Average Error: 7.3 → 0.5
Time: 14.4s
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 r26711607 = x;
        double r26711608 = cosh(r26711607);
        double r26711609 = y;
        double r26711610 = r26711609 / r26711607;
        double r26711611 = r26711608 * r26711610;
        double r26711612 = z;
        double r26711613 = r26711611 / r26711612;
        return r26711613;
}
↓
double f(double x, double y, double z) {
        double r26711614 = z;
        double r26711615 = -6.434118062892472e+63;
        bool r26711616 = r26711614 <= r26711615;
        double r26711617 = x;
        double r26711618 = cosh(r26711617);
        double r26711619 = y;
        double r26711620 = r26711618 * r26711619;
        double r26711621 = r26711617 * r26711614;
        double r26711622 = r26711620 / r26711621;
        double r26711623 = 4.1988639493302256e+51;
        bool r26711624 = r26711614 <= r26711623;
        double r26711625 = exp(r26711617);
        double r26711626 = r26711619 * r26711625;
        double r26711627 = r26711619 / r26711625;
        double r26711628 = r26711626 + r26711627;
        double r26711629 = r26711628 / r26711614;
        double r26711630 = 2.0;
        double r26711631 = r26711617 * r26711630;
        double r26711632 = r26711629 / r26711631;
        double r26711633 = 1.0;
        double r26711634 = r26711633 / r26711614;
        double r26711635 = r26711634 / r26711617;
        double r26711636 = r26711620 * r26711635;
        double r26711637 = r26711624 ? r26711632 : r26711636;
        double r26711638 = r26711616 ? r26711622 : r26711637;
        return r26711638;
}

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))