Details

prune9.9m (38.1%)

simplify9.5m (36.6%)

sample3.8m (14.4%)

Algorithm
60×intervals
Results
1.0m250283×body80valid
44.9s25073×body1280valid
42.0s160850×body80nan
23.1s17713×body640valid
12.9s6576×body2560valid
7.8s9034×body320valid
5.6s2413×body5120valid
3.9s8645×body160valid
2.4s864×body10240exit
664.0ms662×body1280nan
580.0ms8256×pre80true
526.0ms645×body640nan
371.0ms365×body320nan
74.0ms194×body160nan

series1.6m (6.0%)

Calls

458 calls:

2.1s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (/ (/ 1 (cbrt l)) (cbrt l))) (sqrt (/ d (cbrt l))))) (- 1 (* (* 1/2 (* (* (/ M (/ (* d 2) D)) (cbrt h)) (* (/ M (/ (* d 2) D)) (cbrt h)))) (/ (cbrt h) l))))
2.1s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (/ (/ 1 (cbrt l)) (cbrt l))) (sqrt (/ d (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
2.1s
(sqrt (* 2 (* U (+ (* n t) (* (* n (- (/ l Om))) (- (* 2 l) (* (/ l Om) (* n (- U* U)))))))))
2.0s
(sqrt (* 2 (+ (* (* n t) U) (* (* (* n (- (/ l Om))) (- (* 2 l) (* (/ l Om) (* n (- U* U))))) U))))
1.8s
(sqrt (* 2 (* U (+ (* n t) (* n (- (* (/ l Om) (- (* 2 l) (* (/ l Om) (* n (- U* U)))))))))))

rewrite45.2s (2.9%)

Algorithm
118×rewrite-expression-head
Calls

458 calls:

2.6s
(sqrt (- 1 (/ (/ h (/ (/ d (/ (* M D) 2)) (/ 1 l))) (/ d (/ (* M D) 2)))))
1.8s
(* (* 1/2 (* (* (/ M (/ (* d 2) D)) (cbrt h)) (* (/ M (/ (* d 2) D)) (cbrt h)))) (/ (cbrt h) l))
1.4s
(exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
1.2s
(/ (/ NdChar (sqrt (+ (exp (/ (- EDonor (- Ec (+ Vef mu))) KbT)) 1))) (sqrt (+ (exp (/ (- EDonor (- Ec (+ Vef mu))) KbT)) 1)))
789.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
Rules
775899×times-frac
303791×add-sqr-sqrt
303310×*-un-lft-identity
301994×add-cube-cbrt
195062×cbrt-prod
60860×sqrt-prod
18243×div-inv
10346×associate-/l*
6637×add-exp-log
4343×add-cbrt-cube
2717×div-exp
2458×associate-/r/
2336×pow1
2322×prod-exp
1790×associate-*r*
1738×cbrt-undiv
1673×associate-/r*
1468×cbrt-unprod
805×sqrt-div
795×unpow-prod-down
761×associate-*r/
667×frac-times
659×associate-*l*
645×pow-prod-down
641×sqrt-pow1
589×add-log-exp
517×pow-prod-up
512×sqr-pow
466×flip-+ flip3-+
458×insert-posit16
454×unswap-sqr
448×associate-*l/
407×distribute-lft-out
384×pow1/2
374×unpow-prod-up
302×distribute-rgt-out--
267×flip3-- flip--
255×sub-neg
237×pow-sqr
224×distribute-rgt-neg-in
218×distribute-lft-neg-in
213×1-exp
203×pow-exp
185×difference-of-squares
163×pow-plus
153×swap-sqr tan-quot
148×*-commutative
142×frac-add
123×distribute-rgt-in distribute-lft-in
114×rec-exp
111×distribute-lft-out--
106×exp-prod
104×frac-2neg clear-num
92×rem-sqrt-square
87×pow-unpow pow-to-exp
85×pow2
83×distribute-rgt-out
79×associate-/l/
70×neg-mul-1
57×sin-mult
49×pow1/3
39×sum-log
34×+-commutative
33×distribute-lft1-in
32×distribute-rgt1-in
31×cbrt-div
28×diff-log
24×count-2
22×div-sub
20×pow-pow
19×pow-sub
14×associate--r+
11×distribute-neg-frac
10×cube-unmult
9×associate-+l+ sqrt-unprod rem-exp-log
8×difference-of-sqr-1 distribute-neg-in
7×pow-flip inv-pow
6×neg-log unpow2 cos-sum
5×exp-diff sqr-sin
4×sqrt-undiv pow3
3×neg-sub0 log-prod frac-sub exp-sum distribute-rgt-neg-out asin-acos rem-square-sqrt log-pow acos-asin cos-diff associate--r-
2×distribute-lft-neg-out associate--l- remove-posit16 associate-+r+ associate--l+ sub-div un-div-inv associate-+l-
1×associate-+r- sqrt-pow2 rem-log-exp exp-to-pow

regimes18.2s (1.2%)

Accuracy

Total 29.9b remaining (15.3%)

Threshold costs 5.6b (2.9%)

6.1b74.5%Toniolo and Linder, Equation (7)
5.7b3.1%Henrywood and Agarwal, Equation (12)
4.3b-11.8%Henrywood and Agarwal, Equation (13)
2.4b69.3%Toniolo and Linder, Equation (13)
1.9b0%Falkner and Boettcher, Appendix A

localize7.3s (0.5%)

bsearch3.8s (0.2%)

end1.0ms (0.0%)