Average Error: 7.5 → 7.0
Time: 10.8s
Precision: 64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\cosh x \cdot \frac{y}{x \cdot z}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\cosh x \cdot \frac{y}{x \cdot z}
double f(double x, double y, double z) {
        double r352621 = x;
        double r352622 = cosh(r352621);
        double r352623 = y;
        double r352624 = r352623 / r352621;
        double r352625 = r352622 * r352624;
        double r352626 = z;
        double r352627 = r352625 / r352626;
        return r352627;
}
↓
double f(double x, double y, double z) {
        double r352628 = x;
        double r352629 = cosh(r352628);
        double r352630 = y;
        double r352631 = z;
        double r352632 = r352628 * r352631;
        double r352633 = r352630 / r352632;
        double r352634 = r352629 * r352633;
        return r352634;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.5
Target0.4
Herbie7.0
\[\begin{array}{l} \mathbf{if}\;y \lt -4.618902267687041990497740832940559043667 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{elif}\;y \lt 1.038530535935153018369520384190862667426 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -2.4014304081022685e-24 or 0.000273177232586214 < z

    1. Initial program 11.0

      \[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity11.0

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

    4. Applied times-frac11.0

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

    5. Simplified11.0

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

    6. Simplified0.4

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

    if -2.4014304081022685e-24 < z < 0.000273177232586214

    1. Initial program 0.3

      \[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
    2. Using strategy rm

    3. Applied add-cbrt-cube0.4

      \[\leadsto \frac{\color{blue}{\sqrt[3]{\left(\cosh x \cdot \cosh x\right) \cdot \cosh x}} \cdot \frac{y}{x}}{z}\]

    4. Simplified0.4

      \[\leadsto \frac{\sqrt[3]{\color{blue}{{\left(\cosh x\right)}^{3}}} \cdot \frac{y}{x}}{z}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification7.0

    \[\leadsto \cosh x \cdot \frac{y}{x \cdot z}\]

Reproduce

herbie shell --seed 2019298 
(FPCore (x y z)
  :name "Linear.Quaternion:$ctan from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< y -4.618902267687042e-52) (* (/ (/ y z) x) (cosh x)) (if (< y 1.03853053593515302e-39) (/ (/ (* (cosh x) y) x) z) (* (/ (/ y z) x) (cosh x))))

  (/ (* (cosh x) (/ y x)) z))