Details

simplify5.7m (43.8%)

sample5.2m (39.6%)

Algorithm
21×intervals
Results
3.0m38669×body10240exit
30.8s7323×body1280valid
27.3s57376×body80nan
24.0s56582×body80valid
16.8s3391×body2560valid
12.4s4562×body640valid
4.5s2384×body320valid
730.0ms1287×body160valid
301.0ms8356×pre80true
149.0ms35×body5120valid
39.0msbody5120nan
25.0ms17×body2560nan
17.0ms28×body1280nan
6.0ms11×body640nan
4.0msbody320nan
2.0msbody160nan

series1.1m (8.1%)

Calls

100 calls:

8.6s
(sqrt (* (* (cbrt (* (- t (fma (/ l Om) (* l 2.0) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* n 2.0) U))) (cbrt (* (- t (fma (/ l Om) (* l 2.0) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* n 2.0) U)))) (cbrt (* (- t (fma (/ l Om) (* l 2.0) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* n 2.0) U)))))
5.5s
(sqrt (* (- t (fma (/ l Om) (* l 2.0) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* n 2.0) U)))
5.2s
(sqrt (* (- t (fma (/ l Om) (* l 2.0) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* n 2.0) U)))
4.8s
(sqrt (* (- t (fma (/ l Om) (* l 2.0) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* n 2.0) U)))
4.6s
(sqrt (* (- t (fma (/ l Om) (* l 2.0) (* (* (* n (pow (/ l Om) 2.0)) (* (cbrt (- U U*)) (cbrt (- U U*)))) (cbrt (- U U*))))) (* (* n 2.0) U)))

prune43.0s (5.5%)

regimes10.4s (1.3%)

Accuracy

Total 10.3b remaining (4.7%)

Threshold costs 0.6b (0.3%)

8.7b9.7%Toniolo and Linder, Equation (13)
1.1b0%Random Jason Timeout Test 006
0.5b0%Random Jason Timeout Test 012
0.0b0%Random Jason Timeout Test 004
0.0b0%Random Jason Timeout Test 003

rewrite7.5s (1.0%)

Algorithm
31×rewrite-expression-head
Calls

100 calls:

2.4s
(sqrt (* (- t (fma (/ l Om) (* l 2.0) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* n 2.0) U)))
1.0s
(sqrt (* (* (cbrt (* (- t (fma (/ l Om) (* l 2.0) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* n 2.0) U))) (cbrt (* (- t (fma (/ l Om) (* l 2.0) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* n 2.0) U)))) (cbrt (* (- t (fma (/ l Om) (* l 2.0) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* n 2.0) U)))))
177.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
167.0ms
(log (fmod (cosh c) (log1p a)))
154.0ms
(* (* n (pow (/ l Om) 2.0)) (* (cbrt (- U U*)) (cbrt (- U U*))))
Rules
516×add-sqr-sqrt
432×*-un-lft-identity
334×add-cube-cbrt
329×pow1
272×add-exp-log
187×add-cbrt-cube
157×unpow-prod-down
137×sqrt-prod
120×associate-*l/
118×cbrt-div
115×associate-*r*
113×unpow-prod-up
108×prod-diff
102×log1p-expm1-u
100×add-log-exp prod-exp expm1-log1p-u
91×associate-*l*
82×pow-unpow
81×cbrt-prod
77×pow-prod-down
75×times-frac sqrt-pow1
64×frac-times
63×flip-- flip3--
60×sinh-def
57×cbrt-unprod
52×unswap-sqr
47×distribute-lft-out--
43×difference-of-squares
40×associate-*r/
39×pow-pow
35×sqr-pow
34×sqrt-div pow-exp
33×log-prod
31×pow1/2
30×pow1/3
28×pow-to-exp log-pow
27×pow-prod-up
26×swap-sqr
22×pow-plus
20×*-commutative
19×exp-prod
18×pow-sub
13×pow-sqr
12×sub-neg
11×distribute-rgt-in distribute-lft-in
10×rem-sqrt-square pow2
sqrt-pow2
div-sub rem-log-exp
div-exp
associate-/l* pow3 div-inv associate-/r*
expm1-udef
exp-sum
expm1-log1p associate-/l/ acos-asin fma-udef associate-/r/ rem-cbrt-cube sin-diff
cbrt-undiv rem-exp-log e-exp-1 clear-num frac-2neg

localize3.8s (0.5%)

bsearch1.8s (0.2%)

end21.0ms (0.0%)