Details

simplify14.5m (49.1%)

series4.7m (16.1%)

Calls

453 calls:

17.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
17.5s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
17.5s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
17.2s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
3.7s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))

prune4.7m (15.8%)

sample3.3m (11.1%)

Algorithm
61×intervals
Results
42.9s253614×body80valid
40.4s29575×body1280valid
26.0s160606×body80nan
20.1s20413×body640valid
18.3s8910×body2560valid
11.6s3411×body5120valid
5.8s10021×body320valid
2.9s8980×body160valid
1.6s768×body10240exit
350.0ms621×body1280nan
324.0ms650×body640nan
207.0ms8256×pre80true
138.0ms340×body320nan
44.0ms189×body160nan

regimes1.2m (3.9%)

Accuracy

Total 54.0b remaining (28.2%)

Threshold costs 3.9b (2%)

9.9b-3%Henrywood and Agarwal, Equation (13)
8.6b16%Toniolo and Linder, Equation (13)
8.1b12.3%Maksimov and Kolovsky, Equation (3)
6.7b-1.3%Henrywood and Agarwal, Equation (12)
5.4b76.8%Toniolo and Linder, Equation (7)

rewrite50.9s (2.9%)

Algorithm
116×rewrite-expression-head
Calls

453 calls:

1.8s
(/ (log (exp (- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)))))) (+ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (* 1.0 (+ 1.0 (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))))
1.7s
(/ (log (exp (- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)))))) (+ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (* 1.0 (+ 1.0 (sqrt (* (+ 1.0 (* 1 (/ 1.0 (hypot 1.0 x)))) 0.5))))))
1.4s
(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (* (pow (/ (/ 1 (pow k (/ 2.0 2))) (pow t 1.0)) 1.0) 2.0) (/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))))
1.2s
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.2s
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
Rules
45679×add-exp-log
29127×prod-exp
16446×div-exp
16067×pow-exp
13067×times-frac
7883×*-un-lft-identity
7705×add-sqr-sqrt
6972×add-cube-cbrt
5497×pow-to-exp
3154×sqrt-prod
3119×add-cbrt-cube
2958×1-exp rec-exp
1801×unpow-prod-down
1127×associate-*l* pow1
1078×cbrt-unprod
884×associate-/l*
851×cbrt-undiv
724×div-inv
629×associate-*r*
542×add-log-exp
473×associate-*r/
462×associate-/r*
454×pow-unpow
453×insert-posit16
417×cbrt-prod
403×associate-/r/
350×distribute-lft-out
312×sqrt-div
300×sqr-pow
295×pow-prod-down
238×flip-+ flip3-+
221×unswap-sqr
166×flip3-- flip--
146×associate-*l/
141×distribute-lft-out--
133×*-commutative
122×frac-times
116×frac-2neg clear-num
111×sqrt-pow1
109×difference-of-squares
89×pow1/2
85×distribute-rgt-in distribute-lft-in rem-sqrt-square
79×sub-neg
75×associate-/l/
69×exp-prod
62×log-pow
58×frac-add
55×frac-sub
52×div-sub
48×pow1/3
47×swap-sqr
46×pow-pow
31×pow-sub
28×associate--l+
27×cbrt-div distribute-rgt-neg-in tan-quot distribute-lft-neg-in
26×log-prod diff-log
22×pow-prod-up
20×sum-log +-commutative
12×pow-plus associate--r+ pow-sqr
10×associate-+l+
9×neg-mul-1
8×pow2
7×pow-flip
6×neg-sub0 associate-+r+ pow-neg distribute-frac-neg
5×remove-posit16 exp-diff associate--l- exp-sum inv-pow distribute-rgt-out-- rem-log-exp
4×associate-+r- cos-sum log-div
3×un-div-inv acos-asin distribute-rgt-out
2×pow3 sqrt-unprod sub-div asin-acos cos-diff
1×cube-unmult distribute-lft1-in sqrt-pow2 exp-to-pow rem-exp-log rem-square-sqrt rem-cbrt-cube count-2 distribute-rgt1-in

localize16.3s (0.9%)

bsearch3.3s (0.2%)

end1.0ms (0.0%)