Average Error: 20.6 → 20.6
Time: 13.3s
Precision: binary64
\[{\left(a \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} + {\left(b \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)}^{2} \]
↓
\[{\left(a \cdot \log \left(e^{\cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)}\right)\right)}^{2} + {\left(b \cdot \sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right)}^{2} \]
(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 (log (exp (cos (* PI (* angle 0.005555555555555556)))))) 2.0)
  (pow (* b (sin (* 0.005555555555555556 (* PI angle)))) 2.0)))
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 * log(exp(cos((((double) M_PI) * (angle * 0.005555555555555556)))))), 2.0) + pow((b * sin((0.005555555555555556 * (((double) M_PI) * angle)))), 2.0);
}

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.log(Math.exp(Math.cos((Math.PI * (angle * 0.005555555555555556)))))), 2.0) + Math.pow((b * Math.sin((0.005555555555555556 * (Math.PI * angle)))), 2.0);
}

def code(a, b, 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)
↓
def code(a, b, angle):
	return math.pow((a * math.log(math.exp(math.cos((math.pi * (angle * 0.005555555555555556)))))), 2.0) + math.pow((b * math.sin((0.005555555555555556 * (math.pi * angle)))), 2.0)

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 * log(exp(cos(Float64(pi * Float64(angle * 0.005555555555555556)))))) ^ 2.0) + (Float64(b * sin(Float64(0.005555555555555556 * Float64(pi * angle)))) ^ 2.0))
end

function tmp = code(a, b, angle)
	tmp = ((a * cos((pi * (angle / 180.0)))) ^ 2.0) + ((b * sin((pi * (angle / 180.0)))) ^ 2.0);
end
↓
function tmp = code(a, b, angle)
	tmp = ((a * log(exp(cos((pi * (angle * 0.005555555555555556)))))) ^ 2.0) + ((b * sin((0.005555555555555556 * (pi * angle)))) ^ 2.0);
end

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[Log[N[Exp[N[Cos[N[(Pi * N[(angle * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(b * N[Sin[N[(0.005555555555555556 * N[(Pi * angle), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

{\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 \log \left(e^{\cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)}\right)\right)}^{2} + {\left(b \cdot \sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right)}^{2}

Error

Bits error versus a

Bits error versus b

Bits error versus angle

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Taylor expanded in angle around inf 20.6

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

  3. Applied egg-rr20.6

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

  4. Final simplification20.6

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

Reproduce

herbie shell --seed 2022150 
(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)))