Details

simplify1.2hr

Calls

31487 calls:

Slowest
10.9s
(* (/ h (* (cbrt l) (cbrt l))) (/ (* M D) 1))
10.9s
(/ 1 (* l (/ (sqrt (* 2 d)) (* (sqrt M) (sqrt D)))))
10.7s
(/ (cbrt h) (/ (* (sqrt 2) (sqrt d)) D))
10.2s
(sqrt (+ 1 (* (sqrt (* (/ h l) (/ (* M D) (* 2 d)))) (/ (sqrt (* M D)) (* (sqrt 2) (sqrt d))))))
1.6s
(/ (* (* h h) h) (* (* (* l l) l) (/ (* (* (* 2 d) (* 2 d)) (* 2 d)) (* (* (* M D) (* M D)) (* M D)))))

prune6.6m

rewrite3.9m

Algorithm
90×rewrite-expression-head
Calls

346 calls:

Slowest
37.5s
(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
26.3s
(sqrt (* 2 (* U (* n (- (fma (/ (* l l) Om) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*))))))))
16.7s
(pow (- 1 (/ (/ h (* l (/ (* 2 d) (* D M)))) (/ (* 2 d) (* D M)))) (/ 1 2))
8.1s
(sqrt (* (cbrt U) (* n (- (fma (/ (* l l) Om) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))
7.7s
(sqrt (* (cbrt U) (* n (- (fma (* (/ (/ l (cbrt Om)) (cbrt Om)) (/ l (cbrt Om))) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))
Rules
2844924×times-frac
1391189×add-sqr-sqrt
1141676×*-un-lft-identity
1130158×add-cube-cbrt
228581×associate-*r*
225472×associate-*l*
217974×swap-sqr
217574×associate-/r/
182122×frac-times
154114×associate-/l*
142963×associate-/r*
107720×div-inv
96079×unswap-sqr
45951×clear-num
43840×frac-2neg
42803×cbrt-prod
21747×prod-diff
21731×sqrt-prod
21346×associate-*l/
20785×associate-*r/
20451×*-commutative
17164×cos-sum
9018×cbrt-div
6294×associate-/l/
4888×difference-of-squares
4483×unpow-prod-down
4226×un-div-inv
3408×distribute-lft-out
3403×add-exp-log
3086×add-cbrt-cube
3046×sqrt-div
2239×fma-def
2230×frac-add
1911×flip-- flip3--
1656×distribute-rgt-in distribute-lft-in
1450×pow1
1281×div-exp
1242×cbrt-unprod
1034×prod-exp
976×cbrt-undiv
862×sqr-pow
611×distribute-lft-out--
432×pow-prod-down
376×add-log-exp
346×expm1-log1p-u insert-posit16 log1p-expm1-u
272×rem-sqrt-square
261×frac-sub
208×tan-quot
188×fma-neg
160×associate-+r+
156×pow-prod-up
123×pow-unpow
117×pow-exp
109×sqrt-pow1
92×pow-plus
88×pow-sqr
86×unpow2
84×difference-of-sqr-1
75×1-exp rec-exp
67×pow1/2
64×pow-to-exp
57×sub-neg
55×pow2
52×associate-+l+
50×fma-udef
39×+-commutative
35×flip-+ flip3-+
32×pow1/3
29×div-sub
28×distribute-lft-neg-in distribute-rgt-neg-in
23×pow-sub
17×associate--l+ pow-pow
14×sub-div
11×pow-flip remove-double-div
10×diff-log
9×inv-pow
8×log-pow
7×distribute-rgt-out--
6×pow3 acos-asin
5×sum-log
4×neg-mul-1
3×hypot-udef cos-diff
2×associate-+r- distribute-neg-frac asin-acos e-exp-1
1×neg-sub0 sqrt-undiv distribute-frac-neg sqrt-unprod sin-mult sqr-sin associate-+l- unpow1/3 rem-square-sqrt

sample2.0m

Algorithm
44×intervals
Results
34.0s148496×body80valid
26.2s13713×body1280valid
18.1s8132×body10240exit
13.5s10301×body640valid
9.4s48265×body80nan
6.1s5064×body320valid
4.2s7047×body160valid
3.9s3187×body2560valid
321.0ms87×body5120valid
18.0ms22×body640nan
16.0ms17×body1280nan
5.0ms8×body320nan
2.0ms5×body160nan

series1.2m

Calls

346 calls:

Slowest
9.1s
(sqrt (* (cbrt U) (* n (- (fma (* (/ (/ l (cbrt Om)) (cbrt Om)) (/ l (cbrt Om))) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))
9.0s
(sqrt (* (cbrt U) (* n (- (fma (/ (* l l) Om) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))
2.4s
(sqrt (* 2 (* U (* n (- (fma (/ (* l l) Om) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*))))))))
1.4s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
898.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))

regimes6.5s

Accuracy

Total 8.3b remaining (21.4%)

3.9b0%Maksimov and Kolovsky, Equation (3)
1.6b0%Henrywood and Agarwal, Equation (3)
1.0b0%Falkner and Boettcher, Appendix B, 1
0.7b0%VandenBroeck and Keller, Equation (23)
0.3b0%Maksimov and Kolovsky, Equation (4)

localize4.4s

bsearch90.0ms

end1.0ms