Details

simplify15.9m (51.5%)

prune6.4m (20.6%)

sample4.4m (14.1%)

Algorithm
60×intervals
Results
1.0m252810×body80valid
46.5s25690×body1280valid
44.8s159687×body80nan
23.4s17768×body640valid
19.4s8511×body10240exit
17.7s7930×body2560valid
14.8s3433×body5120valid
8.7s8562×body320valid
4.7s8543×body160valid
768.0ms663×body1280nan
705.0ms366×body320nan
555.0ms604×body640nan
328.0ms8256×pre80true
126.0ms204×body160nan

rewrite2.5m (8.2%)

Algorithm
113×rewrite-expression-head
Calls

433 calls:

4.8s
(/ (/ (/ (sqrt 2) (* (cbrt (sin k)) (cbrt (sin k)))) (/ (* (cbrt t) (cbrt t)) (/ l t))) (/ (* (+ 2 (* (/ k t) (/ k t))) (tan k)) (/ (/ (sqrt 2) (cbrt (sin k))) (/ (cbrt t) (/ l t)))))
1.7s
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
1.6s
(/ (/ NdChar (sqrt (+ (exp (/ (- mu (- (- Ec Vef) EDonor)) KbT)) 1))) (sqrt (+ (exp (/ (- mu (- (- Ec Vef) EDonor)) KbT)) 1)))
1.5s
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (/ (* h (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2)))) (* 2 l))))
847.0ms
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
Rules
5142235×times-frac
1375767×*-un-lft-identity
1375478×add-sqr-sqrt
1373987×add-cube-cbrt
577484×cbrt-prod
469671×sqrt-prod
199690×div-inv
45072×associate-/r/
10353×add-exp-log
7996×add-cbrt-cube
7575×associate-/r*
4534×div-exp
3843×cbrt-undiv
3652×prod-exp
2960×cbrt-unprod
2460×unpow-prod-down
2165×associate-*r*
1822×pow1
1397×frac-times
1361×sqrt-div
1331×associate-*l*
1158×associate-/l*
1157×difference-of-squares
1035×associate-*l/
731×associate-*r/
551×pow-prod-down
519×distribute-lft-out
491×add-log-exp
453×sqr-pow
433×insert-posit16
326×flip3-- flip--
269×unswap-sqr
255×flip-+ flip3-+
242×pow-exp
236×swap-sqr
173×pow-prod-up
172×unpow-prod-up
167×*-commutative
154×sub-neg
140×distribute-lft-out--
134×sqrt-pow1
131×pow-unpow
127×1-exp distribute-rgt-in distribute-lft-in
122×cbrt-div
111×pow-to-exp
105×frac-2neg clear-num
99×pow1/2
86×pow-plus
84×pow-sqr
81×frac-add
78×associate-/l/
71×rec-exp
66×rem-sqrt-square
62×pow2
60×sin-mult
40×pow1/3
33×pow-pow
32×tan-quot
25×log-pow
23×log-prod
16×pow-flip div-sub exp-prod
15×sum-log
14×diff-log
13×+-commutative
12×inv-pow pow-sub
associate-+r+
exp-sum rem-log-exp
cube-unmult difference-of-sqr-1 sqr-sin
associate-+l+ frac-sub associate--l+ sqrt-unprod cos-sum
associate-+r- pow3 asin-acos rem-exp-log acos-asin
remove-posit16 sqrt-undiv sqrt-pow2 exp-to-pow cos-diff un-div-inv log-div
sub-div unpow2 rem-square-sqrt rem-cbrt-cube

series1.2m (4.0%)

Calls

433 calls:

2.5s
(sqrt (* U (* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (* (* (cbrt l) (cbrt l)) (* (/ (cbrt l) Om) n))))))))))
2.4s
(sqrt (* U (* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (* (/ (* (cbrt l) (cbrt l)) Om) (* n (cbrt l)))))))))))
2.3s
(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (* (/ (* (cbrt l) (cbrt l)) Om) (* n (cbrt l))))))))))
2.0s
(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n)))))))))
1.8s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

regimes20.8s (1.1%)

Accuracy

Total 47.8b remaining (25.7%)

Threshold costs 4.3b (2.3%)

12.5b3.7%Henrywood and Agarwal, Equation (13)
8.7b-2%Maksimov and Kolovsky, Equation (3)
7.8b30.5%Toniolo and Linder, Equation (13)
5.7b75.5%Toniolo and Linder, Equation (7)
3.8b13.8%Henrywood and Agarwal, Equation (12)

localize6.3s (0.3%)

bsearch4.3s (0.2%)

end1.0ms (0.0%)