Details

prune10.1m

simplify6.4m

sample3.9m

Algorithm
59×intervals
Results
1.0m255689×body80valid
41.8s160617×body80nan
40.3s23874×body1280valid
22.2s16641×body640valid
20.0s8613×body10240exit
8.6s5738×body2560valid
7.9s8250×body320valid
5.7s2486×body5120valid
5.3s8566×body160valid
1.2s632×body1280nan
520.0ms614×body640nan
440.0ms8256×pre80true
251.0ms332×body320nan
55.0ms154×body160nan

series1.7m

Calls

438 calls:

Slowest
16.4s
(sqrt (* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (+ (* (/ l Om) (* (* (/ l Om) (fma (* (cbrt U) (cbrt U)) (cbrt U) (- U*))) n)) (* (* n (/ l Om)) (* (/ l Om) (fma (- U*) 1 U*))))))))
5.7s
(* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (+ (* (/ l Om) (* (* (/ l Om) (fma (* (cbrt U) (cbrt U)) (cbrt U) (- U*))) n)) (* (* n (/ l Om)) (* (/ l Om) (fma (- U*) 1 U*)))))))
2.2s
(sqrt (* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))
2.1s
(sqrt (* U (* (* 2 n) (- t (fma (/ l Om) (* 2 l) (* n (* (* (/ l Om) (/ l Om)) (- U U*))))))))
2.1s
(sqrt (* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* n (* (/ l Om) (* (/ l Om) (- U U*))))))))

rewrite22.5s

Algorithm
115×rewrite-expression-head
Calls

438 calls:

Slowest
1.4s
(+ (sqrt (- (* (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h)) (* M M))) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h))
1.2s
(+ (sqrt (- (* (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h)) (* M M))) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h))
1.1s
(+ (sqrt (- (* (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h)) (* M M))) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h))
593.0ms
(exp (/ (+ EAccept (- (+ Ev Vef) mu)) KbT))
559.0ms
(* (/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (sin k) (* (* (sin k) (/ 1 (/ l t))) t))) (* (cos k) (/ l t)))
Rules
135714×times-frac
57683×add-sqr-sqrt
57502×*-un-lft-identity
56855×add-cube-cbrt
17968×sqrt-prod
5754×add-exp-log
5706×div-inv
4534×add-cbrt-cube
4476×associate-/l*
3748×prod-diff
2209×div-exp
1992×prod-exp
1784×cbrt-undiv
1512×cbrt-unprod
1308×associate-/r/
1188×pow1
910×associate-/r*
683×associate-*r*
659×associate-*l*
505×add-log-exp
439×log1p-expm1-u
438×expm1-log1p-u insert-posit16
394×distribute-rgt-in cbrt-prod distribute-lft-in
388×associate-*r/
327×pow-prod-down
237×tan-quot exp-prod
233×frac-times
220×unswap-sqr
184×associate-*l/
180×unpow-prod-down
176×distribute-lft-out--
175×sqrt-div
174×distribute-lft-out
162×difference-of-squares
157×flip3-- flip--
148×swap-sqr
137×pow-unpow
118×*-commutative
114×sqr-pow
113×frac-2neg cbrt-div clear-num
105×sqrt-pow1
99×1-exp rec-exp
98×pow1/3
86×pow-exp
84×fma-neg
75×sub-neg
66×rem-sqrt-square
62×pow1/2
58×associate-/l/
53×pow-to-exp
51×flip-+ flip3-+
47×pow-prod-up
38×pow-plus
35×pow-sqr
32×div-sub
30×fma-def unpow2
29×fma-udef
27×pow2
22×exp-sum
21×pow-pow diff-log
20×cos-sum
18×pow-flip
17×exp-diff
16×rem-exp-log
15×un-div-inv
14×hypot-udef frac-add pow-sub
12×associate-+r-
11×inv-pow unpow-prod-up
difference-of-sqr-1 expm1-def
pow3
sum-log log-pow
sqrt-unprod +-commutative
frac-sub asin-acos rem-cbrt-cube acos-asin cos-diff sin-mult
log-prod associate--r+
expm1-log1p expm1-udef associate--l+ sqr-sin hypot-def log1p-udef
remove-posit16 cos-mult mul0 log1p-expm1 sub-div exp-to-pow rem-square-sqrt rem-log-exp e-exp-1

regimes17.4s

Accuracy

Total 40.0b remaining (24.6%)

Threshold costs 4.6b (2.9%)

10.4b9.6%Toniolo and Linder, Equation (13)
6.9b20.1%Henrywood and Agarwal, Equation (13)
5.3b-1%Henrywood and Agarwal, Equation (12)
5.2b78%Toniolo and Linder, Equation (7)
3.7b0%Maksimov and Kolovsky, Equation (3)

localize5.8s

bsearch3.0s

end1.0ms