Details

simplify29.6m (64.8%)

prune10.8m (23.7%)

sample3.1m (6.8%)

Algorithm
58×intervals
Results
54.1s232789×body80valid
39.6s23236×body1280valid
27.2s123165×body80nan
18.2s15962×body640valid
12.3s6552×body2560valid
7.1s8066×body320valid
5.3s2444×body5120valid
4.5s8091×body160valid
2.0s683×body10240exit
616.0ms606×body1280nan
512.0ms623×body640nan
338.0ms8256×pre80true
275.0ms344×body320nan
153.0ms207×body160nan

series1.3m (2.8%)

Calls

428 calls:

2.4s
(sqrt (* (* (cbrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n))))))))) (cbrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n)))))))))) (cbrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n)))))))))))
2.2s
(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n)))))))))
2.2s
(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (* (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) (/ (cbrt l) (/ (cbrt Om) n))))))))))
2.1s
(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n)))))))))
2.1s
(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n)))))))))

rewrite28.8s (1.0%)

Algorithm
113×rewrite-expression-head
Calls

432 calls:

1.1s
(+ (sqrt (- (* (* (/ (* c0 (/ d D)) h) (/ (/ d D) w)) (* (/ (* c0 (/ d D)) h) (/ (/ d D) w))) (* M M))) (* (/ (* c0 (/ d D)) h) (/ (/ d D) w)))
809.0ms
(* (* (/ (cbrt (/ 2 (sin k))) (/ (/ (cbrt t) (cbrt (/ l t))) (cbrt (/ l t)))) (/ (/ (cbrt (/ 2 (sin k))) (/ (cbrt t) (cbrt (/ l t)))) (+ 2 (* (/ k t) (/ k t))))) (/ (/ (cbrt (/ 2 (sin k))) (/ (cbrt t) (/ l t))) (tan k)))
632.0ms
(/ NdChar (+ (exp (/ (- mu (- (- Ec Vef) EDonor)) KbT)) 1))
617.0ms
(* (/ (/ (* (cbrt (/ 2 (sin k))) (cbrt (/ 2 (sin k)))) (/ (* (cbrt t) (cbrt t)) (/ l t))) (+ 2 (* (/ k t) (/ k t)))) (/ (/ (cbrt (/ 2 (sin k))) (/ (cbrt t) (/ l t))) (tan k)))
467.0ms
(+ (exp (/ (- mu (- (- Ec Vef) EDonor)) KbT)) 1)
Rules
321699×times-frac
124765×add-sqr-sqrt
123755×*-un-lft-identity
122937×add-cube-cbrt
54807×sqrt-prod
22160×cbrt-prod
13234×div-inv
9159×frac-times
8341×add-exp-log
8116×associate-/r/
8112×associate-/l*
5993×associate-*r/
5863×add-cbrt-cube
5727×associate-*l/
4832×associate-*r*
4451×div-exp
3447×associate-/r*
2770×cbrt-undiv
2241×prod-exp
1844×pow1
1836×cbrt-unprod
1534×sqrt-div
1301×associate-*l*
716×flip3-- flip--
697×difference-of-squares
544×pow-prod-down
516×add-log-exp
360×unswap-sqr
337×1-exp
312×sqrt-pow1
298×flip-+ flip3-+
263×cbrt-div
220×pow-prod-up
188×distribute-lft-out
165×swap-sqr
159×*-commutative
143×frac-add
135×unpow-prod-down
132×rec-exp pow-sqr
128×pow1/3
121×pow1/2
117×distribute-lft-out--
106×pow-plus
94×frac-2neg clear-num
90×pow-unpow
79×rem-sqrt-square
77×associate-/l/
72×pow2
66×pow-exp
64×distribute-rgt-in sqr-pow distribute-lft-in
56×sin-mult
49×sub-neg
40×pow-to-exp
32×sum-log
29×div-sub
28×tan-quot
25×+-commutative
20×pow-pow
16×unpow-prod-up
13×diff-log
12×pow-flip exp-prod
11×associate-+r+
10×cube-prod
9×log-pow pow-sub
8×sqr-sin inv-pow
7×associate-+r-
6×rem-exp-log cube-div
5×pow3 un-div-inv
4×associate-+l+ log-prod difference-of-sqr-1 cos-sum rem-log-exp
3×frac-sub cube-unmult sqrt-unprod rem-square-sqrt acos-asin
2×distribute-lft1-in exp-diff exp-sum associate--l+ asin-acos rem-cbrt-cube cos-diff e-exp-1
1×distribute-lft-neg-out distribute-lft-neg-in unpow3 sub-div sqrt-pow2 distribute-rgt-neg-in unpow2 neg-mul-1 cube-mult

regimes13.4s (0.5%)

Accuracy

Total 43.9b remaining (25.2%)

Threshold costs 3.4b (1.9%)

10.3b-1.3%Henrywood and Agarwal, Equation (13)
8.0b12.3%Maksimov and Kolovsky, Equation (3)
6.8b23%Toniolo and Linder, Equation (13)
6.5b46.5%Henrywood and Agarwal, Equation (3)
5.2b77.7%Toniolo and Linder, Equation (7)

localize5.9s (0.2%)

bsearch3.6s (0.1%)

end1.0ms (0.0%)