Details

sample2.4m (59.4%)

Algorithm
21×intervals
Results
1.4m39837×body10240exit
14.8s7242×body1280valid
12.9s58495×body80nan
10.7s56723×body80valid
9.8s3394×body2560valid
4.7s4699×body640valid
1.9s2303×body320valid
573.0ms1194×body160valid
308.0ms8356×pre80true
93.0ms30×body5120valid
42.0ms14×body5120nan
27.0ms30×body2560nan
13.0ms21×body1280nan
7.0ms14×body640nan
4.0ms14×body160nan
4.0ms11×body320nan

simplify1.1m (27.8%)

prune15.2s (6.2%)

series9.4s (3.8%)

Calls

91 calls:

2.0s
(sqrt (* (* n (* U 2)) (- t (* (/ l Om) (+ (* (* (- U U*) n) (/ l Om)) (* 2 l))))))
1.3s
(sqrt (+ (* t (* n (* U 2))) (- (* (* (* n (* U 2)) (/ l Om)) (fma l 2 (* (- U U*) (* n (/ l Om))))))))
1.3s
(sqrt (+ (* t (* n (* U 2))) (- (* (* n (* (* U 2) (/ l Om))) (fma l 2 (* (- U U*) (* n (/ l Om))))))))
561.0ms
(* (* n (* U 2)) (- t (* (/ l Om) (+ (* (* (- U U*) n) (/ l Om)) (* 2 l)))))
555.0ms
(pow (+ (* t (* n (* U 2))) (- (* (* n (* (* U 2) (/ l Om))) (fma l 2 (* (- U U*) (* n (/ l Om))))))) 1/2)

regimes3.1s (1.3%)

Accuracy

Total 12.4b remaining (5.8%)

Threshold costs 0.9b (0.4%)

9.5b-7%Toniolo and Linder, Equation (13)
2.1b0%Random Jason Timeout Test 006
0.4b0%Random Jason Timeout Test 012
0.2b0%Random Jason Timeout Test 004
0.1b0%Random Jason Timeout Test 003

rewrite1.9s (0.8%)

Algorithm
29×rewrite-expression-head
Calls

91 calls:

198.0ms
(cbrt (* (* (pow (sqrt (sqrt (atan2 b b))) (+ (- b a) (- b a))) (pow (sqrt (sqrt (atan2 b b))) (+ (- b a) (- b a)))) (pow (sqrt (sqrt (atan2 b b))) (+ (- b a) (- b a)))))
175.0ms
(cbrt (* (* (pow (sqrt (sqrt (atan2 b b))) (+ (- b a) (- b a))) (pow (sqrt (sqrt (atan2 b b))) (+ (- b a) (- b a)))) (pow (sqrt (sqrt (atan2 b b))) (+ (- b a) (- b a)))))
148.0ms
(* (/ l Om) (+ (* (* (- U U*) n) (/ l Om)) (* 2 l)))
100.0ms
(sqrt (+ (* t (* n (* U 2))) (- (* (* n (* (* U 2) (/ l Om))) (fma l 2 (* (- U U*) (* n (/ l Om))))))))
87.0ms
(* (* n (* U 2)) (- t (* (/ l Om) (+ (* (* (- U U*) n) (/ l Om)) (* 2 l)))))
Rules
509×add-sqr-sqrt
403×*-un-lft-identity
317×add-cube-cbrt
249×add-exp-log
230×pow1
229×sqrt-prod
220×add-cbrt-cube
189×unpow-prod-down
154×associate-*r*
122×pow-sub
120×unpow-prod-up
101×times-frac
96×prod-diff
93×add-log-exp
92×associate-*l* log1p-expm1-u
91×expm1-log1p-u insert-posit16
83×prod-exp
68×frac-times
67×cbrt-unprod
64×swap-sqr
60×unswap-sqr
57×pow-unpow
56×associate-+r- associate-+l-
52×cbrt-div
48×pow-prod-down
43×associate-*r/ associate-*l/
37×distribute-lft-out--
33×sqr-pow
30×sqrt-pow1
25×difference-of-squares
24×log-prod
23×pow1/2
19×exp-prod
17×div-exp cbrt-undiv log-pow pow-exp pow-to-exp pow-pow
16×sub-neg rem-sqrt-square *-commutative
14×distribute-lft-out pow-prod-up distribute-rgt-out
12×flip3-- flip-- pow-plus
div-inv
rem-log-exp
distribute-lft-in pow2 sqrt-div distribute-rgt-in pow-sqr
expm1-udef associate-/r* associate-/l*
flip3-+ distribute-lft1-in pow3 sqrt-pow2 flip-+ sin-diff distribute-rgt1-in
rem-exp-log exp-sum
sinh-def associate-/l/ associate-/r/ cbrt-prod pow1/3 acos-asin rem-cbrt-cube count-2
div-sub frac-2neg unpow1/2 expm1-log1p clear-num

localize1.3s (0.5%)

bsearch606.0ms (0.2%)

end0.0ms (0.0%)