pow log-div
associate--r- diff-log
exp-diff
rem-exp-log
sqrt-unprod
frac-sub cbrt-div hypot-udef distribute-rgt-out-- sqr-cos
neg-sub0 cos-mult sin-sum associate-+r- associate-+r+ log1p-def cube-unmult distribute-frac-neg un-div-inv distribute-neg-frac rem-square-sqrt
remove-posit16 log1p-expm1 sub-div sqr-sin rem-log-exp exp-neg asin-acos acos-asin cos-diff sin-mult e-exp-1 log1p-udef

regimes15.3s

Accuracy

Total 34.3b remaining (26.4%)

9.4b-7%Henrywood and Agarwal, Equation (13)
5.6b0%Toniolo and Linder, Equation (13)
5.2b77.9%Toniolo and Linder, Equation (7)
4.5b0%Henrywood and Agarwal, Equation (12)
3.6b0%Maksimov and Kolovsky, Equation (3)

localize5.5s

bsearch4.9s

end1.0ms