ab-angle->ABCF C

Average Accuracy: 67.7% → 67.6%

Time: 21.2s

Precision: binary64

Cost: 58688

Math

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

↓

\[{\left(a \cdot {\left(\sqrt[3]{\cos \left({\left(\frac{180}{\pi \cdot angle}\right)}^{-1}\right)}\right)}^{3}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

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 (/ 180.0 (* PI angle)) -1.0))) 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((180.0 / (((double) M_PI) * angle)), -1.0))), 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((180.0 / (Math.PI * angle)), -1.0))), 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(180.0 / Float64(pi * angle)) ^ -1.0))) ^ 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[Power[N[(180.0 / N[(Pi * angle), $MachinePrecision]), $MachinePrecision], -1.0], $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 67.7%

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

2. Applied egg-rr 67.6%

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

   [Start] 67.7	\[ {\left(a \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   *-commutative [=>] 67.7	\[ {\left(a \cdot \cos \color{blue}{\left(\frac{angle}{180} \cdot \pi\right)}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   add-cube-cbrt [=>] 67.6	\[ {\left(a \cdot \cos \left(\frac{\color{blue}{\left(\sqrt[3]{angle} \cdot \sqrt[3]{angle}\right) \cdot \sqrt[3]{angle}}}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   associate-/l* [=>] 67.6	\[ {\left(a \cdot \cos \left(\color{blue}{\frac{\sqrt[3]{angle} \cdot \sqrt[3]{angle}}{\frac{180}{\sqrt[3]{angle}}}} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   associate-*l/ [=>] 67.6	\[ {\left(a \cdot \cos \color{blue}{\left(\frac{\left(\sqrt[3]{angle} \cdot \sqrt[3]{angle}\right) \cdot \pi}{\frac{180}{\sqrt[3]{angle}}}\right)}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   pow2 [=>] 67.6	\[ {\left(a \cdot \cos \left(\frac{\color{blue}{{\left(\sqrt[3]{angle}\right)}^{2}} \cdot \pi}{\frac{180}{\sqrt[3]{angle}}}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

3. Applied egg-rr 67.7%

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

   [Start] 67.6	\[ {\left(a \cdot \cos \left(\frac{{\left(\sqrt[3]{angle}\right)}^{2} \cdot \pi}{\frac{180}{\sqrt[3]{angle}}}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   add-cube-cbrt [=>] 67.6	\[ {\left(a \cdot \color{blue}{\left(\left(\sqrt[3]{\cos \left(\frac{{\left(\sqrt[3]{angle}\right)}^{2} \cdot \pi}{\frac{180}{\sqrt[3]{angle}}}\right)} \cdot \sqrt[3]{\cos \left(\frac{{\left(\sqrt[3]{angle}\right)}^{2} \cdot \pi}{\frac{180}{\sqrt[3]{angle}}}\right)}\right) \cdot \sqrt[3]{\cos \left(\frac{{\left(\sqrt[3]{angle}\right)}^{2} \cdot \pi}{\frac{180}{\sqrt[3]{angle}}}\right)}\right)}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   pow3 [=>] 67.6	\[ {\left(a \cdot \color{blue}{{\left(\sqrt[3]{\cos \left(\frac{{\left(\sqrt[3]{angle}\right)}^{2} \cdot \pi}{\frac{180}{\sqrt[3]{angle}}}\right)}\right)}^{3}}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   *-commutative [=>] 67.6	\[ {\left(a \cdot {\left(\sqrt[3]{\cos \left(\frac{\color{blue}{\pi \cdot {\left(\sqrt[3]{angle}\right)}^{2}}}{\frac{180}{\sqrt[3]{angle}}}\right)}\right)}^{3}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   associate-/l* [=>] 67.6	\[ {\left(a \cdot {\left(\sqrt[3]{\cos \color{blue}{\left(\frac{\pi}{\frac{\frac{180}{\sqrt[3]{angle}}}{{\left(\sqrt[3]{angle}\right)}^{2}}}\right)}}\right)}^{3}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   associate-/l/ [=>] 67.6	\[ {\left(a \cdot {\left(\sqrt[3]{\cos \left(\frac{\pi}{\color{blue}{\frac{180}{{\left(\sqrt[3]{angle}\right)}^{2} \cdot \sqrt[3]{angle}}}}\right)}\right)}^{3}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   pow-plus [=>] 67.7	\[ {\left(a \cdot {\left(\sqrt[3]{\cos \left(\frac{\pi}{\frac{180}{\color{blue}{{\left(\sqrt[3]{angle}\right)}^{\left(2 + 1\right)}}}}\right)}\right)}^{3}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   metadata-eval [=>] 67.7	\[ {\left(a \cdot {\left(\sqrt[3]{\cos \left(\frac{\pi}{\frac{180}{{\left(\sqrt[3]{angle}\right)}^{\color{blue}{3}}}}\right)}\right)}^{3}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   pow3 [<=] 67.6	\[ {\left(a \cdot {\left(\sqrt[3]{\cos \left(\frac{\pi}{\frac{180}{\color{blue}{\left(\sqrt[3]{angle} \cdot \sqrt[3]{angle}\right) \cdot \sqrt[3]{angle}}}}\right)}\right)}^{3}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   add-cube-cbrt [<=] 67.7	\[ {\left(a \cdot {\left(\sqrt[3]{\cos \left(\frac{\pi}{\frac{180}{\color{blue}{angle}}}\right)}\right)}^{3}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

4. Applied egg-rr 67.6%

   \[\leadsto {\left(a \cdot {\left(\sqrt[3]{\cos \color{blue}{\left({\left(\frac{180}{\pi \cdot angle}\right)}^{-1}\right)}}\right)}^{3}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   Proof

   [Start] 67.7	\[ {\left(a \cdot {\left(\sqrt[3]{\cos \left(\frac{\pi}{\frac{180}{angle}}\right)}\right)}^{3}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   clear-num [=>] 67.7	\[ {\left(a \cdot {\left(\sqrt[3]{\cos \color{blue}{\left(\frac{1}{\frac{\frac{180}{angle}}{\pi}}\right)}}\right)}^{3}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   inv-pow [=>] 67.7	\[ {\left(a \cdot {\left(\sqrt[3]{\cos \color{blue}{\left({\left(\frac{\frac{180}{angle}}{\pi}\right)}^{-1}\right)}}\right)}^{3}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   associate-/l/ [=>] 67.6	\[ {\left(a \cdot {\left(\sqrt[3]{\cos \left({\color{blue}{\left(\frac{180}{\pi \cdot angle}\right)}}^{-1}\right)}\right)}^{3}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

5. Final simplification 67.6%

   \[\leadsto {\left(a \cdot {\left(\sqrt[3]{\cos \left({\left(\frac{180}{\pi \cdot angle}\right)}^{-1}\right)}\right)}^{3}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

Alternatives

Alternative 1
Accuracy	67.7%
Cost	58624

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

Alternative 2
Accuracy	67.7%
Cost	52224

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

Alternative 3
Accuracy	67.7%
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	67.7%
Cost	39360

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

Alternative 5
Accuracy	67.7%
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 6
Accuracy	67.6%
Cost	26368

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

Alternative 7
Accuracy	67.6%
Cost	26240

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

Alternative 8
Accuracy	67.6%
Cost	26240

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

Alternative 9
Accuracy	67.6%
Cost	26240

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

Alternative 10
Accuracy	67.3%
Cost	20425

\[\begin{array}{l} \mathbf{if}\;angle \leq -122000000000 \lor \neg \left(angle \leq 0.0046\right):\\ \;\;\;\;{a}^{2} + \frac{b}{\frac{2}{b}} \cdot \left(1 - \cos \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{a}^{2} + {\left(angle \cdot \left(b \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)}^{2}\\ \end{array} \]

Alternative 11
Accuracy	67.3%
Cost	20424

\[\begin{array}{l} t_0 := \frac{b}{\frac{2}{b}}\\ \mathbf{if}\;angle \leq -122000000000:\\ \;\;\;\;{a}^{2} + \left(1 - \cos \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\right) \cdot t_0\\ \mathbf{elif}\;angle \leq 0.005:\\ \;\;\;\;{a}^{2} + {\left(angle \cdot \left(b \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;{a}^{2} + t_0 \cdot \left(1 - \cos \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\\ \end{array} \]

Alternative 12
Accuracy	67.3%
Cost	20424

\[\begin{array}{l} \mathbf{if}\;angle \leq -122000000000:\\ \;\;\;\;{a}^{2} + \frac{b \cdot b}{\frac{2}{1 - \cos \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)}}\\ \mathbf{elif}\;angle \leq 0.0046:\\ \;\;\;\;{a}^{2} + {\left(angle \cdot \left(b \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;{a}^{2} + \frac{b}{\frac{2}{b}} \cdot \left(1 - \cos \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\\ \end{array} \]

Alternative 13
Accuracy	58.6%
Cost	19840

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

Alternative 14
Accuracy	58.8%
Cost	19840

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

Reproduce

herbie shell --seed 2023138 
(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)))