Details

simplify2.2m (37.4%)

sample2.2m (36.7%)

Algorithm
21×intervals
Results
1.3m38710×body10240exit
14.5s7379×body1280valid
10.2s57976×body80nan
9.6s56658×body80valid
8.3s3424×body2560valid
5.7s4689×body640valid
1.4s2266×body320valid
462.0ms1174×body160valid
284.0ms8356×pre80true
151.0ms36×body5120valid
27.0msbody5120nan
23.0ms29×body2560nan
13.0ms23×body1280nan
6.0ms12×body320nan
4.0ms11×body640nan
3.0ms10×body160nan

prune1.2m (19.3%)

series17.9s (5.0%)

Calls

94 calls:

2.9s
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ (* (cbrt n) (cbrt n)) (/ (/ (* (cbrt Om) (cbrt Om)) 1) (/ (cbrt n) (/ (cbrt Om) l)))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
2.5s
(sqrt (* (* U 2) (* n (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))))
2.4s
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ (* (cbrt n) (cbrt n)) (/ (/ Om l) (cbrt n))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
500.0ms
(* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))

regimes2.7s (0.8%)

Accuracy

Total 12.2b remaining (5.6%)

Threshold costs 0.6b (0.3%)

9.8b12.1%Toniolo and Linder, Equation (13)
1.7b0%Random Jason Timeout Test 006
0.4b0%Random Jason Timeout Test 012
0.2b0%Random Jason Timeout Test 004
0.0b0%Random Jason Timeout Test 015

localize1.2s (0.3%)

rewrite1.1s (0.3%)

Algorithm
29×rewrite-expression-head
Calls

94 calls:

91.0ms
(* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
85.0ms
(* (* (* U 2) n) (fma (- U* U) (/ (/ (* (cbrt n) (cbrt n)) (/ (/ (* (cbrt Om) (cbrt Om)) 1) (/ (cbrt n) (/ (cbrt Om) l)))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
73.0ms
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ (* (cbrt n) (cbrt n)) (/ (/ (* (cbrt Om) (cbrt Om)) 1) (/ (cbrt n) (/ (cbrt Om) l)))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
73.0ms
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
71.0ms
(* (* (* U 2) n) (fma (- U* U) (/ (/ (* (cbrt n) (cbrt n)) (/ (/ Om l) (cbrt n))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
Rules
7986×times-frac
3064×add-sqr-sqrt
3039×*-un-lft-identity
2895×add-cube-cbrt
1755×cbrt-prod
1043×associate-/r*
418×div-inv
341×add-exp-log
322×pow1
218×add-cbrt-cube
194×exp-prod
132×div-exp
114×log-pow
96×add-log-exp log1p-expm1-u
94×expm1-log1p-u insert-posit16
91×sqrt-prod
84×cbrt-undiv
72×difference-of-squares distribute-lft-out--
66×unpow-prod-up
61×associate-/r/
57×pow-prod-down prod-exp
54×prod-diff
52×sqrt-pow1
48×unpow-prod-down
45×cbrt-unprod
33×associate-/l*
31×pow1/2
30×log-prod pow-unpow
26×pow-pow
22×associate-*r*
20×flip3-- flip--
16×associate-*l* fma-udef
12×1-exp
rem-log-exp pow1/3 rem-sqrt-square
swap-sqr
frac-2neg distribute-lft-in distribute-rgt-in clear-num *-commutative
pow-to-exp pow-exp unswap-sqr sqr-pow sub-neg sqrt-pow2 pow-sub
pow-prod-up
expm1-udef
associate-/l/ pow-sqr exp-sum rem-exp-log
exp-to-pow sinh-def expm1-log1p acos-asin sin-diff
div-sub rem-square-sqrt pow2 pow-plus sqrt-unprod

bsearch536.0ms (0.1%)

end1.0ms (0.0%)