Details

sample2.4m (48.5%)

Algorithm
21×intervals
Results
1.4m39295×body10240exit
14.6s7366×body1280valid
12.6s57659×body80nan
9.6s56597×body80valid
9.5s3443×body2560valid
5.8s4612×body640valid
1.5s2317×body320valid
475.0ms1207×body160valid
293.0ms8356×pre80true
116.0ms38×body5120valid
73.0ms10×body5120nan
26.0ms31×body2560nan
13.0ms22×body1280nan
5.0ms15×body640nan
3.0msbody320nan
3.0ms10×body160nan

simplify1.8m (36.5%)

prune18.5s (6.3%)

series18.0s (6.1%)

Calls

92 calls:

2.9s
(sqrt (* (* U (fma (* (/ (/ l (* (cbrt Om) (cbrt Om))) 1) (* (/ (/ l (cbrt Om)) Om) (- U* U))) n (fma (* l (/ l Om)) -2 t))) (* 2 n)))
2.9s
(sqrt (* (* U (fma (* (/ (/ (* l l) Om) Om) (- U* U)) n (fma (/ (* l l) Om) -2 t))) (* 2 n)))
2.9s
(sqrt (* (* U (fma (* (/ (/ l (* (cbrt Om) (cbrt Om))) 1) (* (/ (/ l (cbrt Om)) Om) (- U* U))) n (fma (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))) -2 t))) (* 2 n)))
2.9s
(sqrt (* (* U (fma (* (/ (/ l (* (cbrt Om) (cbrt Om))) 1) (* (/ (/ l (cbrt Om)) Om) (- U* U))) n (fma (/ (* l l) Om) -2 t))) (* 2 n)))
525.0ms
(* U (fma (* (/ (/ l (* (cbrt Om) (cbrt Om))) 1) (* (/ (/ l (cbrt Om)) Om) (- U* U))) n (fma (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))) -2 t)))

regimes5.9s (2.0%)

Accuracy

Total 12.7b remaining (5.8%)

Threshold costs 0.4b (0.2%)

8.4b20.9%Toniolo and Linder, Equation (13)
2.2b0%Random Jason Timeout Test 006
1.7b0%Random Jason Timeout Test 004
0.4b0%Random Jason Timeout Test 012
0.0b0%Random Jason Timeout Test 003

localize1.3s (0.4%)

rewrite783.0ms (0.3%)

Algorithm
30×rewrite-expression-head
Calls

92 calls:

64.0ms
(* (/ (/ l (cbrt Om)) Om) (- U* U))
52.0ms
(* (/ (/ l (cbrt Om)) Om) (- U* U))
45.0ms
(* (/ (/ (* l l) Om) Om) (- U* U))
40.0ms
(sqrt (* (* U (fma (* (/ (/ l (* (cbrt Om) (cbrt Om))) 1) (* (/ (/ l (cbrt Om)) Om) (- U* U))) n (fma (/ (* l l) Om) -2 t))) (* 2 n)))
35.0ms
(* (cbrt (pow (atan2 b b) (/ (- b a) 2))) (cbrt (pow (atan2 b b) (/ (- b a) 2))))
Rules
666×add-sqr-sqrt
561×*-un-lft-identity
505×add-cube-cbrt
472×times-frac
261×associate-*l*
251×cbrt-prod
200×pow1
166×add-exp-log
151×add-cbrt-cube
126×prod-diff
112×unpow-prod-down
93×expm1-log1p-u log1p-expm1-u
92×add-log-exp insert-posit16
68×pow-unpow
66×unpow-prod-up
64×sqrt-prod
49×unswap-sqr
46×distribute-rgt-in associate-*r* distribute-lft-in
44×sqrt-pow1
42×pow-prod-down
38×sqr-pow
28×difference-of-squares distribute-lft-out-- pow-pow
25×pow1/3
22×div-inv pow-sub
21×div-exp cbrt-undiv cbrt-unprod prod-exp
20×exp-prod pow1/2 swap-sqr
18×log-prod log-pow
17×div-sub
14×sub-neg cbrt-div associate-/r*
10×frac-times flip3-- flip-- associate-*r/
pow-to-exp associate-/l* pow-exp *-commutative
fma-udef
expm1-udef sinh-def exp-sum rem-sqrt-square associate-*l/ sqrt-pow2
sin-diff
pow-prod-up pow-sqr frac-2neg rem-log-exp clear-num
exp-diff associate-/l/ pow2 associate-/r/ rem-exp-log pow-plus acos-asin log-div
expm1-log1p log1p-expm1 log1p-udef

bsearch5.0ms (0.0%)

end0.0ms (0.0%)