Details

simplify5.6m (34.1%)

prune3.4m (21.0%)

sample3.1m (19.2%)

Algorithm
61×intervals
Results
42.2s253680×body80valid
35.7s29202×body1280valid
27.3s160143×body80nan
20.1s20532×body640valid
18.9s9016×body2560valid
9.4s3411×body5120valid
8.6s9904×body320valid
3.7s8844×body160valid
868.0ms652×body10240exit
491.0ms661×body1280nan
484.0ms8256×pre80true
243.0ms598×body640nan
134.0ms348×body320nan
41.0ms202×body160nan

series2.9m (17.9%)

Calls

420 calls:

15.1s
(sqrt (* (* 2.0 n) (* (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U))) (* (* 2.0 l) (/ l Om)))) U)))
14.9s
(sqrt (* (* 2.0 n) (* (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om)))) U)))
14.6s
(sqrt (* (* 2.0 n) (* (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om)))) U)))
14.0s
(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))
1.7s
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite40.1s (4.1%)

Algorithm
113×rewrite-expression-head
Calls

420 calls:

2.4s
(/ (- (* 1.0 (* 1.0 1.0)) (* (sqrt (* (* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (+ (/ 0.5 (hypot 1.0 x)) 0.5))) (* (* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (+ (/ 0.5 (hypot 1.0 x)) 0.5)))) (+ (+ (* 1.0 1.0) (* (* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (+ (/ 0.5 (hypot 1.0 x)) 0.5))) (* (sqrt (* (* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5)) (+ (/ 0.5 (hypot 1.0 x)) 0.5))) 1.0)))
1.9s
(* (sqrt (exp (/ (+ EAccept (- (+ Vef Ev) mu)) KbT))) (sqrt (exp (/ (+ EAccept (- (+ Vef Ev) mu)) KbT))))
1.3s
(sqrt (* (* 2.0 n) (* (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om)))) U)))
1.2s
(* (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))) (/ (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))) (/ (cbrt (cbrt (sqrt 2.0))) (cos th))))
1.2s
(* (* 2.0 n) (* (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om)))) U))
Rules
40824×add-exp-log
32378×times-frac
27253×prod-exp
16117×add-sqr-sqrt
16040×pow-exp
15842×*-un-lft-identity
14575×add-cube-cbrt
14143×div-exp
9503×cbrt-prod
7911×sqrt-prod
6446×pow-to-exp
4023×associate-*r*
2700×add-cbrt-cube
2490×1-exp rec-exp
2284×unpow-prod-down
1525×pow1
1250×associate-/l*
1046×cbrt-unprod
897×div-inv
728×sqr-pow
726×cbrt-undiv
704×associate-/r*
695×associate-*l*
568×sqrt-div
525×sqrt-pow1
500×add-log-exp
480×pow-prod-down
433×exp-prod
423×associate-*r/
412×distribute-lft-out
389×flip-+ flip3-+
369×associate-/r/
368×difference-of-squares
360×frac-times associate-*l/
326×distribute-lft-out--
303×unswap-sqr
238×pow-unpow pow-prod-up
168×pow-sqr
161×pow1/3
135×*-commutative
121×frac-add
115×flip3-- flip--
92×pow-plus
83×swap-sqr
79×frac-2neg clear-num
78×pow1/2
70×cbrt-div rem-sqrt-square
68×distribute-rgt-in distribute-lft-in
61×pow2
41×tan-quot
39×distribute-lft-neg-in distribute-rgt-neg-in
37×associate-/l/ sub-neg
34×pow-pow
29×sum-log
28×cos-sum
24×div-sub
23×+-commutative
22×associate--l+
21×pow-sub
20×pow-neg
14×neg-sub0
13×associate-+l+
12×diff-log
11×cube-unmult un-div-inv
8×associate-+r-
7×exp-diff sin-mult unpow2
6×pow-flip associate--r+ inv-pow unpow1/3
5×frac-sub pow3 difference-cubes cos-diff
4×associate-+r+ log-pow
3×sqrt-unprod neg-mul-1 asin-acos acos-asin
2×sqr-sin rem-square-sqrt
1×cos-mult sub-div rem-exp-log sqr-cos rem-cbrt-cube

regimes26.1s (2.7%)

Accuracy

Total 59.9b remaining (28.5%)

Threshold costs 3.4b (1.6%)

10.1b25.8%Toniolo and Linder, Equation (13)
8.8b0%Henrywood and Agarwal, Equation (13)
7.5b0.4%Henrywood and Agarwal, Equation (12)
6.1b50.8%Henrywood and Agarwal, Equation (3)
5.5b-1.4%Maksimov and Kolovsky, Equation (3)

localize7.7s (0.8%)

bsearch2.7s (0.3%)

end1.0ms (0.0%)