Details

simplify8.7m (58.8%)

series2.0m (13.4%)

Calls

335 calls:

7.4s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* (pow (/ l Om) 2.0) (- U U*)))))))
7.3s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
7.1s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
6.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))
2.1s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* (pow (/ l Om) 2.0) (- U U*))))))

sample1.7m (11.5%)

Algorithm
46×intervals
Results
25.2s132380×body80valid
20.7s123046×body80nan
18.1s12442×body1280valid
10.9s9928×body640valid
6.2s2834×body2560valid
4.4s2501×body5120valid
2.9s5079×body320valid
915.0ms2795×body160valid
845.0ms682×body10240exit
15.0ms26×body1280nan
7.0ms14×body640nan
5.0ms256×pre80true
1.0msbody160nan
1.0msbody320nan

prune1.4m (9.1%)

rewrite42.8s (4.8%)

Algorithm
90×rewrite-expression-head
Calls

335 calls:

3.1s
(* (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
2.9s
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (* (/ (pow (cbrt t) 3.0) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
2.1s
(+ (sqrt (- (* (* (/ c0 (* w h)) (* (/ d D) (/ d D))) (* (/ c0 (* w h)) (* (/ d D) (/ d D)))) (* M M))) (* (/ c0 (* w h)) (* (/ d D) (/ d D))))
2.1s
(+ (sqrt (- (* (* (/ c0 (* w h)) (* (/ d D) (/ d D))) (* (/ c0 (* w h)) (* (/ d D) (/ d D)))) (* M M))) (* (/ c0 (* w h)) (* (/ d D) (/ d D))))
2.1s
(+ (sqrt (- (* (* (/ c0 (* w h)) (* (/ d D) (/ d D))) (* (/ c0 (* w h)) (* (/ d D) (/ d D)))) (* M M))) (* (/ c0 (* w h)) (* (/ d D) (/ d D))))
Rules
25214×add-exp-log
17031×prod-exp
6721×pow-exp
6519×div-exp
5326×times-frac
4733×add-sqr-sqrt
4412×sqrt-prod
3796×*-un-lft-identity
3403×add-cube-cbrt
2572×add-cbrt-cube
2502×pow-to-exp
1526×associate-*l*
1356×pow1
1297×cbrt-unprod
773×associate-*r*
686×associate-*r/
665×unpow-prod-down
554×1-exp rec-exp
542×frac-times
521×cbrt-undiv
519×associate-*l/
477×pow-prod-down
465×pow-unpow
395×add-log-exp
387×sqrt-div
362×cbrt-prod
278×unswap-sqr
254×difference-of-squares
251×flip3-- flip--
225×div-inv
220×associate-/l*
216×associate-/r/
215×associate-/r*
181×sqr-pow
169×swap-sqr
153×flip-+ flip3-+
145×*-commutative
141×tan-quot
125×distribute-lft-out--
108×distribute-rgt-in distribute-lft-in
91×pow-prod-up
87×distribute-lft-out
76×sub-neg
68×sqrt-pow1
59×pow-sqr
57×frac-2neg clear-num
56×frac-add
53×pow1/3
47×pow-pow
43×pow-plus
37×pow1/2
35×frac-sub
34×cbrt-div
33×pow2
29×rem-sqrt-square
26×distribute-lft-neg-in distribute-rgt-neg-in
23×associate-/l/
20×sum-log div-sub
18×associate--l+
17×+-commutative
13×pow-sub
11×diff-log
10×cos-sum
sqrt-undiv associate-+r+ pow-neg
neg-sub0 log-prod exp-sum cos-diff
exp-prod
distribute-rgt-out-- acos-asin
exp-diff pow-flip log-div sqrt-unprod sub-div neg-mul-1 inv-pow asin-acos rem-square-sqrt
associate-+l+ associate-+r- mul0 un-div-inv rem-exp-log log-pow

regimes12.4s (1.4%)

Accuracy

Total 32.8b remaining (28.4%)

Threshold costs 2.4b (2.1%)

10.3b10.1%Toniolo and Linder, Equation (13)
7.4b14.8%Toniolo and Linder, Equation (10+)
7.0b-3%Henrywood and Agarwal, Equation (12)
5.8b-11.8%Henrywood and Agarwal, Equation (13)
0.4b0%VandenBroeck and Keller, Equation (6)

localize5.8s (0.7%)

bsearch3.4s (0.4%)

end0.0ms (0.0%)