Details

prune9.7m (38.9%)

simplify9.7m (38.8%)

sample2.7m (11.0%)

Algorithm
60×intervals
Results
44.3s250283×body80valid
32.1s25073×body1280valid
29.4s160850×body80nan
16.7s17713×body640valid
10.1s6576×body2560valid
5.3s9034×body320valid
4.3s2413×body5120valid
3.1s8645×body160valid
1.2s864×body10240exit
540.0ms8256×pre80true
407.0ms662×body1280nan
275.0ms645×body640nan
150.0ms365×body320nan
43.0ms194×body160nan

series1.6m (6.4%)

Calls

458 calls:

2.4s
(* (* (* (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))))
2.3s
(* (* (* (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
(sqrt (* 2 (* U (+ (* n t) (* (* n (/ l Om)) (- (- (* 2 l) (* (/ l Om) (* n (- U* U))))))))))
2.1s
(sqrt (* 2 (+ (* (* n t) U) (* (* (* n (/ l Om)) (- (- (* 2 l) (* (/ l Om) (* n (- U* U)))))) U))))
1.9s
(sqrt (* 2 (* U (* n (- t (* (/ l Om) (- (* 2 l) (* (/ l Om) (* n (- U* U))))))))))

rewrite44.6s (3.0%)

Algorithm
118×rewrite-expression-head
Calls

458 calls:

2.7s
(sqrt (- 1 (/ (/ h (/ (/ d (/ (* M D) 2)) (/ 1 l))) (/ d (/ (* M D) 2)))))
1.5s
(* (* 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)))))
1.3s
(/ (/ NdChar (sqrt (+ (exp (/ (- EDonor (- Ec (+ Vef mu))) KbT)) 1))) (sqrt (+ (exp (/ (- EDonor (- Ec (+ Vef mu))) KbT)) 1)))
773.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
Rules
775891×times-frac
303786×add-sqr-sqrt
303302×*-un-lft-identity
301986×add-cube-cbrt
195062×cbrt-prod
60860×sqrt-prod
18242×div-inv
10346×associate-/l*
6645×add-exp-log
4351×add-cbrt-cube
2719×div-exp
2458×associate-/r/
2335×pow1
2326×prod-exp
1776×associate-*r*
1740×cbrt-undiv
1673×associate-/r*
1472×cbrt-unprod
805×sqrt-div
795×unpow-prod-down
761×associate-*r/
667×frac-times
656×associate-*l*
645×pow-prod-down
640×sqrt-pow1
589×add-log-exp
517×pow-prod-up
512×sqr-pow
466×flip-+ flip3-+
458×insert-posit16
455×unswap-sqr
448×associate-*l/
407×distribute-lft-out
383×pow1/2
374×unpow-prod-up
302×distribute-rgt-out--
267×flip3-- flip--
255×sub-neg
237×pow-sqr
213×1-exp
211×distribute-rgt-neg-in
205×distribute-lft-neg-in
203×pow-exp
185×difference-of-squares
161×pow-plus
153×swap-sqr tan-quot
148×*-commutative
142×frac-add
122×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/
69×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
9×associate-+l+ cube-unmult 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 pow3 sqr-sin
4×sqrt-undiv
3×neg-sub0 log-prod frac-sub exp-sum asin-acos rem-square-sqrt log-pow acos-asin cos-diff associate--r-
2×associate--l- remove-posit16 associate-+r+ distribute-rgt-neg-out associate--l+ sub-div un-div-inv associate-+l-
1×distribute-lft-neg-out associate-+r- sqrt-pow2 rem-log-exp exp-to-pow

regimes17.9s (1.2%)

Accuracy

Total 30.0b remaining (15.3%)

Threshold costs 5.5b (2.8%)

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)
2.5b69.2%Toniolo and Linder, Equation (13)
1.9b0%Falkner and Boettcher, Appendix A

localize7.4s (0.5%)

bsearch3.2s (0.2%)

end1.0ms (0.0%)