Details

simplify6.9m (35.5%)

prune6.6m (34.0%)

sample3.1m (15.8%)

Algorithm
61×intervals
Results
48.2s253614×body80valid
36.9s29575×body1280valid
28.0s160606×body80nan
18.2s20413×body640valid
15.5s8910×body2560valid
8.7s3411×body5120valid
6.8s10021×body320valid
3.1s8980×body160valid
1.1s768×body10240exit
545.0ms8256×pre80true
314.0ms650×body640nan
294.0ms621×body1280nan
164.0ms340×body320nan
34.0ms189×body160nan

series1.4m (7.2%)

Calls

457 calls:

2.6s
(sqrt (* 2 (* U (+ (* n t) (* (- (* l 2) (* (* (/ l Om) n) (- U* U))) (- (* (/ l Om) n)))))))
2.2s
(sqrt (* 2 (* U (* n (- t (* (/ l Om) (- (* 2 l) (* (* (/ l Om) n) (- U* U)))))))))
2.2s
(sqrt (* 2 (* U (* n (- t (* (/ l Om) (- (* 2 l) (* (/ l Om) (* n (- U* U))))))))))
2.0s
(sqrt (* U (+ (* n t) (* (- (* l 2) (* (* (/ l Om) n) (- U* U))) (- (* (/ l Om) n))))))
1.7s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite58.4s (5.0%)

Algorithm
117×rewrite-expression-head
Calls

457 calls:

7.4s
(sqrt (- 1 (/ (/ (/ h l) (/ d (/ (* M D) 2))) (/ d (/ (* M D) 2)))))
3.4s
(* (/ 4/3 (- (* PI (* PI PI)) (* (* v v) (* (* PI (* PI PI)) (* (* v v) (* v v)))))) (+ (* PI PI) (+ (* (* (* PI v) v) (* (* PI v) v)) (* PI (* (* PI v) v)))))
3.1s
(* (/ 1 (sqrt (+ (exp (/ (- EDonor (- Ec (+ Vef mu))) KbT)) 1))) (/ NdChar (sqrt (+ (exp (/ (- EDonor (- Ec (+ Vef mu))) KbT)) 1))))
1.9s
(cbrt (* (* (* (* (/ (sqrt 2) 4) (/ (sqrt 2) 4)) (/ (sqrt 2) 4)) (- 1 (* 3 (* v v)))) (* (sqrt (- 1 (* 3 (* v v)))) (* (- 1 (* v v)) (* (- 1 (* v v)) (- 1 (* v v)))))))
1.2s
(/ (/ 2 (sin k)) (* (* (* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t) (/ t l)) (/ t l)))
Rules
130345×times-frac
53645×add-sqr-sqrt
53185×*-un-lft-identity
52412×add-cube-cbrt
20796×cbrt-prod
7913×frac-times
7139×sqrt-prod
5213×add-exp-log
4171×add-cbrt-cube
4133×div-inv
3399×flip3-- flip--
3061×associate-*r/
2941×associate-*l/
2093×associate-/l*
1998×cbrt-div
1874×unpow-prod-down
1865×div-exp
1808×prod-exp
1735×sqrt-div
1587×associate-*l*
1529×cbrt-undiv
1387×associate-*r*
1364×cbrt-unprod
1309×pow1
654×sqr-pow
638×associate-/r/
627×associate-/r*
581×add-log-exp
457×insert-posit16
338×unpow-prod-up
335×pow-prod-down
326×unswap-sqr
281×flip-+ flip3-+
274×distribute-lft-out
247×sub-neg
183×pow-exp
159×difference-of-squares
147×swap-sqr
143×*-commutative
134×distribute-lft-out--
121×pow-unpow
113×sqrt-pow1
106×frac-2neg clear-num
95×pow1/2
89×log-pow
88×frac-add
86×exp-prod
85×tan-quot
84×distribute-rgt-in pow-to-exp distribute-lft-in
75×associate-/l/ rem-sqrt-square
67×pow1/3
64×pow-prod-up
61×log-prod
60×1-exp
56×rec-exp
45×diff-log
39×distribute-rgt-out
32×sin-mult
29×pow-pow
27×pow-plus
26×exp-sum pow-sqr
25×frac-sub
21×distribute-lft1-in pow2
20×sum-log
19×pow-sub
18×associate--r+
16×+-commutative
13×div-sub
12×distribute-neg-in
11×pow-flip
10×cube-prod
9×rem-log-exp count-2 distribute-rgt1-in
8×pow3 log-div
7×exp-diff inv-pow unpow2
6×associate--l+ neg-log distribute-rgt-neg-in exp-neg cube-div
5×associate--r-
4×associate-+l+ remove-posit16 associate-+r+ cube-unmult difference-of-sqr-1 un-div-inv distribute-rgt-out-- cos-sum rem-exp-log
3×neg-sub0 distribute-lft-neg-out associate-+r- distribute-rgt-neg-out associate--l- exp-to-pow asin-acos acos-asin
2×sqrt-undiv sqrt-unprod sub-div sqr-sin associate-+l- cos-diff rem-cbrt-cube
1×unpow3 sqrt-pow2 rem-square-sqrt cube-mult

regimes19.5s (1.7%)

Accuracy

Total 56.4b remaining (30.7%)

Threshold costs 3.3b (1.8%)

12.4b0.2%Henrywood and Agarwal, Equation (13)
7.2b22%Toniolo and Linder, Equation (13)
5.2b77.5%Toniolo and Linder, Equation (7)
4.7b13.3%Toniolo and Linder, Equation (3a)
4.6b0%Maksimov and Kolovsky, Equation (3)

localize6.5s (0.6%)

bsearch2.8s (0.2%)

end1.0ms (0.0%)