Details

sample2.4m (45.8%)

Algorithm
21×intervals
Results
1.3m38487×body10240exit
15.3s7319×body1280valid
12.7s58356×body80nan
10.6s56645×body80valid
9.8s3439×body2560valid
5.5s4530×body640valid
1.5s2396×body320valid
545.0ms1226×body160valid
365.0ms8356×pre80true
100.0ms34×body5120valid
35.0msbody5120nan
33.0ms25×body2560nan
17.0ms24×body1280nan
9.0ms16×body640nan
8.0ms14×body320nan
5.0ms11×body160nan

simplify2.2m (42.8%)

prune15.2s (4.9%)

series11.8s (3.8%)

Calls

94 calls:

1.6s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.6s
(sqrt (+ (* (* 2 n) (* U (fma -2 (* (/ l Om) l) t))) (* (* 2 n) (* (* (/ l Om) (* (* (cbrt (- (* (/ l Om) n))) (cbrt (- (* (/ l Om) n)))) (* (cbrt (- (* (/ l Om) n))) U))) (- U U*)))))
1.4s
(sqrt (+ (* (* 2 n) (* U (fma -2 (* (/ l Om) l) t))) (* (* 2 n) (* (* (/ l Om) (* (- (* (/ l Om) n)) U)) (- U U*)))))
1.4s
(sqrt (+ (* (* 2 n) (* U (fma -2 (* (/ l Om) l) t))) (* (* 2 n) (* (* U (- (* (/ l Om) (* n (/ l Om))))) (- U U*)))))
630.0ms
(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))

regimes4.3s (1.4%)

Accuracy

Total 16.5b remaining (7.5%)

Threshold costs 0.5b (0.3%)

13.9b-4.8%Toniolo and Linder, Equation (13)
2.0b0%Random Jason Timeout Test 006
0.4b0%Random Jason Timeout Test 012
0.1b0%Random Jason Timeout Test 004
0.0b0%Random Jason Timeout Test 003

localize1.4s (0.5%)

bsearch1.3s (0.4%)

rewrite1.2s (0.4%)

Algorithm
29×rewrite-expression-head
Calls

94 calls:

142.0ms
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
139.0ms
(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
104.0ms
(* (* (/ l Om) (* (- (* (/ l Om) n)) U)) (- U U*))
58.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
55.0ms
(* (* U (- (* (/ l Om) (* n (/ l Om))))) (- U U*))
Rules
361×add-sqr-sqrt
304×*-un-lft-identity
264×add-cube-cbrt
218×pow1
186×add-exp-log
172×add-cbrt-cube
115×sqrt-prod
102×prod-diff
95×log1p-expm1-u
94×add-log-exp expm1-log1p-u insert-posit16
67×associate-*r*
66×unpow-prod-up
63×unpow-prod-down
48×prod-exp times-frac
47×sqrt-pow1
46×pow-prod-down associate-*r/
45×cbrt-unprod
40×distribute-rgt-in distribute-lft-in
36×pow1/2
35×associate-*l* cbrt-prod
30×pow-unpow
29×associate-*l/
26×pow-pow
20×flip3-- flip-- distribute-lft-out-- difference-of-squares
19×distribute-neg-frac
18×frac-times unswap-sqr
17×rem-sqrt-square
16×log-pow
14×sub-neg swap-sqr
12×exp-prod sqrt-div log-prod *-commutative
10×pow1/3 fma-udef associate--l+
frac-sub pow-exp sqr-pow associate-/r*
div-exp pow-prod-up pow-to-exp
cbrt-undiv associate-/l* sqrt-pow2 pow-sub
pow-sqr
rem-log-exp distribute-lft-neg-in distribute-lft-neg-out div-inv neg-mul-1 distribute-rgt-neg-in
expm1-udef flip3-+ distribute-lft-out cbrt-div flip-+
sinh-def unpow2 associate-/l/ frac-2neg pow2 associate-/r/ distribute-rgt-neg-out pow-plus acos-asin clear-num sin-diff
div-sub expm1-log1p rem-square-sqrt sqrt-unprod

end0.0ms (0.0%)