ab-angle->ABCF C

Average Error: 20.3 → 20.4

Time: 18.3s

Precision: binary64

Cost: 78656

Math

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

↓

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

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 (* b (sin (* PI (* angle 0.005555555555555556))))))
   (+
    (pow (* a (cos (* PI (/ angle 180.0)))) 2.0)
    (*
     (cbrt (pow (* (sin (* 0.005555555555555556 (* PI angle))) b) 2.0))
     (* t_0 (cbrt t_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 = b * sin((((double) M_PI) * (angle * 0.005555555555555556)));
	return pow((a * cos((((double) M_PI) * (angle / 180.0)))), 2.0) + (cbrt(pow((sin((0.005555555555555556 * (((double) M_PI) * angle))) * b), 2.0)) * (t_0 * cbrt(t_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 = b * Math.sin((Math.PI * (angle * 0.005555555555555556)));
	return Math.pow((a * Math.cos((Math.PI * (angle / 180.0)))), 2.0) + (Math.cbrt(Math.pow((Math.sin((0.005555555555555556 * (Math.PI * angle))) * b), 2.0)) * (t_0 * Math.cbrt(t_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 = Float64(b * sin(Float64(pi * Float64(angle * 0.005555555555555556))))
	return Float64((Float64(a * cos(Float64(pi * Float64(angle / 180.0)))) ^ 2.0) + Float64(cbrt((Float64(sin(Float64(0.005555555555555556 * Float64(pi * angle))) * b) ^ 2.0)) * Float64(t_0 * cbrt(t_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[(b * N[Sin[N[(Pi * N[(angle * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, N[(N[Power[N[(a * N[Cos[N[(Pi * N[(angle / 180.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[(N[Power[N[Power[N[(N[Sin[N[(0.005555555555555556 * N[(Pi * angle), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * b), $MachinePrecision], 2.0], $MachinePrecision], 1/3], $MachinePrecision] * N[(t$95$0 * N[Power[t$95$0, 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 20.3

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

2. Applied egg-rr 38.6

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

3. Applied egg-rr 20.4

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

4. Taylor expanded in angle around inf 20.4

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

5. Final simplification 20.4

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

Alternatives

Alternative 1
Error	20.3
Cost	39360

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

Alternative 2
Error	20.3
Cost	39360

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

Alternative 3
Error	20.3
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
Error	20.4
Cost	26240

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

Alternative 5
Error	20.7
Cost	20425

\[\begin{array}{l} \mathbf{if}\;angle \leq -950000000 \lor \neg \left(angle \leq 0.0036\right):\\ \;\;\;\;{a}^{2} + \frac{b}{\frac{2}{b}} \cdot \left(1 - \cos \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{a}^{2} + 3.08641975308642 \cdot 10^{-5} \cdot \left(\pi \cdot \left(\left(angle \cdot b\right) \cdot \left(\pi \cdot \left(angle \cdot b\right)\right)\right)\right)\\ \end{array} \]

Alternative 6
Error	26.0
Cost	20096

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

Alternative 7
Error	26.0
Cost	19840

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

Reproduce

herbie shell --seed 2023034 
(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)))