ab-angle->ABCF C

Average Error: 20.6 → 20.7

Time: 18.8s

Precision: binary64

Cost: 65088

Math

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

↓

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

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 (cbrt PI) 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(cbrt(((double) M_PI)), 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.cbrt(Math.PI), 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(pi) ^ 2.0) / Float64(180.0 / Float64(cbrt(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[Pi, 1/3], $MachinePrecision], 2.0], $MachinePrecision] / N[(180.0 / N[(N[Power[Pi, 1/3], $MachinePrecision] * angle), $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 20.6

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

2. Applied egg-rr 20.7

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

3. Final simplification 20.7

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

Alternatives

Alternative 1
Error	20.6
Cost	52224

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

Alternative 2
Error	20.6
Cost	52224

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

Alternative 3
Error	20.6
Cost	52160

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

Alternative 4
Error	20.6
Cost	52160

\[{\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(a \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\cos \left(angle \cdot \frac{\pi}{180}\right)\right)\right)\right)}^{2} \]

Alternative 5
Error	20.8
Cost	32832

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

Alternative 6
Error	20.8
Cost	26240

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

Alternative 7
Error	22.1
Cost	20488

\[\begin{array}{l} t_0 := b \cdot \left(angle \cdot 0.005555555555555556\right)\\ \mathbf{if}\;angle \leq -0.0042:\\ \;\;\;\;{a}^{2} + \frac{b}{\frac{2}{b}} \cdot \left(1 - \cos \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{elif}\;angle \leq 3.5 \cdot 10^{-64}:\\ \;\;\;\;{a}^{2} + \left(t_0 \cdot t_0\right) \cdot {\pi}^{2}\\ \mathbf{else}:\\ \;\;\;\;{a}^{2} + \frac{b \cdot b}{2} \cdot \left(1 - \cos \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\right)\\ \end{array} \]

Alternative 8
Error	22.2
Cost	20425

\[\begin{array}{l} \mathbf{if}\;angle \leq -0.0042 \lor \neg \left(angle \leq 3.5 \cdot 10^{-64}\right):\\ \;\;\;\;{a}^{2} + \frac{b}{\frac{2}{b}} \cdot \left(1 - \cos \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{a}^{2} + 3.08641975308642 \cdot 10^{-5} \cdot {\left(\pi \cdot \left(angle \cdot b\right)\right)}^{2}\\ \end{array} \]

Alternative 9
Error	22.2
Cost	20424

\[\begin{array}{l} t_0 := 1 - \cos \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\\ \mathbf{if}\;angle \leq -0.0042:\\ \;\;\;\;{a}^{2} + \frac{b}{\frac{2}{b}} \cdot t_0\\ \mathbf{elif}\;angle \leq 3.5 \cdot 10^{-64}:\\ \;\;\;\;{a}^{2} + 3.08641975308642 \cdot 10^{-5} \cdot {\left(\pi \cdot \left(angle \cdot b\right)\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;{a}^{2} + t_0 \cdot \frac{b \cdot b}{2}\\ \end{array} \]

Alternative 10
Error	22.2
Cost	20424

\[\begin{array}{l} \mathbf{if}\;angle \leq -0.0042:\\ \;\;\;\;{a}^{2} + \frac{b}{\frac{2}{b}} \cdot \left(1 - \cos \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{elif}\;angle \leq 3.5 \cdot 10^{-64}:\\ \;\;\;\;{a}^{2} + 3.08641975308642 \cdot 10^{-5} \cdot {\left(\pi \cdot \left(angle \cdot b\right)\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;{a}^{2} + \frac{b \cdot b}{2} \cdot \left(1 - \cos \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\right)\\ \end{array} \]

Alternative 11
Error	26.5
Cost	19840

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

Alternative 12
Error	26.5
Cost	19840

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

Reproduce

herbie shell --seed 2023045 
(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)))