Average Error: 0.2 → 0.2
Time: 6.4s
Precision: binary64
\[\cosh x \cdot \frac{\sin y}{y} \]
↓
\[\frac{0.5 \cdot \left(\sin y \cdot e^{x}\right) + 0.5 \cdot \frac{\sin y}{e^{x}}}{y} \]
(FPCore (x y) :precision binary64 (* (cosh x) (/ (sin y) y)))
↓
(FPCore (x y)
 :precision binary64
 (/ (+ (* 0.5 (* (sin y) (exp x))) (* 0.5 (/ (sin y) (exp x)))) y))
double code(double x, double y) {
	return cosh(x) * (sin(y) / y);
}
↓
double code(double x, double y) {
	return ((0.5 * (sin(y) * exp(x))) + (0.5 * (sin(y) / exp(x)))) / y;
}

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = cosh(x) * (sin(y) / y)
end function
↓
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((0.5d0 * (sin(y) * exp(x))) + (0.5d0 * (sin(y) / exp(x)))) / y
end function

public static double code(double x, double y) {
	return Math.cosh(x) * (Math.sin(y) / y);
}
↓
public static double code(double x, double y) {
	return ((0.5 * (Math.sin(y) * Math.exp(x))) + (0.5 * (Math.sin(y) / Math.exp(x)))) / y;
}

def code(x, y):
	return math.cosh(x) * (math.sin(y) / y)
↓
def code(x, y):
	return ((0.5 * (math.sin(y) * math.exp(x))) + (0.5 * (math.sin(y) / math.exp(x)))) / y

function code(x, y)
	return Float64(cosh(x) * Float64(sin(y) / y))
end
↓
function code(x, y)
	return Float64(Float64(Float64(0.5 * Float64(sin(y) * exp(x))) + Float64(0.5 * Float64(sin(y) / exp(x)))) / y)
end

function tmp = code(x, y)
	tmp = cosh(x) * (sin(y) / y);
end
↓
function tmp = code(x, y)
	tmp = ((0.5 * (sin(y) * exp(x))) + (0.5 * (sin(y) / exp(x)))) / y;
end

code[x_, y_] := N[(N[Cosh[x], $MachinePrecision] * N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_] := N[(N[(N[(0.5 * N[(N[Sin[y], $MachinePrecision] * N[Exp[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(N[Sin[y], $MachinePrecision] / N[Exp[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

\cosh x \cdot \frac{\sin y}{y}
↓
\frac{0.5 \cdot \left(\sin y \cdot e^{x}\right) + 0.5 \cdot \frac{\sin y}{e^{x}}}{y}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.2
Herbie0.2
\[\frac{\cosh x \cdot \sin y}{y} \]

Derivation

  1. Initial program 0.2

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

  2. Taylor expanded in y around inf 0.2

    \[\leadsto \color{blue}{\frac{0.5 \cdot \left(\sin y \cdot e^{x}\right) + 0.5 \cdot \frac{\sin y}{e^{x}}}{y}} \]

  3. Final simplification0.2

    \[\leadsto \frac{0.5 \cdot \left(\sin y \cdot e^{x}\right) + 0.5 \cdot \frac{\sin y}{e^{x}}}{y} \]

Reproduce

herbie shell --seed 2022130 
(FPCore (x y)
  :name "Linear.Quaternion:$csinh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (/ (* (cosh x) (sin y)) y)

  (* (cosh x) (/ (sin y) y)))