Average Error: 0.1 → 0.2
Time: 7.2s
Precision: binary64
\[\cosh x \cdot \frac{\sin y}{y} \]
↓
\[\begin{array}{l} t_0 := \sqrt{\cosh x}\\ \frac{\sin y}{\frac{1}{t_0} \cdot \frac{y}{t_0}} \end{array} \]
(FPCore (x y) :precision binary64 (* (cosh x) (/ (sin y) y)))
↓
(FPCore (x y)
 :precision binary64
 (let* ((t_0 (sqrt (cosh x)))) (/ (sin y) (* (/ 1.0 t_0) (/ y t_0)))))
double code(double x, double y) {
	return cosh(x) * (sin(y) / y);
}
↓
double code(double x, double y) {
	double t_0 = sqrt(cosh(x));
	return sin(y) / ((1.0 / t_0) * (y / t_0));
}

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
    real(8) :: t_0
    t_0 = sqrt(cosh(x))
    code = sin(y) / ((1.0d0 / t_0) * (y / t_0))
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) {
	double t_0 = Math.sqrt(Math.cosh(x));
	return Math.sin(y) / ((1.0 / t_0) * (y / t_0));
}

def code(x, y):
	return math.cosh(x) * (math.sin(y) / y)
↓
def code(x, y):
	t_0 = math.sqrt(math.cosh(x))
	return math.sin(y) / ((1.0 / t_0) * (y / t_0))

function code(x, y)
	return Float64(cosh(x) * Float64(sin(y) / y))
end
↓
function code(x, y)
	t_0 = sqrt(cosh(x))
	return Float64(sin(y) / Float64(Float64(1.0 / t_0) * Float64(y / t_0)))
end

function tmp = code(x, y)
	tmp = cosh(x) * (sin(y) / y);
end
↓
function tmp = code(x, y)
	t_0 = sqrt(cosh(x));
	tmp = sin(y) / ((1.0 / t_0) * (y / t_0));
end

code[x_, y_] := N[(N[Cosh[x], $MachinePrecision] * N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_] := Block[{t$95$0 = N[Sqrt[N[Cosh[x], $MachinePrecision]], $MachinePrecision]}, N[(N[Sin[y], $MachinePrecision] / N[(N[(1.0 / t$95$0), $MachinePrecision] * N[(y / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

\cosh x \cdot \frac{\sin y}{y}
↓
\begin{array}{l}
t_0 := \sqrt{\cosh x}\\
\frac{\sin y}{\frac{1}{t_0} \cdot \frac{y}{t_0}}
\end{array}

Error

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.2
\[\frac{\cosh x \cdot \sin y}{y} \]

Derivation

  1. Initial program 0.1

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

  2. Simplified0.2

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

  3. Applied egg-rr0.2

    \[\leadsto \frac{\sin y}{\color{blue}{\frac{1}{\sqrt{\cosh x}} \cdot \frac{y}{\sqrt{\cosh x}}}} \]

  4. Final simplification0.2

    \[\leadsto \frac{\sin y}{\frac{1}{\sqrt{\cosh x}} \cdot \frac{y}{\sqrt{\cosh x}}} \]

Reproduce

herbie shell --seed 2022206 
(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)))