Details

prune9.2m (46.4%)

sample4.3m (21.4%)

Algorithm
61×intervals
Results
1.1m252624×body80valid
53.1s28799×body1280valid
40.4s160368×body80nan
27.0s20582×body640valid
22.7s8763×body2560valid
12.1s3433×body5120valid
8.8s10107×body320valid
4.6s9126×body160valid
2.0s640×body10240exit
697.0ms638×body1280nan
585.0ms631×body640nan
311.0ms8256×pre80true
231.0ms356×body320nan
73.0ms199×body160nan

simplify3.7m (18.5%)

series1.6m (7.9%)

Calls

445 calls:

2.3s
(sqrt (* (* (cbrt (* (* U 2) (* n (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U*)) (* (* (/ l Om) 2) l)))))) (cbrt (* (* U 2) (* n (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U*)) (* (* (/ l Om) 2) l))))))) (cbrt (* (* U 2) (* n (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U*)) (* (* (/ l Om) 2) l))))))))
2.2s
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (sqrt (/ d (cbrt h)))) (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) l)))) (- 1 (* (* (* 1/2 (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d)))) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))))
2.2s
(sqrt (* (* U 2) (* n (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U*)) (* (* (/ l Om) 2) l))))))
2.1s
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (sqrt (/ d (cbrt h)))) (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) l)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
2.1s
(sqrt (* (* U 2) (* n (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U*)) (* (* (/ l Om) 2) l))))))

rewrite41.8s (3.5%)

Algorithm
115×rewrite-expression-head
Calls

445 calls:

2.6s
(* (* (* 1/2 (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d)))) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))
1.8s
(/ (/ (- 1 (* (* (* (+ 1/2 (/ 1/2 (hypot 1 x))) (sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))) (* (+ 1/2 (/ 1/2 (hypot 1 x))) (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))) (* (+ 1/2 (/ 1/2 (hypot 1 x))) (sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))))) (+ (+ (* (* (+ 1/2 (/ 1/2 (hypot 1 x))) (sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))) (* (+ 1/2 (/ 1/2 (hypot 1 x))) (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))) (* (+ 1/2 (/ 1/2 (hypot 1 x))) (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))) 1)) (+ (+ (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 1))
1.6s
(* (sqrt (exp (/ (+ (+ EAccept (- Ev mu)) Vef) KbT))) (sqrt (exp (/ (+ (+ EAccept (- Ev mu)) Vef) KbT))))
1.1s
(* (* J (+ (+ (* (* 1/3 (* l l)) l) (+ l l)) (* (pow l 5) 1/60))) (cos (/ K 2)))
946.0ms
(sqrt (* (* U 2) (* n (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U*)) (* (* (/ l Om) 2) l))))))
Rules
41088×times-frac
33068×add-exp-log
19992×add-sqr-sqrt
19759×*-un-lft-identity
19198×div-exp
18332×add-cube-cbrt
11976×prod-exp
8785×add-cbrt-cube
3830×cbrt-undiv
3399×cbrt-unprod
2948×1-exp
2836×sqrt-prod
2224×associate-*l*
2018×associate-*r*
2003×rec-exp
1816×div-inv
1680×pow1
1338×associate-/l*
1141×cbrt-prod
1082×frac-times
972×associate-*r/
944×sqrt-div
775×associate-*l/
675×distribute-lft-out
662×associate-/r/
620×associate-/r*
614×flip-+ flip3-+
554×pow-prod-down
549×sqrt-pow1
538×add-log-exp
464×unpow-prod-down
445×insert-posit16
431×exp-prod
403×unswap-sqr
331×frac-add
304×pow-exp
263×pow-prod-up
227×flip3-- flip--
207×cbrt-div
177×distribute-lft-out--
154×pow-sqr
149×*-commutative
143×sqr-pow
138×pow-to-exp
136×pow1/3
127×pow1/2
112×swap-sqr
110×tan-quot
103×difference-of-squares
102×pow-unpow
95×frac-2neg clear-num
85×rem-sqrt-square
77×pow-plus
74×associate-/l/
71×distribute-rgt-in distribute-lft-in
68×sub-neg
50×distribute-rgt-out
48×pow2
46×sin-mult
36×sum-log
32×unpow-prod-up
29×pow-sub
27×+-commutative
24×pow-pow
23×div-sub
18×pow-flip
16×associate-+r- associate-+l-
15×exp-diff pow3
12×frac-sub
11×diff-log
10×cube-prod inv-pow cos-sum
associate-+l+ distribute-lft1-in
associate-+r+ un-div-inv
log-pow cube-div distribute-rgt1-in
cos-diff
difference-of-sqr-1 sqr-sin distribute-rgt-out--
log-prod cube-unmult asin-acos rem-exp-log count-2
associate--l+ pow-div sub-div associate--r+ unpow1/3 pow-neg
neg-sub0 unpow3 sqrt-unprod sqrt-pow2 exp-to-pow unpow2 rem-square-sqrt rem-cbrt-cube cube-mult acos-asin rem-log-exp

regimes18.2s (1.5%)

Accuracy

Total 40.7b remaining (20%)

Threshold costs 4.5b (2.2%)

8.4b4.4%Henrywood and Agarwal, Equation (12)
5.6b39.8%Toniolo and Linder, Equation (13)
5.1b77.9%Toniolo and Linder, Equation (7)
5.0b-13%Henrywood and Agarwal, Equation (13)
4.8b0%Maksimov and Kolovsky, Equation (3)

localize8.0s (0.7%)

bsearch2.0s (0.2%)

end1.0ms (0.0%)