Details

simplify4.1m (46.6%)

series1.5m (17.3%)

Calls

415 calls:

2.0s
(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))) (* (* 2.0 n) U)))
1.9s
(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) (* (* 2.0 n) U)))
1.9s
(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))
1.9s
(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))
1.1s
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))

sample1.4m (16.1%)

Algorithm
61×intervals
Results
15.7s253795×body80valid
15.5s29368×body1280valid
9.8s161044×body80nan
8.9s8782×body2560valid
7.0s20111×body640valid
5.2s3342×body5120valid
2.4s9995×body320valid
1.2s9039×body160valid
432.0ms890×body10240exit
142.0ms609×body1280nan
109.0ms613×body640nan
102.0ms8256×pre80true
51.0ms353×body320nan
18.0ms199×body160nan

prune58.7s (11.1%)

rewrite31.3s (5.9%)

Algorithm
114×rewrite-expression-head
Calls

415 calls:

5.8s
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
943.0ms
(/ (- 1.0 (* 5.0 (* v v))) (* (* PI (* (* t (* (cbrt (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) (cbrt (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))) (cbrt (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))) (- 1.0 (* v v))))
909.0ms
(/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
908.0ms
(cbrt (pow (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))) 3))
852.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
Rules
33023×add-exp-log
23212×prod-exp
12215×pow-exp
9666×div-exp
6571×times-frac
5577×pow-to-exp
5502×add-sqr-sqrt
5188×*-un-lft-identity
4213×add-cube-cbrt
2487×add-cbrt-cube
1387×1-exp rec-exp
1190×sqrt-prod
1183×unpow-prod-down
1091×pow1
1044×prod-diff
1010×associate-*r*
999×cbrt-unprod
879×associate-*l*
864×cbrt-prod
816×associate-*r/
483×cbrt-undiv
461×add-log-exp
415×log1p-expm1-u expm1-log1p-u
404×sqrt-div
397×associate-/r*
396×div-inv
389×associate-/l*
376×frac-times
364×associate-*l/
350×distribute-rgt-neg-in
345×cos-sum
341×pow-prod-down
340×unswap-sqr
334×distribute-lft-neg-in
331×distribute-lft-out--
326×sqr-pow
316×pow-unpow
299×sin-sum
288×associate-/r/
281×flip3-- flip--
274×cbrt-div
226×distribute-lft-out
186×exp-prod
177×exp-sum
176×difference-of-squares
175×fma-def
133×*-commutative
127×distribute-rgt-in distribute-lft-in
109×tan-quot
108×log-prod
102×clear-num frac-2neg
79×cube-prod
77×flip-+ flip3-+ sqrt-pow1
68×unpow2
60×pow1/2
53×neg-mul-1
50×pow1/3
47×rem-sqrt-square
44×pow-pow
42×associate-/l/
40×sub-neg
29×fma-udef
26×div-sub
24×swap-sqr
21×fma-neg
20×pow-sub
19×neg-sub0
16×sum-log
13×hypot-def
12×+-commutative
11×pow-prod-up
10×pow-neg pow-flip
9×pow-sqr distribute-neg-frac
8×rem-cube-cbrt
7×frac-add log-pow
6×rem-exp-log inv-pow unpow3 cube-mult distribute-frac-neg
5×diff-log exp-diff rem-log-exp
4×pow-plus pow2 asin-acos
3×cube-div exp-neg neg-log cos-diff hypot-udef acos-asin distribute-rgt-out-- associate-+l-
2×rem-cbrt-cube log-div
1×associate-+l+ un-div-inv sqrt-unprod associate-+r- sum-cubes unsub-neg rem-square-sqrt distribute-rgt-out sub-div frac-sub associate--r- mul0 sin-diff

regimes11.8s (2.2%)

Accuracy

Total 46.6b remaining (22.1%)

Threshold costs 4.2b (2%)

9.5b13.6%Toniolo and Linder, Equation (13)
7.7b-10.7%Toniolo and Linder, Equation (10+)
5.4b56%Henrywood and Agarwal, Equation (3)
5.4b26.4%Toniolo and Linder, Equation (10-)
5.2b77.9%Toniolo and Linder, Equation (7)

localize2.2s (0.4%)

bsearch1.5s (0.3%)

end0.0ms (0.0%)