Details

simplify50.8m

Calls

17354 calls:

Slowest
2.3s
(/ (* (* (/ 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 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))))
2.0s
(/ (/ (* (* 2 2) 2) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2))) (* (* (* (* (sin k) (sin k)) (sin k)) (* (* (tan k) (tan k)) (tan k))) (/ (* (* t t) t) (* (* (* (/ l t) (/ l t)) (/ l t)) (* (* (/ l t) (/ l t)) (/ l t))))))
2.0s
(/ (/ (* (* 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))))))
1.9s
(/ (/ (* (* 2 2) 2) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2))) (* (* (* (* (sin k) (sin k)) (sin k)) (* (* (tan k) (tan k)) (tan k))) (/ (* (* t t) t) (* (/ (* (* l l) l) (* (* t t) t)) (/ (* (* l l) l) (* (* t t) t))))))

prune4.6m

sample3.2m

Algorithm
53×intervals
Results
54.4s234800×body80valid
38.7s157985×body80nan
24.7s16095×body1280valid
20.0s8633×body10240exit
15.2s12783×body640valid
7.9s5048×body2560valid
5.6s2363×body5120valid
5.1s6470×body320valid
3.9s7446×body160valid
721.0ms622×body1280nan
595.0ms380×body320nan
454.0ms595×body640nan
100.0ms197×body160nan

series1.2m

Calls

384 calls:

Slowest
1.7s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (pow (/ d 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 (pow (* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h) 1)))
1.7s
(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*))))))
1.6s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

rewrite25.6s

Algorithm
104×rewrite-expression-head
Calls

384 calls:

Slowest
2.0s
(+ (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
(log (exp (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))))
1.6s
(exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
1.5s
(exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
1.5s
(exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
Rules
24279×times-frac
13673×add-sqr-sqrt
13402×*-un-lft-identity
11919×add-cube-cbrt
5200×add-exp-log
3601×add-cbrt-cube
3268×sqrt-prod
2155×prod-diff
1996×prod-exp
1775×div-exp
1541×pow1
1293×cbrt-undiv
1260×div-inv
1175×cbrt-unprod
1065×associate-/l*
989×unpow-prod-down
852×associate-*l*
767×difference-of-squares
748×pow-unpow
705×associate-/r*
685×associate-/r/
635×associate-*r*
577×distribute-rgt-neg-in
565×distribute-lft-neg-in
558×distribute-lft-out--
532×exp-sum
507×cbrt-prod
497×associate-*r/
480×add-log-exp
455×pow-prod-down
384×expm1-log1p-u insert-posit16 log1p-expm1-u
368×distribute-rgt-in distribute-lft-in
334×exp-prod
273×pow-exp
272×sqr-pow
250×associate-*l/
243×frac-times
196×unswap-sqr
188×flip3-- flip--
164×distribute-lft-out
157×pow-prod-up
149×fma-neg
137×log-pow
134×*-commutative
108×pow-to-exp
102×frac-2neg clear-num
99×pow-sqr
95×1-exp rec-exp
91×swap-sqr
89×unpow2 sqrt-div
79×pow-plus sub-neg
73×sqrt-pow1 frac-sub
59×pow2 neg-mul-1
55×pow1/2
47×rem-sqrt-square
44×diff-log
42×associate--l+
41×associate-/l/
37×pow1/3 fma-udef
36×fma-def
33×associate--r+ pow-pow div-sub
30×tan-quot
24×cos-sum
18×rem-exp-log
17×flip-+ flip3-+
16×difference-of-sqr-1
14×pow-flip
13×pow-sub
12×distribute-rgt-out-- cbrt-div neg-log
10×inv-pow
neg-sub0
un-div-inv
sum-log +-commutative associate--r-
exp-diff distribute-frac-neg distribute-neg-frac
associate-+r+ acos-asin
log-prod exp-neg sub-div associate--l- asin-acos
mul0 frac-add e-exp-1
expm1-log1p quot-tan expm1-udef remove-posit16 sin-sum associate-+r- sqrt-undiv sqrt-unprod sqr-sin hypot-udef rem-square-sqrt cos-diff sin-mult rem-log-exp

regimes17.4s

Accuracy

Total 40.1b remaining (30.9%)

8.9b23.4%Toniolo and Linder, Equation (13)
7.9b0.3%Henrywood and Agarwal, Equation (13)
6.6b46.2%Henrywood and Agarwal, Equation (3)
5.1b78.1%Toniolo and Linder, Equation (7)
4.0b0%Maksimov and Kolovsky, Equation (3)

localize5.8s

bsearch3.3s

end1.0ms