Details

sample2.3m (45.6%)

Algorithm
21×intervals
Results
1.3m38373×body10240exit
14.0s7462×body1280valid
11.3s57470×body80nan
10.9s56666×body80valid
9.3s3509×body2560valid
5.0s4498×body640valid
1.5s2303×body320valid
490.0ms1167×body160valid
340.0ms24×body1280nan
294.0ms8356×pre80true
75.0ms24×body5120valid
38.0ms37×body2560nan
16.0msbody5120nan
6.0ms13×body640nan
3.0msbody320nan
2.0msbody160nan

simplify1.9m (39.1%)

prune23.6s (7.9%)

series15.3s (5.1%)

Calls

93 calls:

2.5s
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
2.5s
(sqrt (* (* (cbrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))) (cbrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))) (cbrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ 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)))))
710.0ms
(cbrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
707.0ms
(cbrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

regimes3.8s (1.3%)

Accuracy

Total 10.2b remaining (4.8%)

Threshold costs 0.7b (0.3%)

7.4b-6.1%Toniolo and Linder, Equation (13)
2.2b0%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 003

localize1.5s (0.5%)

rewrite812.0ms (0.3%)

Algorithm
29×rewrite-expression-head
Calls

93 calls:

119.0ms
(sqrt (* (* (cbrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))) (cbrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))) (cbrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))))
46.0ms
(* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
38.0ms
(* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
38.0ms
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
38.0ms
(* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
Rules
354×add-sqr-sqrt
329×pow1
311×*-un-lft-identity
275×add-cube-cbrt
181×add-exp-log
177×sqrt-prod
171×add-cbrt-cube
100×times-frac
94×log1p-expm1-u
93×add-log-exp expm1-log1p-u insert-posit16
91×unpow-prod-up
78×unpow-prod-down
72×prod-diff
65×pow-prod-down sqrt-pow1
44×cbrt-unprod prod-exp
40×pow-prod-up
38×pow-unpow
37×pow-plus
35×pow1/2
33×associate-*r*
30×rem-sqrt-square
28×pow-pow
23×associate-*l*
21×fma-udef
18×log-prod distribute-lft-out-- difference-of-squares associate-/r*
14×pow-sqr pow1/3 distribute-lft-in distribute-rgt-in
13×pow2 *-commutative
12×log-pow sqr-pow
10×exp-prod unswap-sqr pow-exp
associate-/l* sub-neg pow-to-exp pow-sub
pow3
sqrt-pow2 div-inv cbrt-prod
rem-log-exp div-exp cbrt-undiv
associate-/r/ exp-sum swap-sqr
sinh-def associate-/l/ flip3-- flip-- frac-2neg sqrt-div expm1-udef acos-asin clear-num e-exp-1
div-sub expm1-log1p rem-exp-log rem-cbrt-cube sin-diff

bsearch578.0ms (0.2%)

end0.0ms (0.0%)