Details

sample2.3m (45.4%)

Algorithm
21×intervals
Results
1.3m39003×body10240exit
15.5s7274×body1280valid
12.6s58027×body80nan
10.7s56576×body80valid
9.5s3432×body2560valid
5.2s4747×body640valid
1.6s2337×body320valid
473.0ms1199×body160valid
309.0ms8356×pre80true
104.0ms30×body5120valid
29.0ms33×body2560nan
22.0msbody5120nan
11.0ms21×body1280nan
4.0ms11×body640nan
3.0msbody160nan
1.0msbody320nan

simplify1.7m (33.8%)

prune36.4s (11.8%)

series19.8s (6.4%)

Calls

99 calls:

2.6s
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
2.5s
(sqrt (* (* (* (* U 2) n) (* (cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))) (cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))) (cbrt (* (* (cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))) (cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))) (cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))))
2.5s
(sqrt (* (* (* (* U 2) n) (* (cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))) (cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))) (cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
2.4s
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
1.1s
(cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))

regimes4.3s (1.4%)

Accuracy

Total 13.8b remaining (6.3%)

Threshold costs 1.6b (0.7%)

10.6b11.9%Toniolo and Linder, Equation (13)
1.6b0%Random Jason Timeout Test 006
0.5b0%Random Jason Timeout Test 002
0.5b0%Random Jason Timeout Test 014
0.5b0%Random Jason Timeout Test 012

localize1.4s (0.5%)

rewrite1.2s (0.4%)

Algorithm
31×rewrite-expression-head
Calls

99 calls:

306.0ms
(sqrt (* (* (* (* U 2) n) (* (cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))) (cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))) (cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
239.0ms
(sqrt (* (* (* (* U 2) n) (* (cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))) (cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))) (cbrt (* (* (cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))) (cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))) (cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))))
88.0ms
(* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
72.0ms
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
29.0ms
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
Rules
487×add-sqr-sqrt
446×*-un-lft-identity
406×add-cube-cbrt
275×pow1
193×times-frac
187×sqrt-prod
166×add-exp-log
165×log-prod
154×unpow-prod-up
144×add-cbrt-cube
126×prod-diff
120×unpow-prod-down
101×log1p-expm1-u
99×add-log-exp expm1-log1p-u insert-posit16
82×sqrt-pow1
80×pow-prod-down
43×pow1/2
40×pow-unpow
38×cbrt-prod
37×associate-/r*
36×pow-pow
30×log-pow
25×associate-*r*
23×rem-log-exp associate-*l*
20×distribute-lft-out-- difference-of-squares
19×cbrt-unprod prod-exp
17×associate-/l*
15×rem-sqrt-square exp-prod
14×pow-to-exp pow1/3 pow-exp sqr-pow sub-neg swap-sqr pow-sub
13×fma-udef div-inv
11×unswap-sqr
div-exp cbrt-undiv
sqrt-pow2
pow-prod-up *-commutative
distribute-lft-in log-div distribute-rgt-in
pow-sqr frac-2neg clear-num
expm1-udef associate-/r/
sinh-def expm1-log1p associate-/l/ flip3-- flip-- pow2 pow-plus acos-asin sin-diff
div-sub rem-square-sqrt sqrt-unprod

bsearch790.0ms (0.3%)

end0.0ms (0.0%)