Average Error: 0.0 → 0.0
Time: 6.1s
Precision: binary64
\[\cos x \cdot \frac{\sinh y}{y} \]
↓
\[\frac{\cos x}{{\left(\mathsf{log1p}\left(\mathsf{expm1}\left(\sqrt{\frac{y}{\sinh y}}\right)\right)\right)}^{2}} \]
(FPCore (x y) :precision binary64 (* (cos x) (/ (sinh y) y)))
↓
(FPCore (x y)
 :precision binary64
 (/ (cos x) (pow (log1p (expm1 (sqrt (/ y (sinh y))))) 2.0)))
double code(double x, double y) {
	return cos(x) * (sinh(y) / y);
}
↓
double code(double x, double y) {
	return cos(x) / pow(log1p(expm1(sqrt((y / sinh(y))))), 2.0);
}

public static double code(double x, double y) {
	return Math.cos(x) * (Math.sinh(y) / y);
}
↓
public static double code(double x, double y) {
	return Math.cos(x) / Math.pow(Math.log1p(Math.expm1(Math.sqrt((y / Math.sinh(y))))), 2.0);
}

def code(x, y):
	return math.cos(x) * (math.sinh(y) / y)
↓
def code(x, y):
	return math.cos(x) / math.pow(math.log1p(math.expm1(math.sqrt((y / math.sinh(y))))), 2.0)

function code(x, y)
	return Float64(cos(x) * Float64(sinh(y) / y))
end
↓
function code(x, y)
	return Float64(cos(x) / (log1p(expm1(sqrt(Float64(y / sinh(y))))) ^ 2.0))
end

code[x_, y_] := N[(N[Cos[x], $MachinePrecision] * N[(N[Sinh[y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_] := N[(N[Cos[x], $MachinePrecision] / N[Power[N[Log[1 + N[(Exp[N[Sqrt[N[(y / N[Sinh[y], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]] - 1), $MachinePrecision]], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

\cos x \cdot \frac{\sinh y}{y}
↓
\frac{\cos x}{{\left(\mathsf{log1p}\left(\mathsf{expm1}\left(\sqrt{\frac{y}{\sinh y}}\right)\right)\right)}^{2}}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\cos x \cdot \frac{\sinh y}{y} \]

  2. Applied egg-rr0.0

    \[\leadsto \color{blue}{\frac{\cos x}{\frac{y}{\sinh y}}} \]

  3. Applied egg-rr0.0

    \[\leadsto \frac{\cos x}{\color{blue}{{\left(\sqrt{\frac{y}{\sinh y}}\right)}^{2}}} \]

  4. Applied egg-rr0.0

    \[\leadsto \frac{\cos x}{{\color{blue}{\left(\mathsf{log1p}\left(\mathsf{expm1}\left(\sqrt{\frac{y}{\sinh y}}\right)\right)\right)}}^{2}} \]

  5. Final simplification0.0

    \[\leadsto \frac{\cos x}{{\left(\mathsf{log1p}\left(\mathsf{expm1}\left(\sqrt{\frac{y}{\sinh y}}\right)\right)\right)}^{2}} \]

Reproduce

herbie shell --seed 2022133 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))