Details

prune10.1m (44.8%)

simplify5.4m (23.8%)

sample4.8m (21.4%)

Algorithm
60×intervals
Results
1.2m257610×body80valid
55.4s27972×body1280valid
45.7s160268×body80nan
28.5s18950×body640valid
21.6s8621×body10240exit
19.1s7950×body2560valid
14.6s3405×body5120valid
10.3s9698×body320valid
4.7s8913×body160valid
866.0ms581×body1280nan
586.0ms669×body640nan
281.0ms8256×pre80true
209.0ms355×body320nan
85.0ms211×body160nan

series1.4m (6.1%)

Calls

427 calls:

Slowest
2.5s
(fma (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l))) (sqrt (/ d h))) (* (/ (/ M (/ 2 (/ D d))) (/ (* (cbrt l) (cbrt l)) (* (cbrt h) (cbrt h)))) (/ (* -1/2 (/ M (/ 2 (/ D d)))) (/ (cbrt l) (cbrt h)))) (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l))) (sqrt (/ d h))))
2.1s
(sqrt (* (* U 2) (* n (- t (fma (/ l Om) (* 2 l) (+ (* (* n (/ l Om)) (* (/ l Om) (- U U*))) (* (* n (* (/ l Om) (/ l Om))) (+ (- U*) U*))))))))
1.8s
(sqrt (* (* U 2) (* n (- t (fma (/ l Om) (* 2 l) (* (* n (* (/ l Om) (/ l Om))) (- U U*)))))))
1.4s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
1.4s
(fma (* (sqrt (/ d l)) (sqrt (/ d h))) (* (/ (/ M (/ 2 (/ D d))) (/ (* (cbrt l) (cbrt l)) (* (cbrt h) (cbrt h)))) (/ (* -1/2 (/ M (/ 2 (/ D d)))) (/ (cbrt l) (cbrt h)))) (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l))) (sqrt (/ d h))))

rewrite17.5s (1.3%)

Algorithm
113×rewrite-expression-head
Calls

427 calls:

Slowest
2.3s
(* (/ c0 (* w 2)) (+ (sqrt (- (* (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h)) (* M M))) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h)))
1.3s
(+ (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))
699.0ms
(/ NdChar (+ (exp (/ (- mu (- (- Ec Vef) EDonor)) KbT)) 1))
408.0ms
(* (/ (/ (/ 1 (cbrt (tan k))) (cbrt (tan k))) (/ 1 (/ l t))) (/ (/ 2 (cbrt (tan k))) (* (/ t (/ (/ l t) (sin k))) (fma (/ k t) (/ k t) 2))))
Rules
75814×times-frac
34965×add-sqr-sqrt
34090×*-un-lft-identity
33794×add-cube-cbrt
11739×cbrt-prod
9625×sqrt-prod
8881×add-exp-log
7696×associate-*l*
4978×prod-diff
4889×add-cbrt-cube
4812×div-exp
4551×unpow-prod-up
2893×div-inv
2476×prod-exp
2265×cbrt-undiv
1500×cbrt-unprod
1436×pow1
1300×associate-/l*
1070×associate-/r/
688×associate-*r*
656×tan-quot
652×cbrt-div
489×add-log-exp
478×associate-/r*
430×expm1-log1p-u
428×log1p-expm1-u
427×insert-posit16
398×1-exp
351×pow-prod-down
308×rec-exp unswap-sqr
189×pow-prod-up
188×associate-*r/
180×associate-*l/
170×unpow-prod-down
166×sqrt-pow1
150×sub-neg
147×distribute-rgt-in distribute-lft-in
140×sqr-pow
136×difference-of-squares
110×*-commutative
105×sqrt-div
102×pow1/3
101×pow-sqr
97×pow-plus
96×fma-neg
95×frac-2neg clear-num
94×frac-times pow1/2
80×pow-unpow
79×flip3-- flip--
77×swap-sqr
76×distribute-lft-out--
70×rem-sqrt-square
61×pow-exp
57×pow2
52×associate-/l/
46×fma-udef
43×distribute-lft-out
40×fma-def
39×pow-to-exp
32×frac-add
31×flip-+ flip3-+
30×associate--r+
23×diff-log
22×pow-pow
19×log-pow exp-prod
13×associate--l+
9×sum-log +-commutative
8×remove-posit16 pow-sub
7×log-prod
6×div-sub
5×cos-sum
4×pow-flip distribute-lft-neg-in frac-sub distribute-rgt-out-- log1p-expm1 inv-pow distribute-rgt-out log1p-udef
3×expm1-log1p expm1-udef sub-div distribute-rgt-neg-in un-div-inv asin-acos acos-asin
2×distribute-lft1-in exp-sum pow3 sqrt-unprod neg-mul-1 rem-log-exp hypot-udef hypot-def rem-square-sqrt associate--r-
1×associate-+r- sqr-sin rem-cbrt-cube rem-exp-log cos-diff sin-mult

regimes16.4s (1.2%)

Accuracy

Total 53.2b remaining (30.5%)

Threshold costs 2.6b (1.5%)

12.9b-16.1%Henrywood and Agarwal, Equation (13)
8.6b40.8%Henrywood and Agarwal, Equation (3)
6.1b32.7%Toniolo and Linder, Equation (13)
5.6b76.1%Toniolo and Linder, Equation (7)
4.5b-18%Maksimov and Kolovsky, Equation (3)

bsearch13.8s (1.0%)

localize6.7s (0.5%)

end2.0ms (0.0%)