Details

simplify4.0m (31.9%)

sample3.3m (26.6%)

Algorithm
61×intervals
Results
44.4s253197×body80valid
39.1s29526×body1280valid
28.1s160776×body80nan
18.8s20109×body640valid
17.2s8730×body2560valid
10.1s3246×body5120valid
7.5s9991×body320valid
3.2s9054×body160valid
968.0ms780×body10240exit
661.0ms651×body1280nan
514.0ms8256×pre80true
419.0ms617×body640nan
125.0ms174×body160nan
101.0ms314×body320nan

series2.4m (19.2%)

Calls

427 calls:

3.7s
(/ (- (pow 1.0 6) (log1p (expm1 (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)))) (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 1.0 (pow 1.0 3))))
2.9s
(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) 2.0))) (- U U*)))) (* (* 2.0 n) U)))
2.9s
(/ (- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 1.0 (pow 1.0 3))))
2.8s
(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (+ (* (pow (/ l Om) 2.0) (* n (- U U*))) (* n (* (pow (/ l Om) 2.0) (+ U* (- U*))))))) (* (* 2.0 n) U)))
2.7s
(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))

prune1.8m (14.4%)

rewrite34.9s (4.7%)

Algorithm
114×rewrite-expression-head
Calls

427 calls:

9.8s
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
1.3s
(/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
842.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
807.0ms
(/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)
655.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt d) l) (/ 1.0 2.0)))) (- 1.0 (* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
Rules
44509×add-exp-log
30925×prod-exp
23080×pow-exp
18337×div-exp
11448×pow-to-exp
8308×times-frac
5478×add-sqr-sqrt
5073×*-un-lft-identity
4602×add-cube-cbrt
3587×1-exp rec-exp
2700×add-cbrt-cube
1265×sqrt-prod
1253×unpow-prod-down
1012×pow1
965×cbrt-unprod
835×cbrt-undiv
832×cbrt-prod
797×associate-*r*
721×associate-/l*
704×div-inv
684×associate-*l*
571×associate-/r/
538×prod-diff
476×add-log-exp
437×associate-*r/
429×log1p-expm1-u
427×expm1-log1p-u
390×associate-/r*
379×pow-unpow
327×associate-*l/
295×sqr-pow
277×pow-prod-down
234×unswap-sqr
179×difference-of-squares
162×distribute-rgt-in distribute-lft-in
155×distribute-lft-out--
133×fma-def
125×distribute-rgt-neg-in
123×exp-sum
122×*-commutative
120×distribute-lft-out
108×sqrt-div
104×distribute-lft-neg-in
103×clear-num frac-2neg
97×sqrt-pow1
96×flip3-- flip--
90×cos-sum
89×frac-times
67×pow1/2
64×tan-quot
56×pow1/3
52×rem-sqrt-square
50×pow-pow
48×exp-prod
47×cube-prod
44×sin-sum unpow2
43×sub-neg
38×swap-sqr
37×fma-udef
33×flip-+ flip3-+
30×associate-/l/
27×log-pow
23×div-sub
22×fma-neg
18×unpow3 cube-mult sum-log
16×cbrt-div
15×cube-div
14×+-commutative neg-mul-1
13×pow-prod-up hypot-def
12×rem-cube-cbrt
11×pow-sub
9×pow-sqr neg-sub0
7×diff-log
6×associate-+r+
5×pow-neg inv-pow pow-flip
4×exp-diff frac-add distribute-rgt-out acos-asin distribute-neg-frac
3×pow-plus un-div-inv cos-diff expm1-log1p hypot-udef log-prod rem-cbrt-cube expm1-udef pow2
2×associate-+l+ asin-acos log1p-udef associate-+r- distribute-rgt1-in unsub-neg neg-log associate-+l-
1×rem-exp-log sqrt-unprod log1p-expm1 rem-square-sqrt distribute-frac-neg associate--r- mul0 rem-log-exp sin-diff

regimes16.3s (2.2%)

Accuracy

Total 45.7b remaining (21.5%)

Threshold costs 5.2b (2.5%)

9.0b15.1%Toniolo and Linder, Equation (13)
7.4b68.8%Toniolo and Linder, Equation (7)
7.3b42.1%Henrywood and Agarwal, Equation (3)
5.7b27.4%Toniolo and Linder, Equation (10-)
4.8b0%Henrywood and Agarwal, Equation (12)

localize4.5s (0.6%)

bsearch2.8s (0.4%)

end1.0ms (0.0%)