Details

simplify24.6m (56.3%)

prune12.4m (28.5%)

sample4.0m (9.2%)

Algorithm
60×intervals
Results
1.0m246813×body80valid
46.8s27460×body1280valid
34.1s160249×body80nan
24.5s18446×body640valid
22.5s8671×body2560valid
15.2s3391×body5120valid
9.0s9230×body320valid
5.3s8482×body160valid
2.0s818×body10240exit
1.0s624×body1280nan
763.0ms8256×pre80true
567.0ms646×body640nan
230.0ms348×body320nan
102.0ms205×body160nan

series1.4m (3.2%)

Calls

443 calls:

3.3s
(sqrt (* U (* (- t (* (- (* 2 l) (* (/ l Om) (* n (- U* U)))) (/ l Om))) (* 2 n))))
3.2s
(sqrt (* U (* (- t (* (- (* 2 l) (* (* (/ l Om) n) (- U* U))) (/ l Om))) (* 2 n))))
2.3s
(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n)))))))))
2.2s
(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n)))))))))
2.1s
(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n)))))))))

rewrite41.7s (1.6%)

Algorithm
114×rewrite-expression-head
Calls

443 calls:

4.0s
(/ (+ (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (- (* (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M))) (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)))) (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)))))) (/ (+ (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)) (* (- (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))))) (+ (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M))))))
2.8s
(/ (+ (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))))) (* (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M))) (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)))) (+ (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)) (* (- (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (sqrt (- (* (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D))))) (* M M)))) (* (/ (/ d D) h) (/ c0 (/ w (/ d D)))))))
1.3s
(* (/ (* (pow k m) a) (+ (* (* (* k (+ k 10)) (* k (+ k 10))) (* k (+ k 10))) 1)) (+ (* (* k (+ k 10)) (* k (+ k 10))) (- (* 1 1) (* (* k (+ k 10)) 1))))
802.0ms
(* (* (* (/ (* M D) (* 2 d)) (cbrt h)) (* (/ (* M D) (* 2 d)) (cbrt h))) (/ (cbrt h) l))
736.0ms
(* (exp (exp (/ (- mu (- (- Ec EDonor) Vef)) KbT))) E)
Rules
294527×times-frac
86669×add-sqr-sqrt
86307×*-un-lft-identity
84932×add-cube-cbrt
46604×cbrt-prod
16625×sqrt-prod
14713×frac-times
12215×div-inv
10635×associate-/r/
9541×associate-*r/
8825×associate-*l/
8667×add-exp-log
6711×add-cbrt-cube
6118×sqrt-div
4109×associate-/r*
3910×div-exp
3494×frac-add
3263×cbrt-undiv
2869×prod-exp
2715×flip3-- flip--
2680×cbrt-unprod
1998×associate-/l*
1992×associate-/l/
1797×associate-*l*
1576×pow1
1412×frac-sub
1258×flip-+ flip3-+
1203×unpow-prod-down
1102×associate-*r*
730×difference-of-squares
569×add-log-exp
507×pow-prod-down
443×insert-posit16
434×sqr-pow
415×distribute-lft-out
344×unswap-sqr
315×unpow-prod-up
236×swap-sqr
228×sqrt-pow1
204×sub-neg
156×1-exp
152×*-commutative
140×distribute-lft-out--
135×pow1/2
126×cbrt-div
107×pow-exp
100×frac-2neg rec-exp clear-num
85×pow-prod-up
80×rem-sqrt-square
79×sub-div
73×distribute-rgt-in distribute-lft-in
62×pow-to-exp exp-prod
61×sin-mult
57×log-prod pow1/3
53×log-pow
50×pow-sqr
49×pow-unpow
47×sum-log
41×exp-sum pow-plus
36×pow-sub
30×tan-quot
28×pow2
27×+-commutative
23×pow-pow diff-log
22×pow-flip associate-+r+ distribute-neg-in
20×div-sub
19×associate-+l+
13×associate-+r- cube-unmult
12×inv-pow
11×log-div
rem-log-exp
exp-diff acos-asin
sum-cubes sqr-sin remove-posit16
exp-neg sqrt-unprod un-div-inv rem-square-sqrt rem-exp-log
e-exp-1
distribute-lft-neg-out distribute-rgt-neg-out associate--l+ asin-acos associate-+l- cos-sum
cos-mult pow3 difference-of-sqr-1 sqrt-pow2 exp-to-pow sqr-cos cos-diff

regimes18.3s (0.7%)

Accuracy

Total 61.4b remaining (31.2%)

Threshold costs 4.8b (2.4%)

11.1b2.3%Toniolo and Linder, Equation (13)
11.1b-10%Henrywood and Agarwal, Equation (13)
8.1b-33.2%Given's Rotation SVD example
7.7b13.1%Maksimov and Kolovsky, Equation (3)
5.4b30.5%Henrywood and Agarwal, Equation (3)

localize6.7s (0.3%)

bsearch4.6s (0.2%)

end1.0ms (0.0%)