ab-angle->ABCF C

Average Error: 20.5 → 20.6

Time: 21.1s

Precision: binary64

Cost: 84480

Math

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

↓

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

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
    (cos
     (/
      (pow (pow (cbrt (* (cbrt PI) (cbrt angle))) 3.0) 2.0)
      (/ 180.0 (cbrt (* PI angle))))))
   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 * cos((pow(pow(cbrt((cbrt(((double) M_PI)) * cbrt(angle))), 3.0), 2.0) / (180.0 / cbrt((((double) M_PI) * angle)))))), 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.cos((Math.pow(Math.pow(Math.cbrt((Math.cbrt(Math.PI) * Math.cbrt(angle))), 3.0), 2.0) / (180.0 / Math.cbrt((Math.PI * angle)))))), 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 * cos(Float64(((cbrt(Float64(cbrt(pi) * cbrt(angle))) ^ 3.0) ^ 2.0) / Float64(180.0 / cbrt(Float64(pi * angle)))))) ^ 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[Cos[N[(N[Power[N[Power[N[Power[N[(N[Power[Pi, 1/3], $MachinePrecision] * N[Power[angle, 1/3], $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision], 2.0], $MachinePrecision] / N[(180.0 / N[Power[N[(Pi * angle), $MachinePrecision], 1/3], $MachinePrecision]), $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 20.5

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

2. Applied egg-rr 20.5

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

3. Applied egg-rr 20.5

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

4. Applied egg-rr 20.6

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

5. Applied egg-rr 20.6

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

6. Final simplification 20.6

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

Alternatives

Alternative 1
Error	20.6
Cost	78080

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

Alternative 2
Error	20.5
Cost	65216

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

Alternative 3
Error	20.5
Cost	58752

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

Alternative 4
Error	20.5
Cost	52160

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

Alternative 5
Error	20.5
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 6
Error	20.5
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 7
Error	20.6
Cost	26240

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

Alternative 8
Error	20.6
Cost	26240

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

Alternative 9
Error	20.6
Cost	26240

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

Alternative 10
Error	20.6
Cost	26240

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

Alternative 11
Error	20.6
Cost	20425

\[\begin{array}{l} \mathbf{if}\;angle \leq -0.09 \lor \neg \left(angle \leq 0.0046\right):\\ \;\;\;\;{a}^{2} + \frac{b}{\frac{2}{b}} \cdot \left(1 - \cos \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{a}^{2} + \left(\pi \cdot \left(\left(angle \cdot b\right) \cdot \left(\pi \cdot \left(angle \cdot b\right)\right)\right)\right) \cdot 3.08641975308642 \cdot 10^{-5}\\ \end{array} \]

Alternative 12
Error	26.3
Cost	20096

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

Alternative 13
Error	26.3
Cost	19840

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

Alternative 14
Error	26.3
Cost	19840

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

Reproduce

herbie shell --seed 2023039 
(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)))