Details

prune17.0m (60.1%)

simplify4.7m (16.7%)

sample4.2m (14.9%)

Algorithm
61×intervals
Results
1.0m252766×body80valid
53.4s29602×body1280valid
39.3s160249×body80nan
26.2s20103×body640valid
20.5s8671×body2560valid
12.3s3391×body5120valid
10.5s10122×body320valid
5.3s8905×body160valid
2.2s818×body10240exit
674.0ms624×body1280nan
564.0ms646×body640nan
554.0ms8256×pre80true
182.0ms348×body320nan
72.0ms205×body160nan

series1.4m (5.0%)

Calls

447 calls:

1.7s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (/ l Om)) (* (/ l Om) (- U U*))))))
1.7s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))
1.7s
(sqrt (- 1 (* (* (* (cbrt (/ (/ 1 (sqrt 2)) l)) (cbrt (/ (/ 1 (sqrt 2)) l))) (* (cbrt (/ (/ 1 (sqrt 2)) l)) (/ (/ (/ (* M D) d) (sqrt 2)) (/ 1 h)))) (/ (/ (* M D) d) 2))))
1.6s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.6s
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

rewrite29.8s (1.8%)

Algorithm
118×rewrite-expression-head
Calls

447 calls:

3.0s
(cbrt (* (* (+ (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT)) 1) (+ (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT)) 1)) (+ (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT)) 1)))
1.4s
(+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)))
1.2s
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (- 1 (/ (/ (* (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) h) l) 2)))
1.1s
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
1.0s
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
Rules
199717×times-frac
97260×*-un-lft-identity
88255×add-sqr-sqrt
70004×add-cube-cbrt
24167×sqrt-prod
16147×cbrt-prod
10377×difference-of-squares
8373×div-inv
7949×add-exp-log
5923×distribute-lft-out
5296×add-cbrt-cube
5117×associate-*l*
5053×distribute-lft-out--
3721×div-exp
2995×prod-diff
2517×associate-/r/
2461×prod-exp
2363×cbrt-undiv
2290×associate-*r*
2227×associate-/r*
1672×unpow-prod-up
1497×cbrt-unprod
1372×pow1
1059×associate-/l*
911×flip-+ flip3-+
774×sqrt-div
688×frac-times
675×unswap-sqr
554×associate-*r/
512×add-log-exp
509×associate-*l/
507×flip3-- flip--
506×swap-sqr
448×expm1-log1p-u
447×log1p-expm1-u insert-posit16
435×pow-prod-down
423×unpow-prod-down
329×1-exp
227×distribute-rgt-in distribute-lft-in
223×pow-exp
161×sqr-pow
158×rec-exp
157×sqrt-pow1
139×*-commutative tan-quot
137×pow-unpow
136×distribute-rgt-neg-in
132×distribute-lft-neg-in
119×frac-2neg clear-num
113×sub-neg
106×frac-sub
97×fma-neg
95×pow-to-exp
93×pow1/2
67×associate-/l/
59×pow1/3
54×pow-prod-up
53×log-pow
52×cbrt-div unpow2
50×fma-udef
46×rem-sqrt-square exp-prod
42×associate--l+
39×fma-def
36×pow-sqr
34×pow-pow
31×log-prod
27×associate--r+ cos-sum
24×pow-plus
22×diff-log
19×pow2
13×div-sub
12×sum-log neg-mul-1
11×pow-flip +-commutative inv-pow
10×hypot-udef
hypot-def pow-sub
exp-sum rem-log-exp
frac-add
acos-asin
associate-+r+ neg-log sqrt-unprod rem-square-sqrt log-div
un-div-inv asin-acos rem-exp-log
associate-+l+ expm1-log1p neg-sub0 expm1-udef exp-diff sin-sum associate-+r- pow3 associate--l- sqr-sin associate-+l- log1p-def associate--r- sin-mult
cube-unmult log1p-expm1 sqrt-pow2 exp-to-pow rem-cbrt-cube cos-diff log1p-udef

regimes19.8s (1.2%)

Accuracy

Total 46.3b remaining (25.3%)

Threshold costs 5.8b (3.2%)

7.7b17%Toniolo and Linder, Equation (13)
6.1b20.1%Henrywood and Agarwal, Equation (13)
5.7b18.2%Henrywood and Agarwal, Equation (12)
5.4b30.5%Henrywood and Agarwal, Equation (3)
5.2b78.3%Toniolo and Linder, Equation (7)

localize6.2s (0.4%)

bsearch2.1s (0.1%)

end1.0ms (0.0%)