Average Error: 0.1 → 0.1
Time: 6.8s
Precision: binary64
\[\sin x \cdot \frac{\sinh y}{y} \]
↓
\[\frac{\sin x}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{y}{\sinh y}\right)\right)} \]
(FPCore (x y) :precision binary64 (* (sin x) (/ (sinh y) y)))
↓
(FPCore (x y) :precision binary64 (/ (sin x) (log1p (expm1 (/ y (sinh y))))))
double code(double x, double y) {
	return sin(x) * (sinh(y) / y);
}
↓
double code(double x, double y) {
	return sin(x) / log1p(expm1((y / sinh(y))));
}

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

def code(x, y):
	return math.sin(x) * (math.sinh(y) / y)
↓
def code(x, y):
	return math.sin(x) / math.log1p(math.expm1((y / math.sinh(y))))

function code(x, y)
	return Float64(sin(x) * Float64(sinh(y) / y))
end
↓
function code(x, y)
	return Float64(sin(x) / log1p(expm1(Float64(y / sinh(y)))))
end

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

\sin x \cdot \frac{\sinh y}{y}
↓
\frac{\sin x}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{y}{\sinh y}\right)\right)}

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 0.1

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

  2. Applied egg-rr0.1

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

  3. Applied egg-rr0.1

    \[\leadsto \frac{\sin x}{\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{y}{\sinh y}\right)\right)}} \]

  4. Final simplification0.1

    \[\leadsto \frac{\sin x}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{y}{\sinh y}\right)\right)} \]

Reproduce

herbie shell --seed 2022153 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))