Details

simplify42.3m

Calls

15653 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))))
2.0s
(/ (/ (* (* 2 2) 2) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 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 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))))))
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))))))
1.9s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 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))))))

prune4.2m

sample3.1m

Algorithm
52×intervals
Results
54.6s229575×body80valid
34.9s152378×body80nan
25.7s15396×body1280valid
18.6s8561×body10240exit
14.7s12342×body640valid
7.7s4827×body2560valid
5.3s6407×body320valid
5.3s2386×body5120valid
3.6s7678×body160valid
724.0ms649×body1280nan
683.0ms651×body640nan
222.0ms361×body320nan
69.0ms190×body160nan

series1.3m

Calls

384 calls:

Slowest
1.7s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.7s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.7s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))
1.5s
(* (* (/ (+ EAccept (- (+ Ev Vef) mu)) KbT) (/ (+ EAccept (- (+ Ev Vef) mu)) KbT)) (/ (+ EAccept (- (+ Ev Vef) mu)) KbT))
1.5s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite20.2s

Algorithm
102×rewrite-expression-head
Calls

384 calls:

Slowest
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))
1.6s
(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
715.0ms
(cbrt (* (* (* (* a a) (* a a)) (* a a)) (* (* (* a a) (* a a)) (* a a))))
706.0ms
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ 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))))
697.0ms
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ 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)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
Rules
41279×times-frac
19611×add-sqr-sqrt
19477×*-un-lft-identity
18109×add-cube-cbrt
6937×sqrt-prod
5982×add-exp-log
3271×add-cbrt-cube
2703×associate-*r*
2466×prod-exp
2030×div-exp
1749×associate-/l*
1655×div-inv
1550×pow1
1246×cbrt-undiv
1228×difference-of-squares
1160×cbrt-prod
1019×associate-/r/
1014×prod-diff
972×cbrt-unprod
731×associate-*l*
697×associate-/r*
506×pow-exp
443×pow-unpow
427×add-log-exp
424×pow-prod-down
418×associate-*r/
384×expm1-log1p-u insert-posit16 log1p-expm1-u
300×flip3-- flip--
288×associate-*l/
272×unpow-prod-down
265×frac-times
262×unswap-sqr
251×distribute-lft-out
204×distribute-rgt-in distribute-lft-in
200×pow-to-exp
197×distribute-lft-out--
194×pow-prod-up
149×1-exp
136×swap-sqr
126×*-commutative
125×sqrt-div
116×rec-exp
115×pow-plus
113×pow-sqr
107×frac-2neg clear-num
89×sqr-pow
78×exp-prod
72×pow2
65×associate-/l/
63×frac-sub
60×sqrt-pow1
59×pow1/3
56×distribute-lft-neg-in distribute-rgt-neg-in
53×div-sub
52×sub-neg
51×fma-def
45×pow1/2
44×fma-neg rem-sqrt-square
38×associate--l+
36×fma-udef
33×tan-quot
32×pow-pow
31×flip-+ flip3-+
29×log-pow
25×pow-sub
21×log-prod
15×sum-log
14×cbrt-div cos-sum
11×+-commutative
10×pow-flip
pow3
neg-mul-1 inv-pow frac-add
unpow2
exp-sum acos-asin diff-log
rem-exp-log
associate-+r- rem-log-exp distribute-neg-frac sum-cubes rem-cbrt-cube
cube-prod
associate-+l+ expm1-log1p neg-sub0 expm1-udef exp-diff associate-+r+ distribute-frac-neg hypot-udef asin-acos cos-diff un-div-inv
remove-posit16 sqrt-undiv mul0 unpow3 sub-div sqr-sin cube-mult sin-mult

regimes14.3s

Accuracy

Total 41.5b remaining (31.8%)

8.8b-21.8%Henrywood and Agarwal, Equation (13)
8.3b34.9%Toniolo and Linder, Equation (13)
7.7b46%Henrywood and Agarwal, Equation (3)
4.9b79.3%Toniolo and Linder, Equation (7)
4.4b0%Henrywood and Agarwal, Equation (12)

localize5.2s

bsearch2.0s

end1.0ms