Details

sample2.3m (47.3%)

Algorithm
21×intervals
Results
1.3m39324×body10240exit
13.5s7174×body1280valid
13.3s58209×body80nan
10.3s56625×body80valid
8.6s3416×body2560valid
5.2s4771×body640valid
2.0s2289×body320valid
927.0ms1251×body160valid
305.0ms8356×pre80true
70.0ms23×body5120valid
31.0ms27×body2560nan
22.0msbody5120nan
12.0ms22×body1280nan
5.0ms11×body640nan
5.0ms12×body320nan
2.0msbody160nan

simplify1.9m (37.8%)

series20.0s (6.8%)

Calls

89 calls:

2.8s
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
2.5s
(sqrt (* (* U 2) (* (* (cbrt n) (cbrt n)) (* (cbrt n) (fma (- U* U) (/ (/ n (/ 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)))))
2.5s
(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) (/ (* (* (cbrt l) (cbrt l)) (/ n (/ Om (cbrt l)))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

prune17.2s (5.8%)

regimes4.0s (1.4%)

Accuracy

Total 10.0b remaining (4.7%)

Threshold costs 0.5b (0.2%)

5.5b40.3%Toniolo and Linder, Equation (13)
2.2b0%Random Jason Timeout Test 006
1.9b0%Random Jason Timeout Test 004
0.4b0%Random Jason Timeout Test 012
0.0b0%Random Jason Timeout Test 003

localize1.5s (0.5%)

rewrite1.3s (0.5%)

Algorithm
27×rewrite-expression-head
Calls

89 calls:

157.0ms
(* (* U 2) (* (* (cbrt n) (cbrt n)) (* (cbrt n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
147.0ms
(* (* (* (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (atan2 (expm1 (sin (expm1 a))) (atan a)))
134.0ms
(sqrt (* (* U 2) (* (* (cbrt n) (cbrt n)) (* (cbrt n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))))
122.0ms
(* (* (* (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (atan2 (expm1 (sin (expm1 a))) (atan a)))
101.0ms
(cbrt (* (* (* (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))))) (atan2 (expm1 (sin (expm1 a))) (atan a))))
Rules
665×add-sqr-sqrt
532×*-un-lft-identity
496×add-cube-cbrt
400×times-frac
354×pow1
282×sqrt-prod
240×add-exp-log
210×unpow-prod-down
192×add-cbrt-cube
162×unpow-prod-up
139×pow-prod-down
126×prod-diff
90×expm1-log1p-u log1p-expm1-u
89×add-log-exp insert-posit16
84×sqrt-pow1
83×prod-exp
71×swap-sqr
70×associate-/r* associate-*r*
67×cbrt-unprod
64×associate-*l*
57×unswap-sqr
38×pow1/2
35×cbrt-prod
34×sqr-pow
30×pow-unpow pow-pow
26×div-inv
21×distribute-rgt-in distribute-lft-in
20×rem-sqrt-square associate-/l*
19×fma-udef
18×pow-to-exp difference-of-squares sub-neg distribute-lft-out-- pow-exp
17×pow1/3
16×div-exp cbrt-undiv
14×pow-sub
11×pow-prod-up *-commutative
log-pow pow-plus
associate-/r/ pow-sqr
log-prod frac-2neg pow2 exp-prod clear-num sqrt-pow2
frac-times associate-/l/ pow3 flip3-- flip-- associate-*r/ rem-log-exp acos-asin associate-*l/
expm1-log1p expm1-udef div-sub log1p-expm1 log1p-udef rem-cbrt-cube

bsearch167.0ms (0.1%)

end0.0ms (0.0%)