Details

simplify34.8m

Calls

13887 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))))
2.5s
(/ (* (* (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h) (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h)) (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h)) (* (* (* 2 l) (* 2 l)) (* 2 l)))
2.4s
(* (* (/ (* (* (* D M) (* D M)) (* D M)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* (* D M) (* D M)) (* D M)) (* (* (* 2 2) 2) (* (* d d) d)))) (* (* h h) h))
2.2s
(* (* (/ (* (* (* D D) D) (* (* M M) M)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* D D) D) (* (* M M) M)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* h h) h))
2.2s
(* (* (/ (* (* (* D D) D) (* (* M M) M)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* (* D D) D) (* (* M M) M)) (* (* (* 2 2) 2) (* (* d d) d)))) (* (* h h) h))

prune4.1m

sample3.4m

Algorithm
54×intervals
Results
56.2s238791×body80valid
35.9s159416×body80nan
32.6s17810×body1280valid
19.5s8686×body10240exit
18.5s14155×body640valid
7.4s5010×body2560valid
7.3s7372×body320valid
5.5s2331×body5120valid
4.4s8088×body160valid
694.0ms647×body1280nan
593.0ms657×body640nan
255.0ms352×body320nan
62.0ms174×body160nan

series1.3m

Calls

389 calls:

Slowest
2.5s
(sqrt (* 2 (* U (* n (- (fma (/ l (/ Om l)) -2 t) (* (* n (* (/ l Om) (/ l Om))) (- U U*)))))))
2.3s
(sqrt (* 2 (* U (* n (- (fma (/ l (/ Om l)) -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*))))))))
1.6s
(* (* (* (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))))
1.5s
(* (* (* (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 (/ (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h) (* 2 l))))

rewrite19.1s

Algorithm
104×rewrite-expression-head
Calls

389 calls:

Slowest
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))
1.0s
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
935.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
720.0ms
(* (* (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2))) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2))) (pow n (/ (- 1 k) 2)))
581.0ms
(* (* (* (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))))
Rules
18892×times-frac
10962×*-un-lft-identity
10306×add-sqr-sqrt
9189×add-cube-cbrt
6543×add-exp-log
3490×sqrt-prod
3485×add-cbrt-cube
3413×prod-exp
1782×div-exp
1369×pow1
1191×cbrt-undiv
1190×cbrt-unprod
1063×prod-diff
1034×associate-/l*
1004×div-inv
828×associate-*r*
813×pow-exp
736×associate-*l*
594×associate-/r/
567×distribute-lft-out--
539×distribute-rgt-neg-in
509×distribute-lft-neg-in
507×associate-/r*
473×distribute-lft-out
465×add-log-exp
452×pow-to-exp
393×log1p-expm1-u
389×expm1-log1p-u insert-posit16
384×pow-prod-down
359×associate-*r/
342×difference-of-squares
324×unpow-prod-down
290×associate-*l/
279×cbrt-prod
270×frac-times
231×unswap-sqr
224×distribute-rgt-in distribute-lft-in
212×swap-sqr
189×1-exp rec-exp
176×pow-unpow
165×exp-prod
135×*-commutative
123×pow-prod-up
117×fma-neg
113×div-sub
99×sqr-pow
91×frac-2neg clear-num
85×sqrt-div
83×flip3-- flip--
79×pow-sqr
64×sqrt-pow1
62×pow-plus
61×pow1/3 pow-sub
59×neg-mul-1
56×sub-neg
51×pow1/2
47×pow2
46×log-prod tan-quot
45×associate-/l/
43×fma-udef
37×rem-sqrt-square
33×associate--r+
32×flip-+ fma-def flip3-+
30×unpow2
27×diff-log
26×log-pow
24×cos-sum
22×pow-flip associate-+r+
20×pow-pow
14×sum-log associate--l+
12×difference-of-sqr-1
10×inv-pow distribute-neg-frac
associate-+l+ neg-sub0 cbrt-div
+-commutative
associate-+r- distribute-frac-neg neg-log rem-exp-log
exp-diff
expm1-log1p expm1-udef remove-posit16 rem-log-exp acos-asin
frac-sub exp-sum associate--l- associate--r- distribute-rgt-out--
mul0 log1p-expm1 sqr-sin asin-acos hypot-def un-div-inv frac-add sin-mult log1p-udef
sin-sum sqrt-undiv exp-neg sqrt-unprod sub-div hypot-udef rem-square-sqrt cos-diff log-div

regimes16.4s

Accuracy

Total 38.2b remaining (27%)

8.7b30.9%Henrywood and Agarwal, Equation (3)
7.0b-4.3%Toniolo and Linder, Equation (13)
5.5b76.4%Toniolo and Linder, Equation (7)
5.4b26.1%Henrywood and Agarwal, Equation (13)
3.9b0%Maksimov and Kolovsky, Equation (3)

localize5.6s

bsearch3.6s

end1.0ms