Details

simplify20.7m (55.6%)

prune10.0m (26.9%)

sample3.9m (10.4%)

Algorithm
59×intervals
Results
59.3s246000×body80valid
41.7s23794×body1280valid
41.4s157259×body80nan
22.9s16648×body640valid
19.8s8681×body10240exit
8.2s8556×body320valid
7.9s5848×body2560valid
5.6s2430×body5120valid
5.2s8710×body160valid
658.0ms589×body1280nan
648.0ms326×body320nan
455.0ms601×body640nan
359.0ms8256×pre80true
71.0ms208×body160nan

series1.5m (3.9%)

Calls

450 calls:

2.2s
(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ n (/ Om l)) (- U* U))))))))
2.1s
(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ 1 (/ (/ Om l) n)) (- U* U))))))))
2.1s
(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ n (/ Om l)) (- U* U))))))))
1.9s
(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ n (/ Om l)) (- U* U))))))))
1.8s
(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ (/ n (* (cbrt (/ Om l)) (cbrt (/ Om l)))) (cbrt (/ Om l))) (- U* U))))))))

rewrite44.7s (2.0%)

Algorithm
115×rewrite-expression-head
Calls

450 calls:

7.9s
(sqrt (- 1 (/ (/ M (/ d D)) (/ (/ l h) (/ (/ M (/ d D)) 4)))))
2.0s
(/ (/ 1 (sqrt (+ (exp (/ (+ (- EDonor (- Ec Vef)) mu) KbT)) 1))) (sqrt (sqrt (+ (exp (/ (+ (- EDonor (- Ec Vef)) mu) KbT)) 1))))
1.8s
(/ (/ NdChar (sqrt (+ (exp (/ (+ (- EDonor (- Ec Vef)) mu) KbT)) 1))) (sqrt (+ (exp (/ (+ (- EDonor (- Ec Vef)) mu) KbT)) 1)))
873.0ms
(sqrt (sqrt (+ (exp (/ (+ (- EDonor (- Ec Vef)) mu) KbT)) 1)))
821.0ms
(sqrt (sqrt (+ (exp (/ (+ (- EDonor (- Ec Vef)) mu) KbT)) 1)))
Rules
215946×times-frac
89126×add-sqr-sqrt
87561×*-un-lft-identity
86658×add-cube-cbrt
23535×add-exp-log
22413×associate-*r*
17171×cbrt-prod
14164×add-cbrt-cube
13676×div-exp
13093×sqrt-prod
8415×cbrt-undiv
7998×div-inv
6865×prod-exp
4825×cbrt-unprod
1974×pow1
1518×associate-/l*
1485×associate-/r*
1449×associate-*l*
1221×associate-/r/
750×tan-quot
729×sqrt-div
544×add-log-exp
542×frac-times
520×pow-prod-down
497×unswap-sqr
450×insert-posit16
421×flip-+ flip3-+
414×1-exp rec-exp
391×associate-*r/
358×associate-*l/
310×distribute-lft-out
251×pow-prod-up
211×difference-of-squares flip3-- flip--
171×swap-sqr
166×associate-/l/
165×sqrt-pow1
154×*-commutative
136×pow-sqr
129×frac-add
128×unpow-prod-down
127×pow-plus
124×exp-prod pow1/2
102×rem-sqrt-square
100×sub-neg
93×frac-2neg clear-num
92×distribute-lft-out--
91×pow2
84×unpow-prod-up
75×distribute-rgt-in distribute-lft-in
71×sqr-pow
69×pow-exp
65×pow-unpow
50×sin-mult
48×pow-to-exp
29×sum-log +-commutative
27×pow1/3 pow-flip
21×pow-pow
18×log-pow
16×div-sub
15×diff-log
13×inv-pow
10×cos-sum pow-sub
log-prod asin-acos
pow-div cube-unmult difference-of-sqr-1 sqr-sin associate-+l-
cbrt-div
associate-+r- pow3
exp-diff rem-exp-log cos-diff
remove-posit16 frac-sub associate-+r+
distribute-rgt-out-- rem-log-exp
associate-+l+ associate--l+ sqrt-unprod associate--r-
quot-tan sub-div sqrt-pow2 exp-to-pow unpow2 sum-cubes rem-cbrt-cube acos-asin distribute-rgt1-in

regimes18.2s (0.8%)

Accuracy

Total 39.2b remaining (20.2%)

Threshold costs 5.1b (2.7%)

9.1b2.4%Maksimov and Kolovsky, Equation (3)
7.9b13%Toniolo and Linder, Equation (13)
5.4b76.7%Toniolo and Linder, Equation (7)
4.6b-30.1%Henrywood and Agarwal, Equation (13)
2.8b18.8%Henrywood and Agarwal, Equation (12)

localize6.8s (0.3%)

bsearch3.3s (0.1%)

end1.0ms (0.0%)