ab-angle->ABCF A

Average Error: 19.9 → 20.0

Time: 17.7s

Precision: binary64

Cost: 84672

Math

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

↓

\[\begin{array}{l} t_0 := \sqrt[3]{\left(angle \cdot \pi\right) \cdot 0.005555555555555556}\\ {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left({\left({\left({t_0}^{2}\right)}^{0.3333333333333333} \cdot \sqrt[3]{t_0}\right)}^{3}\right)\right)}^{2} \end{array} \]

FPCore

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

↓

(FPCore (a b angle)
 :precision binary64
 (let* ((t_0 (cbrt (* (* angle PI) 0.005555555555555556))))
   (+
    (pow (* a (sin (* (/ angle 180.0) PI))) 2.0)
    (pow
     (*
      b
      (cos (pow (* (pow (pow t_0 2.0) 0.3333333333333333) (cbrt t_0)) 3.0)))
     2.0))))

C

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

↓

double code(double a, double b, double angle) {
	double t_0 = cbrt(((angle * ((double) M_PI)) * 0.005555555555555556));
	return pow((a * sin(((angle / 180.0) * ((double) M_PI)))), 2.0) + pow((b * cos(pow((pow(pow(t_0, 2.0), 0.3333333333333333) * cbrt(t_0)), 3.0))), 2.0);
}

Java

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

↓

public static double code(double a, double b, double angle) {
	double t_0 = Math.cbrt(((angle * Math.PI) * 0.005555555555555556));
	return Math.pow((a * Math.sin(((angle / 180.0) * Math.PI))), 2.0) + Math.pow((b * Math.cos(Math.pow((Math.pow(Math.pow(t_0, 2.0), 0.3333333333333333) * Math.cbrt(t_0)), 3.0))), 2.0);
}

Julia

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

↓

function code(a, b, angle)
	t_0 = cbrt(Float64(Float64(angle * pi) * 0.005555555555555556))
	return Float64((Float64(a * sin(Float64(Float64(angle / 180.0) * pi))) ^ 2.0) + (Float64(b * cos((Float64(((t_0 ^ 2.0) ^ 0.3333333333333333) * cbrt(t_0)) ^ 3.0))) ^ 2.0))
end

Wolfram

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

↓

code[a_, b_, angle_] := Block[{t$95$0 = N[Power[N[(N[(angle * Pi), $MachinePrecision] * 0.005555555555555556), $MachinePrecision], 1/3], $MachinePrecision]}, N[(N[Power[N[(a * N[Sin[N[(N[(angle / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(b * N[Cos[N[Power[N[(N[Power[N[Power[t$95$0, 2.0], $MachinePrecision], 0.3333333333333333], $MachinePrecision] * N[Power[t$95$0, 1/3], $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 19.9

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

2. Applied egg-rr 42.2

   \[\leadsto {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \color{blue}{\left(e^{\left(3 \cdot \log \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right) \cdot 0.3333333333333333}\right)}\right)}^{2} \]

3. Applied egg-rr 20.0

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

4. Applied egg-rr 20.0

   \[\leadsto {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left({\color{blue}{\left({\left({\left(\sqrt[3]{\left(angle \cdot \pi\right) \cdot 0.005555555555555556}\right)}^{2}\right)}^{0.3333333333333333} \cdot \sqrt[3]{\sqrt[3]{\left(angle \cdot \pi\right) \cdot 0.005555555555555556}}\right)}}^{3}\right)\right)}^{2} \]

5. Final simplification 20.0

   \[\leadsto {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left({\left({\left({\left(\sqrt[3]{\left(angle \cdot \pi\right) \cdot 0.005555555555555556}\right)}^{2}\right)}^{0.3333333333333333} \cdot \sqrt[3]{\sqrt[3]{\left(angle \cdot \pi\right) \cdot 0.005555555555555556}}\right)}^{3}\right)\right)}^{2} \]

Alternatives

Alternative 1
Error	20.0
Cost	84672

\[\begin{array}{l} t_0 := \sqrt[3]{angle \cdot \left(\pi \cdot 0.005555555555555556\right)}\\ {\left(a \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)}^{2} + {\left(b \cdot \cos \left({\left({\left({t_0}^{2}\right)}^{0.3333333333333333} \cdot \sqrt[3]{t_0}\right)}^{3}\right)\right)}^{2} \end{array} \]

Alternative 2
Error	20.0
Cost	52224

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

Alternative 3
Error	20.0
Cost	52224

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

Alternative 4
Error	20.1
Cost	26240

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

Alternative 5
Error	25.5
Cost	20224

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

Alternative 6
Error	25.6
Cost	20096

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

Alternative 7
Error	25.6
Cost	20096

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

Alternative 8
Error	25.6
Cost	19840

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

Reproduce

herbie shell --seed 2022329 
(FPCore (a b angle)
  :name "ab-angle->ABCF A"
  :precision binary64
  (+ (pow (* a (sin (* (/ angle 180.0) PI))) 2.0) (pow (* b (cos (* (/ angle 180.0) PI))) 2.0)))