ab-angle->ABCF C

Average Accuracy: 67.3% → 67.3%

Time: 19.4s

Precision: binary64

Cost: 65216

Math

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

↓

\[\begin{array}{l} t_0 := \sqrt[3]{\pi \cdot angle}\\ {\left(a \cdot \cos \left(\frac{{t_0}^{2}}{\frac{180}{t_0}}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \end{array} \]

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
 (let* ((t_0 (cbrt (* PI angle))))
   (+
    (pow (* a (cos (/ (pow t_0 2.0) (/ 180.0 t_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) {
	double t_0 = cbrt((((double) M_PI) * angle));
	return pow((a * cos((pow(t_0, 2.0) / (180.0 / t_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) {
	double t_0 = Math.cbrt((Math.PI * angle));
	return Math.pow((a * Math.cos((Math.pow(t_0, 2.0) / (180.0 / t_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)
	t_0 = cbrt(Float64(pi * angle))
	return Float64((Float64(a * cos(Float64((t_0 ^ 2.0) / Float64(180.0 / t_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_] := Block[{t$95$0 = N[Power[N[(Pi * angle), $MachinePrecision], 1/3], $MachinePrecision]}, N[(N[Power[N[(a * N[Cos[N[(N[Power[t$95$0, 2.0], $MachinePrecision] / N[(180.0 / t$95$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]]

Derivation

1. Initial program 67.3%

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

2. Applied egg-rr 67.3%

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

   [Start] 67.3	\[ {\left(a \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   associate-*r/ [=>] 67.3	\[ {\left(a \cdot \cos \color{blue}{\left(\frac{\pi \cdot angle}{180}\right)}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   add-cube-cbrt [=>] 67.3	\[ {\left(a \cdot \cos \left(\frac{\color{blue}{\left(\sqrt[3]{\pi \cdot angle} \cdot \sqrt[3]{\pi \cdot angle}\right) \cdot \sqrt[3]{\pi \cdot angle}}}{180}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   associate-/l* [=>] 67.3	\[ {\left(a \cdot \cos \color{blue}{\left(\frac{\sqrt[3]{\pi \cdot angle} \cdot \sqrt[3]{\pi \cdot angle}}{\frac{180}{\sqrt[3]{\pi \cdot angle}}}\right)}\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

3. Applied egg-rr 67.3%

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

   [Start] 67.3	\[ {\left(a \cdot \cos \left(\frac{\sqrt[3]{\pi \cdot angle} \cdot \sqrt[3]{\pi \cdot angle}}{\frac{180}{\sqrt[3]{\pi \cdot angle}}}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
   pow2 [=>] 67.3	\[ {\left(a \cdot \cos \left(\frac{\color{blue}{{\left(\sqrt[3]{\pi \cdot angle}\right)}^{2}}}{\frac{180}{\sqrt[3]{\pi \cdot angle}}}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]

4. Final simplification 67.3%

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

Alternatives

Alternative 1
Accuracy	67.3%
Cost	39360

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

Alternative 2
Accuracy	67.3%
Cost	39360

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

Alternative 3
Accuracy	67.3%
Cost	39360

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

Alternative 4
Accuracy	67.3%
Cost	39360

\[\begin{array}{l} t_0 := \pi \cdot \frac{angle}{180}\\ {\left(b \cdot \sin t_0\right)}^{2} + {\left(a \cdot \cos t_0\right)}^{2} \end{array} \]

Alternative 5
Accuracy	67.3%
Cost	26240

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

Alternative 6
Accuracy	67.4%
Cost	26240

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

Alternative 7
Accuracy	67.3%
Cost	26240

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

Alternative 8
Accuracy	67.3%
Cost	26240

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

Alternative 9
Accuracy	66.9%
Cost	20425

\[\begin{array}{l} \mathbf{if}\;angle \leq -2.2 \cdot 10^{+22} \lor \neg \left(angle \leq 0.0028\right):\\ \;\;\;\;{a}^{2} + \left(1 - \cos \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right) \cdot \frac{b}{\frac{2}{b}}\\ \mathbf{else}:\\ \;\;\;\;{a}^{2} + {\left(b \cdot \left(angle \cdot \frac{\pi}{180}\right)\right)}^{2}\\ \end{array} \]

Alternative 10
Accuracy	66.9%
Cost	20425

\[\begin{array}{l} \mathbf{if}\;angle \leq -2.2 \cdot 10^{+22} \lor \neg \left(angle \leq 0.008\right):\\ \;\;\;\;{a}^{2} + \frac{b \cdot b}{2} \cdot \left(1 - \cos \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{a}^{2} + {\left(b \cdot \left(angle \cdot \frac{\pi}{180}\right)\right)}^{2}\\ \end{array} \]

Alternative 11
Accuracy	66.9%
Cost	20424

\[\begin{array}{l} t_0 := 1 - \cos \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\\ \mathbf{if}\;angle \leq -2.2 \cdot 10^{+22}:\\ \;\;\;\;{a}^{2} + \frac{b \cdot b}{2} \cdot t_0\\ \mathbf{elif}\;angle \leq 0.0092:\\ \;\;\;\;{a}^{2} + {\left(b \cdot \left(angle \cdot \frac{\pi}{180}\right)\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;{a}^{2} + t_0 \cdot \frac{b}{\frac{2}{b}}\\ \end{array} \]

Alternative 12
Accuracy	58.2%
Cost	19840

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

Alternative 13
Accuracy	58.3%
Cost	19840

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

Alternative 14
Accuracy	58.4%
Cost	19840

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

Alternative 15
Accuracy	58.4%
Cost	19840

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

Reproduce

herbie shell --seed 2023131 
(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)))