Average Error: 7.3 → 0.5
Time: 16.3s
Precision: 64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -6.434118062892472 \cdot 10^{+63}:\\ \;\;\;\;\frac{\cosh x \cdot y}{x \cdot z}\\ \mathbf{elif}\;z \le 4.1988639493302256 \cdot 10^{+51}:\\ \;\;\;\;\frac{\frac{y \cdot e^{x} + \frac{y}{e^{x}}}{z}}{x \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\left(\cosh x \cdot y\right) \cdot \frac{\frac{1}{z}}{x}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -6.434118062892472 \cdot 10^{+63}:\\
\;\;\;\;\frac{\cosh x \cdot y}{x \cdot z}\\

\mathbf{elif}\;z \le 4.1988639493302256 \cdot 10^{+51}:\\
\;\;\;\;\frac{\frac{y \cdot e^{x} + \frac{y}{e^{x}}}{z}}{x \cdot 2}\\

\mathbf{else}:\\
\;\;\;\;\left(\cosh x \cdot y\right) \cdot \frac{\frac{1}{z}}{x}\\

\end{array}
double f(double x, double y, double z) {
        double r24275139 = x;
        double r24275140 = cosh(r24275139);
        double r24275141 = y;
        double r24275142 = r24275141 / r24275139;
        double r24275143 = r24275140 * r24275142;
        double r24275144 = z;
        double r24275145 = r24275143 / r24275144;
        return r24275145;
}
↓
double f(double x, double y, double z) {
        double r24275146 = z;
        double r24275147 = -6.434118062892472e+63;
        bool r24275148 = r24275146 <= r24275147;
        double r24275149 = x;
        double r24275150 = cosh(r24275149);
        double r24275151 = y;
        double r24275152 = r24275150 * r24275151;
        double r24275153 = r24275149 * r24275146;
        double r24275154 = r24275152 / r24275153;
        double r24275155 = 4.1988639493302256e+51;
        bool r24275156 = r24275146 <= r24275155;
        double r24275157 = exp(r24275149);
        double r24275158 = r24275151 * r24275157;
        double r24275159 = r24275151 / r24275157;
        double r24275160 = r24275158 + r24275159;
        double r24275161 = r24275160 / r24275146;
        double r24275162 = 2.0;
        double r24275163 = r24275149 * r24275162;
        double r24275164 = r24275161 / r24275163;
        double r24275165 = 1.0;
        double r24275166 = r24275165 / r24275146;
        double r24275167 = r24275166 / r24275149;
        double r24275168 = r24275152 * r24275167;
        double r24275169 = r24275156 ? r24275164 : r24275168;
        double r24275170 = r24275148 ? r24275154 : r24275169;
        return r24275170;
}

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

Original7.3
Target0.5
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;y \lt -4.618902267687042 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{elif}\;y \lt 1.038530535935153 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if z < -6.434118062892472e+63

    1. Initial program 12.8

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

    3. Applied associate-*r/12.8

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

    4. Applied associate-/l/0.2

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

    if -6.434118062892472e+63 < z < 4.1988639493302256e+51

    1. Initial program 1.1

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

    3. Applied associate-*r/1.1

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

    4. Applied associate-/l/14.5

      \[\leadsto \color{blue}{\frac{\cosh x \cdot y}{z \cdot x}}\]
    5. Using strategy rm

    6. Applied clear-num14.6

      \[\leadsto \color{blue}{\frac{1}{\frac{z \cdot x}{\cosh x \cdot y}}}\]
    7. Using strategy rm

    8. Applied div-inv14.7

      \[\leadsto \frac{1}{\color{blue}{\left(z \cdot x\right) \cdot \frac{1}{\cosh x \cdot y}}}\]

    9. Applied add-cube-cbrt14.7

      \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\left(z \cdot x\right) \cdot \frac{1}{\cosh x \cdot y}}\]

    10. Applied times-frac15.8

      \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{z \cdot x} \cdot \frac{\sqrt[3]{1}}{\frac{1}{\cosh x \cdot y}}}\]

    11. Simplified15.8

      \[\leadsto \color{blue}{\frac{\frac{1}{z}}{x}} \cdot \frac{\sqrt[3]{1}}{\frac{1}{\cosh x \cdot y}}\]

    12. Simplified15.7

      \[\leadsto \frac{\frac{1}{z}}{x} \cdot \color{blue}{\left(y \cdot \cosh x\right)}\]
    13. Using strategy rm

    14. Applied cosh-def15.7

      \[\leadsto \frac{\frac{1}{z}}{x} \cdot \left(y \cdot \color{blue}{\frac{e^{x} + e^{-x}}{2}}\right)\]

    15. Applied associate-*r/15.7

      \[\leadsto \frac{\frac{1}{z}}{x} \cdot \color{blue}{\frac{y \cdot \left(e^{x} + e^{-x}\right)}{2}}\]

    16. Applied frac-times1.0

      \[\leadsto \color{blue}{\frac{\frac{1}{z} \cdot \left(y \cdot \left(e^{x} + e^{-x}\right)\right)}{x \cdot 2}}\]

    17. Simplified0.8

      \[\leadsto \frac{\color{blue}{\frac{e^{x} \cdot y + \frac{y}{e^{x}}}{z}}}{x \cdot 2}\]

    if 4.1988639493302256e+51 < z

    1. Initial program 12.2

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

    3. Applied associate-*r/12.2

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

    4. Applied associate-/l/0.3

      \[\leadsto \color{blue}{\frac{\cosh x \cdot y}{z \cdot x}}\]
    5. Using strategy rm

    6. Applied clear-num0.6

      \[\leadsto \color{blue}{\frac{1}{\frac{z \cdot x}{\cosh x \cdot y}}}\]
    7. Using strategy rm

    8. Applied div-inv0.7

      \[\leadsto \frac{1}{\color{blue}{\left(z \cdot x\right) \cdot \frac{1}{\cosh x \cdot y}}}\]

    9. Applied add-cube-cbrt0.7

      \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\left(z \cdot x\right) \cdot \frac{1}{\cosh x \cdot y}}\]

    10. Applied times-frac0.4

      \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{z \cdot x} \cdot \frac{\sqrt[3]{1}}{\frac{1}{\cosh x \cdot y}}}\]

    11. Simplified0.4

      \[\leadsto \color{blue}{\frac{\frac{1}{z}}{x}} \cdot \frac{\sqrt[3]{1}}{\frac{1}{\cosh x \cdot y}}\]

    12. Simplified0.4

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -6.434118062892472 \cdot 10^{+63}:\\ \;\;\;\;\frac{\cosh x \cdot y}{x \cdot z}\\ \mathbf{elif}\;z \le 4.1988639493302256 \cdot 10^{+51}:\\ \;\;\;\;\frac{\frac{y \cdot e^{x} + \frac{y}{e^{x}}}{z}}{x \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\left(\cosh x \cdot y\right) \cdot \frac{\frac{1}{z}}{x}\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z)
  :name "Linear.Quaternion:$ctan from linear-1.19.1.3"

  :herbie-target
  (if (< y -4.618902267687042e-52) (* (/ (/ y z) x) (cosh x)) (if (< y 1.038530535935153e-39) (/ (/ (* (cosh x) y) x) z) (* (/ (/ y z) x) (cosh x))))

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