Details

simplify43.5m

Calls

16384 calls:

Slowest
3.9s
(/ (/ (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* d 2) (* d 2)) (* d 2))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* d 2) (* d 2)) (* d 2)))) (* (* 2 2) 2)) (* (* l l) l))
3.4s
(/ (/ (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* d d) d) (* (* 2 2) 2))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* d d) d) (* (* 2 2) 2)))) (* (* 2 2) 2)) (* (* l l) l))
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))))
2.1s
(/ (/ (* (* 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
(* (* (* h h) h) (* (* (* (/ 1 l) (/ 1 l)) (/ 1 l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))))

prune4.5m

sample3.6m

Algorithm
57×intervals
Results
1.0m242107×body80valid
40.4s152570×body80nan
33.8s21702×body1280valid
19.4s8484×body10240exit
18.5s15235×body640valid
9.7s5745×body2560valid
6.9s7523×body320valid
5.8s2412×body5120valid
4.3s8084×body160valid
988.0ms584×body1280nan
588.0ms636×body640nan
362.0ms8256×pre80true
179.0ms320×body320nan
68.0ms188×body160nan

series1.5m

Calls

433 calls:

Slowest
2.4s
(* (- (* (/ (- Ec (+ (+ Vef mu) EDonor)) KbT) (/ (- Ec (+ (+ Vef mu) EDonor)) KbT))) (/ (- Ec (+ (+ Vef mu) EDonor)) KbT))
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 (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.7s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.6s
(sqrt (* (* 2 n) (* U (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*))))))

rewrite29.3s

Algorithm
113×rewrite-expression-head
Calls

433 calls:

Slowest
4.2s
(* (/ c0 (* w 2)) (+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)))
1.8s
(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
1.3s
(/ NdChar (+ (exp (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT)) 1))
709.0ms
(* (+ 1 (exp (/ (+ EAccept (- (+ Ev Vef) mu)) KbT))) (+ 1 (exp (/ (+ EAccept (- (+ Ev Vef) mu)) KbT))))
674.0ms
(+ (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))))
Rules
62495×times-frac
28770×*-un-lft-identity
28536×add-sqr-sqrt
28155×sqrt-prod
27340×add-cube-cbrt
6337×add-exp-log
3796×add-cbrt-cube
2680×prod-exp
2101×div-exp
1762×associate-/r/
1724×div-inv
1397×sqrt-div
1390×cbrt-undiv
1387×pow1
1363×associate-*r*
1217×associate-/l*
1184×cbrt-unprod
1137×prod-diff
923×associate-/r*
852×associate-*l*
843×cbrt-prod
751×flip-- flip3--
479×distribute-lft-out add-log-exp
475×pow-exp
453×associate-*r/
433×expm1-log1p-u log1p-expm1-u insert-posit16
397×pow-prod-down
374×frac-times
368×difference-of-squares
330×associate-*l/
325×distribute-lft-out--
321×pow-to-exp
309×unpow-prod-down
290×unswap-sqr
253×swap-sqr
205×pow-unpow
200×distribute-rgt-in distribute-lft-in
158×1-exp
156×rec-exp
143×*-commutative
136×sqrt-pow1
110×frac-2neg clear-num
100×sqr-pow
97×pow-prod-up
87×div-sub
82×pow1/3
77×pow-sub
76×exp-prod
74×log-pow
70×pow1/2
67×pow-sqr
65×sub-neg
60×associate--l+
57×distribute-lft-neg-in distribute-rgt-neg-in associate-/l/
53×fma-neg
51×flip-+ flip3-+ rem-sqrt-square
50×pow-plus
45×cbrt-div
41×pow2
38×fma-def fma-udef
34×frac-sub tan-quot
30×frac-add
25×pow-flip
24×exp-sum
21×difference-of-sqr-1 cos-sum
18×log-prod
17×pow-pow
16×distribute-neg-frac
15×inv-pow
11×sum-log +-commutative diff-log
10×unpow2
neg-mul-1
sqrt-undiv un-div-inv
pow-div
sin-sum asin-acos
rem-log-exp rem-exp-log
associate-+r- hypot-udef cos-diff
neg-sub0 exp-diff associate-+r+ distribute-frac-neg sqrt-unprod acos-asin
distribute-lft-neg-out sqr-sin sin-mult rem-square-sqrt associate--r- sin-diff

regimes17.3s

Accuracy

Total 38.6b remaining (26.8%)

9.7b-5.1%Henrywood and Agarwal, Equation (13)
8.2b32.4%Toniolo and Linder, Equation (13)
5.2b-36.8%Maksimov and Kolovsky, Equation (3)
5.0b78.5%Toniolo and Linder, Equation (7)
3.7b0%Henrywood and Agarwal, Equation (12)

localize6.1s

bsearch2.8s

end1.0ms