ab-angle->ABCF C

Average Error: 20.2 → 20.2

Time: 21.0s

Precision: binary64

Cost: 71616

Math

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

↓

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

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 angle)) 3.0) 2.0) PI)
      (/ 180.0 (cbrt 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(angle)), 3.0), 2.0) * ((double) M_PI)) / (180.0 / cbrt(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(angle)), 3.0), 2.0) * Math.PI) / (180.0 / Math.cbrt(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(Float64(((cbrt(cbrt(angle)) ^ 3.0) ^ 2.0) * pi) / Float64(180.0 / cbrt(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[(N[Power[N[Power[N[Power[N[Power[angle, 1/3], $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision], 2.0], $MachinePrecision] * Pi), $MachinePrecision] / N[(180.0 / N[Power[angle, 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 20.2

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

2. Applied egg-rr 20.2

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

3. Applied egg-rr 20.2

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

4. Final simplification 20.2

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

Alternatives

Alternative 1
Error	20.2
Cost	58752

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

Alternative 2
Error	20.2
Cost	58624

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

Alternative 3
Error	20.2
Cost	39360

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

Alternative 4
Error	20.2
Cost	26240

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

Alternative 5
Error	20.2
Cost	26240

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

Alternative 6
Error	20.3
Cost	20488

\[\begin{array}{l} t_0 := \frac{b \cdot b}{2}\\ t_1 := 0.005555555555555556 \cdot \left(angle \cdot b\right)\\ \mathbf{if}\;angle \leq -0.0046:\\ \;\;\;\;{a}^{2} + t_0 \cdot \left(1 - \cos \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{elif}\;angle \leq 4500:\\ \;\;\;\;{a}^{2} + \left(t_1 \cdot t_1\right) \cdot {\pi}^{2}\\ \mathbf{else}:\\ \;\;\;\;{a}^{2} + t_0 \cdot \left(1 - \cos \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\\ \end{array} \]

Alternative 7
Error	20.5
Cost	20425

\[\begin{array}{l} \mathbf{if}\;angle \leq -0.0042 \lor \neg \left(angle \leq 4500\right):\\ \;\;\;\;{a}^{2} + \left(1 - \cos \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right) \cdot \frac{b}{\frac{2}{b}}\\ \mathbf{else}:\\ \;\;\;\;{a}^{2} + {\left(angle \cdot \left(\pi \cdot b\right)\right)}^{2} \cdot 3.08641975308642 \cdot 10^{-5}\\ \end{array} \]

Alternative 8
Error	20.4
Cost	20424

\[\begin{array}{l} t_0 := \frac{b}{\frac{2}{b}}\\ \mathbf{if}\;angle \leq -0.0042:\\ \;\;\;\;{a}^{2} + \left(1 - \cos \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\right) \cdot t_0\\ \mathbf{elif}\;angle \leq 0.0029:\\ \;\;\;\;{a}^{2} + {\left(angle \cdot \left(\pi \cdot b\right)\right)}^{2} \cdot 3.08641975308642 \cdot 10^{-5}\\ \mathbf{else}:\\ \;\;\;\;{a}^{2} + \left(1 - \cos \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right) \cdot t_0\\ \end{array} \]

Alternative 9
Error	20.4
Cost	20424

\[\begin{array}{l} \mathbf{if}\;angle \leq -0.0042:\\ \;\;\;\;{a}^{2} + \left(1 - \cos \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\right) \cdot \frac{b}{\frac{2}{b}}\\ \mathbf{elif}\;angle \leq 0.0029:\\ \;\;\;\;{a}^{2} + {\left(angle \cdot \left(\pi \cdot b\right)\right)}^{2} \cdot 3.08641975308642 \cdot 10^{-5}\\ \mathbf{else}:\\ \;\;\;\;{a}^{2} + \frac{b \cdot b}{2} \cdot \left(1 - \cos \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\\ \end{array} \]

Alternative 10
Error	20.5
Cost	20424

\[\begin{array}{l} t_0 := \frac{b \cdot b}{2}\\ \mathbf{if}\;angle \leq -0.0042:\\ \;\;\;\;{a}^{2} + t_0 \cdot \left(1 - \cos \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{elif}\;angle \leq 4500:\\ \;\;\;\;{a}^{2} + {\left(angle \cdot \left(\pi \cdot b\right)\right)}^{2} \cdot 3.08641975308642 \cdot 10^{-5}\\ \mathbf{else}:\\ \;\;\;\;{a}^{2} + t_0 \cdot \left(1 - \cos \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\\ \end{array} \]

Alternative 11
Error	24.0
Cost	20361

\[\begin{array}{l} \mathbf{if}\;angle \leq -7.5 \cdot 10^{-85} \lor \neg \left(angle \leq 5000\right):\\ \;\;\;\;{a}^{2} + 3.08641975308642 \cdot 10^{-5} \cdot \left({\pi}^{2} \cdot \left(angle \cdot \left(angle \cdot \left(b \cdot b\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{a}^{2} + {\left(angle \cdot \left(\pi \cdot b\right)\right)}^{2} \cdot 3.08641975308642 \cdot 10^{-5}\\ \end{array} \]

Alternative 12
Error	23.6
Cost	20360

\[\begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+141}:\\ \;\;\;\;{a}^{2} + 3.08641975308642 \cdot 10^{-5} \cdot \left(\left(angle \cdot b\right) \cdot \left(\pi \cdot \left(\pi \cdot \left(angle \cdot b\right)\right)\right)\right)\\ \mathbf{elif}\;b \leq 10^{+62}:\\ \;\;\;\;{a}^{2} + 3.08641975308642 \cdot 10^{-5} \cdot \left({\pi}^{2} \cdot \left(angle \cdot \left(angle \cdot \left(b \cdot b\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{a}^{2} + {\left(angle \cdot \left(\pi \cdot b\right)\right)}^{2} \cdot 3.08641975308642 \cdot 10^{-5}\\ \end{array} \]

Alternative 13
Error	24.1
Cost	20360

\[\begin{array}{l} t_0 := \pi \cdot \left(angle \cdot b\right)\\ \mathbf{if}\;b \leq -1.25 \cdot 10^{+141}:\\ \;\;\;\;{a}^{2} + 3.08641975308642 \cdot 10^{-5} \cdot \left(\left(angle \cdot b\right) \cdot \left(\pi \cdot t_0\right)\right)\\ \mathbf{elif}\;b \leq 10^{-68}:\\ \;\;\;\;{a}^{2} + 3.08641975308642 \cdot 10^{-5} \cdot \left({\pi}^{2} \cdot \left(angle \cdot \left(angle \cdot \left(b \cdot b\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{a}^{2} + 3.08641975308642 \cdot 10^{-5} \cdot \left(b \cdot \left(\left(angle \cdot \pi\right) \cdot t_0\right)\right)\\ \end{array} \]

Alternative 14
Error	24.1
Cost	20360

\[\begin{array}{l} t_0 := \pi \cdot \left(angle \cdot b\right)\\ \mathbf{if}\;b \leq -1.45 \cdot 10^{+141}:\\ \;\;\;\;{a}^{2} + 3.08641975308642 \cdot 10^{-5} \cdot \left(\pi \cdot \left(\left(angle \cdot b\right) \cdot t_0\right)\right)\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{-68}:\\ \;\;\;\;{a}^{2} + 3.08641975308642 \cdot 10^{-5} \cdot \left({\pi}^{2} \cdot \left(angle \cdot \left(angle \cdot \left(b \cdot b\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{a}^{2} + 3.08641975308642 \cdot 10^{-5} \cdot \left(b \cdot \left(\left(angle \cdot \pi\right) \cdot t_0\right)\right)\\ \end{array} \]

Alternative 15
Error	25.8
Cost	19840

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

Reproduce

herbie shell --seed 2023057 
(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)))