Average Error: 7.8 → 6.8
Time: 13.4s
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 r376603 = x;
        double r376604 = cosh(r376603);
        double r376605 = y;
        double r376606 = r376605 / r376603;
        double r376607 = r376604 * r376606;
        double r376608 = z;
        double r376609 = r376607 / r376608;
        return r376609;
}
↓
double f(double x, double y, double z) {
        double r376610 = x;
        double r376611 = cosh(r376610);
        double r376612 = y;
        double r376613 = z;
        double r376614 = r376610 * r376613;
        double r376615 = r376612 / r376614;
        double r376616 = r376611 * r376615;
        return r376616;
}

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

Original7.8
Target0.4
Herbie6.8
\[\begin{array}{l} \mathbf{if}\;y \lt -4.618902267687041990497740832940559043667 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{elif}\;y \lt 1.038530535935153018369520384190862667426 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -1.3966363234461108e-77 or 1.2004827862446334e-54 < y

    1. Initial program 16.1

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

    3. Applied *-un-lft-identity16.1

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

    4. Applied times-frac16.0

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

    5. Simplified16.0

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

    6. Simplified1.2

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

    if -1.3966363234461108e-77 < y < 1.2004827862446334e-54

    1. Initial program 0.3

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

    3. Applied div-inv0.4

      \[\leadsto \color{blue}{\left(\cosh x \cdot \frac{y}{x}\right) \cdot \frac{1}{z}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification6.8

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

Reproduce

herbie shell --seed 2019297 
(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))