ab-angle->ABCF C

Average Accuracy: 42.9% → 42.9%

Time: 39.8s

Precision: binary64

Cost: 78208

Math

\[{\left(a \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

↓

\[{\left(a \cdot {\left(\sqrt[3]{\cos \left({\left(\sqrt[3]{\frac{180}{\pi \cdot angle}}\right)}^{-2} \cdot \sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}\right)}\right)}^{3}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

FPCore

(FPCore (a b angle)
 :precision binary64
 (+
  (pow (* a (cos (* PI (/ angle 180.0)))) 2.0)
  (pow (* b (sin (* PI (/ angle 180.0)))) 2.0)))

↓

(FPCore (a b angle)
 :precision binary64
 (+
  (pow
   (*
    a
    (pow
     (cbrt
      (cos
       (*
        (pow (cbrt (/ 180.0 (* PI angle))) -2.0)
        (cbrt (* PI (* angle 0.005555555555555556))))))
     3.0))
   2.0)
  (pow (* b (sin (* PI (/ angle 180.0)))) 2.0)))

C

double code(double a, double b, double angle) {
	return pow((a * cos((((double) M_PI) * (angle / 180.0)))), 2.0) + pow((b * sin((((double) M_PI) * (angle / 180.0)))), 2.0);
}

↓

double code(double a, double b, double angle) {
	return pow((a * pow(cbrt(cos((pow(cbrt((180.0 / (((double) M_PI) * angle))), -2.0) * cbrt((((double) M_PI) * (angle * 0.005555555555555556)))))), 3.0)), 2.0) + pow((b * sin((((double) M_PI) * (angle / 180.0)))), 2.0);
}

Java

public static double code(double a, double b, double angle) {
	return Math.pow((a * Math.cos((Math.PI * (angle / 180.0)))), 2.0) + Math.pow((b * Math.sin((Math.PI * (angle / 180.0)))), 2.0);
}

↓

public static double code(double a, double b, double angle) {
	return Math.pow((a * Math.pow(Math.cbrt(Math.cos((Math.pow(Math.cbrt((180.0 / (Math.PI * angle))), -2.0) * Math.cbrt((Math.PI * (angle * 0.005555555555555556)))))), 3.0)), 2.0) + Math.pow((b * Math.sin((Math.PI * (angle / 180.0)))), 2.0);
}

Julia

function code(a, b, angle)
	return Float64((Float64(a * cos(Float64(pi * Float64(angle / 180.0)))) ^ 2.0) + (Float64(b * sin(Float64(pi * Float64(angle / 180.0)))) ^ 2.0))
end

↓

function code(a, b, angle)
	return Float64((Float64(a * (cbrt(cos(Float64((cbrt(Float64(180.0 / Float64(pi * angle))) ^ -2.0) * cbrt(Float64(pi * Float64(angle * 0.005555555555555556)))))) ^ 3.0)) ^ 2.0) + (Float64(b * sin(Float64(pi * Float64(angle / 180.0)))) ^ 2.0))
end

Wolfram

code[a_, b_, angle_] := N[(N[Power[N[(a * N[Cos[N[(Pi * N[(angle / 180.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(b * N[Sin[N[(Pi * N[(angle / 180.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

↓

code[a_, b_, angle_] := N[(N[Power[N[(a * N[Power[N[Power[N[Cos[N[(N[Power[N[Power[N[(180.0 / N[(Pi * angle), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision], -2.0], $MachinePrecision] * N[Power[N[(Pi * N[(angle * 0.005555555555555556), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(b * N[Sin[N[(Pi * N[(angle / 180.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 42.7%

   \[{\left(a \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

2. Applied egg-rr 42.8%

   \[\leadsto {\left(a \cdot \cos \color{blue}{\left(\frac{1}{\frac{180}{\pi \cdot angle}}\right)}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   Step-by-step derivation

   [Start] 42.7	\[ {\left(a \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   associate-*r/ [=>] 42.8	\[ {\left(a \cdot \cos \color{blue}{\left(\frac{\pi \cdot angle}{180}\right)}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   clear-num [=>] 42.8	\[ {\left(a \cdot \cos \color{blue}{\left(\frac{1}{\frac{180}{\pi \cdot angle}}\right)}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

3. Applied egg-rr 42.8%

   \[\leadsto {\left(a \cdot \cos \color{blue}{\left({\left(\sqrt[3]{\frac{180}{\pi \cdot angle}}\right)}^{-2} \cdot \sqrt[3]{\left(\pi \cdot angle\right) \cdot 0.005555555555555556}\right)}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   Step-by-step derivation

   [Start] 42.8	\[ {\left(a \cdot \cos \left(\frac{1}{\frac{180}{\pi \cdot angle}}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   inv-pow [=>] 42.8	\[ {\left(a \cdot \cos \color{blue}{\left({\left(\frac{180}{\pi \cdot angle}\right)}^{-1}\right)}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   add-cube-cbrt [=>] 42.7	\[ {\left(a \cdot \cos \left({\color{blue}{\left(\left(\sqrt[3]{\frac{180}{\pi \cdot angle}} \cdot \sqrt[3]{\frac{180}{\pi \cdot angle}}\right) \cdot \sqrt[3]{\frac{180}{\pi \cdot angle}}\right)}}^{-1}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   unpow-prod-down [=>] 42.8	\[ {\left(a \cdot \cos \color{blue}{\left({\left(\sqrt[3]{\frac{180}{\pi \cdot angle}} \cdot \sqrt[3]{\frac{180}{\pi \cdot angle}}\right)}^{-1} \cdot {\left(\sqrt[3]{\frac{180}{\pi \cdot angle}}\right)}^{-1}\right)}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   pow2 [=>] 42.8	\[ {\left(a \cdot \cos \left({\color{blue}{\left({\left(\sqrt[3]{\frac{180}{\pi \cdot angle}}\right)}^{2}\right)}}^{-1} \cdot {\left(\sqrt[3]{\frac{180}{\pi \cdot angle}}\right)}^{-1}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   metadata-eval [<=] 42.8	\[ {\left(a \cdot \cos \left({\left({\left(\sqrt[3]{\frac{180}{\pi \cdot angle}}\right)}^{\color{blue}{\left(1 + 1\right)}}\right)}^{-1} \cdot {\left(\sqrt[3]{\frac{180}{\pi \cdot angle}}\right)}^{-1}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   pow-pow [=>] 42.7	\[ {\left(a \cdot \cos \left(\color{blue}{{\left(\sqrt[3]{\frac{180}{\pi \cdot angle}}\right)}^{\left(\left(1 + 1\right) \cdot -1\right)}} \cdot {\left(\sqrt[3]{\frac{180}{\pi \cdot angle}}\right)}^{-1}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   metadata-eval [=>] 42.7	\[ {\left(a \cdot \cos \left({\left(\sqrt[3]{\frac{180}{\pi \cdot angle}}\right)}^{\left(\color{blue}{2} \cdot -1\right)} \cdot {\left(\sqrt[3]{\frac{180}{\pi \cdot angle}}\right)}^{-1}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   metadata-eval [=>] 42.7	\[ {\left(a \cdot \cos \left({\left(\sqrt[3]{\frac{180}{\pi \cdot angle}}\right)}^{\color{blue}{-2}} \cdot {\left(\sqrt[3]{\frac{180}{\pi \cdot angle}}\right)}^{-1}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   inv-pow [<=] 42.7	\[ {\left(a \cdot \cos \left({\left(\sqrt[3]{\frac{180}{\pi \cdot angle}}\right)}^{-2} \cdot \color{blue}{\frac{1}{\sqrt[3]{\frac{180}{\pi \cdot angle}}}}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   metadata-eval [<=] 42.7	\[ {\left(a \cdot \cos \left({\left(\sqrt[3]{\frac{180}{\pi \cdot angle}}\right)}^{-2} \cdot \frac{\color{blue}{\sqrt[3]{1}}}{\sqrt[3]{\frac{180}{\pi \cdot angle}}}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   cbrt-div [<=] 42.8	\[ {\left(a \cdot \cos \left({\left(\sqrt[3]{\frac{180}{\pi \cdot angle}}\right)}^{-2} \cdot \color{blue}{\sqrt[3]{\frac{1}{\frac{180}{\pi \cdot angle}}}}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   clear-num [<=] 42.8	\[ {\left(a \cdot \cos \left({\left(\sqrt[3]{\frac{180}{\pi \cdot angle}}\right)}^{-2} \cdot \sqrt[3]{\color{blue}{\frac{\pi \cdot angle}{180}}}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   div-inv [=>] 42.8	\[ {\left(a \cdot \cos \left({\left(\sqrt[3]{\frac{180}{\pi \cdot angle}}\right)}^{-2} \cdot \sqrt[3]{\color{blue}{\left(\pi \cdot angle\right) \cdot \frac{1}{180}}}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   metadata-eval [=>] 42.8	\[ {\left(a \cdot \cos \left({\left(\sqrt[3]{\frac{180}{\pi \cdot angle}}\right)}^{-2} \cdot \sqrt[3]{\left(\pi \cdot angle\right) \cdot \color{blue}{0.005555555555555556}}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

4. Applied egg-rr 42.9%

   \[\leadsto {\left(a \cdot \color{blue}{{\left(\sqrt[3]{\cos \left({\left(\sqrt[3]{\frac{180}{\pi \cdot angle}}\right)}^{-2} \cdot \sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}\right)}\right)}^{3}}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   Step-by-step derivation

   [Start] 42.8	\[ {\left(a \cdot \cos \left({\left(\sqrt[3]{\frac{180}{\pi \cdot angle}}\right)}^{-2} \cdot \sqrt[3]{\left(\pi \cdot angle\right) \cdot 0.005555555555555556}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   add-cube-cbrt [=>] 42.8	\[ {\left(a \cdot \color{blue}{\left(\left(\sqrt[3]{\cos \left({\left(\sqrt[3]{\frac{180}{\pi \cdot angle}}\right)}^{-2} \cdot \sqrt[3]{\left(\pi \cdot angle\right) \cdot 0.005555555555555556}\right)} \cdot \sqrt[3]{\cos \left({\left(\sqrt[3]{\frac{180}{\pi \cdot angle}}\right)}^{-2} \cdot \sqrt[3]{\left(\pi \cdot angle\right) \cdot 0.005555555555555556}\right)}\right) \cdot \sqrt[3]{\cos \left({\left(\sqrt[3]{\frac{180}{\pi \cdot angle}}\right)}^{-2} \cdot \sqrt[3]{\left(\pi \cdot angle\right) \cdot 0.005555555555555556}\right)}\right)}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   pow3 [=>] 42.8	\[ {\left(a \cdot \color{blue}{{\left(\sqrt[3]{\cos \left({\left(\sqrt[3]{\frac{180}{\pi \cdot angle}}\right)}^{-2} \cdot \sqrt[3]{\left(\pi \cdot angle\right) \cdot 0.005555555555555556}\right)}\right)}^{3}}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   associate-*l* [=>] 42.9	\[ {\left(a \cdot {\left(\sqrt[3]{\cos \left({\left(\sqrt[3]{\frac{180}{\pi \cdot angle}}\right)}^{-2} \cdot \sqrt[3]{\color{blue}{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}}\right)}\right)}^{3}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

5. Final simplification 42.9%

   \[\leadsto {\left(a \cdot {\left(\sqrt[3]{\cos \left({\left(\sqrt[3]{\frac{180}{\pi \cdot angle}}\right)}^{-2} \cdot \sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}\right)}\right)}^{3}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

Alternatives

Alternative 1
Accuracy	42.9%
Cost	78144

\[{\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(a \cdot \log \left(e^{\cos \left({\left(\sqrt[3]{\frac{180}{\pi \cdot angle}}\right)}^{-2} \cdot \sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}\right)}\right)\right)}^{2} \]

Alternative 2
Accuracy	42.8%
Cost	39488

\[{\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(a \cdot \cos \left(\frac{1}{\frac{180}{\pi \cdot angle}}\right)\right)}^{2} \]

Alternative 3
Accuracy	42.9%
Cost	39360

\[{\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(a \cdot \cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right)}^{2} \]

Alternative 4
Accuracy	42.9%
Cost	39360

\[{\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(a \cdot \cos \left(\frac{\pi}{\frac{180}{angle}}\right)\right)}^{2} \]

Alternative 5
Accuracy	42.7%
Cost	26240

\[{a}^{2} + {\left(b \cdot \sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right)}^{2} \]

Alternative 6
Accuracy	42.7%
Cost	26240

\[{\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {a}^{2} \]

Alternative 7
Accuracy	37.2%
Cost	19840

\[{a}^{2} + {\left(angle \cdot \left(\pi \cdot b\right)\right)}^{2} \cdot 3.08641975308642 \cdot 10^{-5} \]

Reproduce

herbie shell --seed 2023157 
(FPCore (a b angle)
  :name "ab-angle->ABCF C"
  :precision binary64
  (+ (pow (* a (cos (* PI (/ angle 180.0)))) 2.0) (pow (* b (sin (* PI (/ angle 180.0)))) 2.0)))