Details

simplify11.3m (46.5%)

prune5.7m (23.4%)

sample4.6m (18.9%)

Algorithm
61×intervals
Results
1.1m258727×body80valid
53.3s27743×body1280valid
40.4s159687×body80nan
29.3s19527×body640valid
19.6s8511×body10240exit
18.3s7930×body2560valid
14.6s3433×body5120valid
9.3s9391×body320valid
4.7s8986×body160valid
930.0ms604×body640nan
798.0ms663×body1280nan
403.0ms8256×pre80true
238.0ms366×body320nan
102.0ms204×body160nan

series1.6m (6.8%)

Calls

433 calls:

3.0s
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
2.6s
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
2.6s
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
2.6s
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
2.6s
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

rewrite36.3s (2.5%)

Algorithm
115×rewrite-expression-head
Calls

433 calls:

6.9s
(* (/ NaChar (fma (* (exp (/ (+ EAccept (+ Ev (- Vef mu))) KbT)) (exp (/ (+ EAccept (+ Ev (- Vef mu))) KbT))) (exp (/ (+ EAccept (+ Ev (- Vef mu))) KbT)) 1)) (+ (* 1 1) (- (* (exp (/ (+ (+ EAccept Ev) (- Vef mu)) KbT)) (exp (/ (+ (+ EAccept Ev) (- Vef mu)) KbT))) (* 1 (exp (/ (+ (+ EAccept Ev) (- Vef mu)) KbT))))))
1.7s
(/ (/ NdChar (sqrt (+ (exp (/ (- mu (- (- Ec Vef) EDonor)) KbT)) 1))) (sqrt (+ (exp (/ (- mu (- (- Ec Vef) EDonor)) KbT)) 1)))
1.6s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
1.6s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
1.5s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
Rules
14948×times-frac
9740×add-sqr-sqrt
9446×*-un-lft-identity
8571×add-cube-cbrt
6283×add-exp-log
4870×add-cbrt-cube
4414×sqrt-prod
2704×pow1
2630×prod-exp
2181×prod-diff
2008×div-exp
1954×cbrt-unprod
1795×unpow-prod-up
1549×cbrt-undiv
1545×frac-times
1384×associate-*l/
1158×associate-/r*
1081×sqrt-div
1056×cbrt-prod
954×associate-*r*
798×associate-*l*
779×associate-*r/
774×difference-of-squares
749×pow-prod-down
704×div-inv
664×associate-/r/
570×pow-prod-up
563×associate-/l*
496×add-log-exp
435×expm1-log1p-u
433×log1p-expm1-u insert-posit16
333×flip3-- flip--
287×pow-sqr
282×unswap-sqr
264×pow-exp
258×pow-plus
206×distribute-lft-out
204×unpow-prod-down
194×swap-sqr
177×pow2
151×sqrt-pow1
136×pow-to-exp
132×*-commutative
126×pow1/3
108×frac-2neg clear-num
106×sqr-pow
100×sub-neg
90×cbrt-div
80×distribute-lft-out--
78×pow-unpow
74×1-exp rec-exp
73×pow1/2
69×fma-neg
65×distribute-rgt-in distribute-lft-in
58×flip-+ flip3-+
56×associate-/l/
49×fma-def
48×exp-prod
47×log-pow
46×distribute-lft-neg-in neg-mul-1 distribute-rgt-neg-in
45×rem-sqrt-square
44×tan-quot
41×fma-udef
40×frac-add
24×pow-sub
19×pow-pow diff-log
18×div-sub
15×sum-log log-prod associate-+r-
14×pow-flip
13×exp-diff
12×inv-pow
10×+-commutative cos-sum
distribute-rgt-out--
frac-sub hypot-udef
exp-sum un-div-inv
associate--l+
log-div
difference-of-sqr-1 sqrt-unprod sub-div asin-acos acos-asin expm1-def
expm1-log1p expm1-udef log1p-expm1 rem-log-exp distribute-neg-frac unpow2 cos-diff log1p-udef
remove-posit16 sqrt-undiv cube-unmult pow3 rem-exp-log sqr-sin rem-square-sqrt sin-mult count-2 distribute-rgt-out

regimes17.9s (1.2%)

Accuracy

Total 46.4b remaining (28.6%)

Threshold costs 5.0b (3.1%)

9.5b25.5%Toniolo and Linder, Equation (10-)
7.8b0%Henrywood and Agarwal, Equation (13)
5.9b75.2%Toniolo and Linder, Equation (7)
5.2b2%Henrywood and Agarwal, Equation (12)
5.1b40.6%Toniolo and Linder, Equation (13)

localize6.3s (0.4%)

bsearch4.2s (0.3%)

end1.0ms (0.0%)