Average Error: 7.7 → 0.5
Time: 3.6s
Precision: 64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -6.8080066842813633 \cdot 10^{50} \lor \neg \left(z \le 4.55122421414426669 \cdot 10^{48}\right):\\ \;\;\;\;\frac{\cosh x \cdot y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{z}}{x}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -6.8080066842813633 \cdot 10^{50} \lor \neg \left(z \le 4.55122421414426669 \cdot 10^{48}\right):\\
\;\;\;\;\frac{\cosh x \cdot y}{x \cdot z}\\

\mathbf{else}:\\
\;\;\;\;\frac{\cosh x \cdot \frac{y}{z}}{x}\\

\end{array}
double f(double x, double y, double z) {
        double r592374 = x;
        double r592375 = cosh(r592374);
        double r592376 = y;
        double r592377 = r592376 / r592374;
        double r592378 = r592375 * r592377;
        double r592379 = z;
        double r592380 = r592378 / r592379;
        return r592380;
}
↓
double f(double x, double y, double z) {
        double r592381 = z;
        double r592382 = -6.808006684281363e+50;
        bool r592383 = r592381 <= r592382;
        double r592384 = 4.551224214144267e+48;
        bool r592385 = r592381 <= r592384;
        double r592386 = !r592385;
        bool r592387 = r592383 || r592386;
        double r592388 = x;
        double r592389 = cosh(r592388);
        double r592390 = y;
        double r592391 = r592389 * r592390;
        double r592392 = r592388 * r592381;
        double r592393 = r592391 / r592392;
        double r592394 = r592390 / r592381;
        double r592395 = r592389 * r592394;
        double r592396 = r592395 / r592388;
        double r592397 = r592387 ? r592393 : r592396;
        return r592397;
}

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

Original7.7
Target0.5
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;y \lt -4.618902267687042 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{elif}\;y \lt 1.0385305359351529 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -6.808006684281363e+50 or 4.551224214144267e+48 < z

    1. Initial program 13.0

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

    3. Applied *-un-lft-identity13.0

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

    4. Applied times-frac13.0

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

    5. Simplified13.0

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

    6. Simplified0.3

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

    8. Applied associate-*r/0.3

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

    if -6.808006684281363e+50 < z < 4.551224214144267e+48

    1. Initial program 0.9

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

    3. Applied *-un-lft-identity0.9

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

    4. Applied times-frac0.9

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

    5. Simplified0.9

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

    6. Simplified15.6

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

    8. Applied *-un-lft-identity15.6

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

    9. Applied times-frac0.7

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

    10. Applied associate-*r*0.7

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

    11. Simplified0.7

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

    13. Applied associate-*l/0.7

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -6.8080066842813633 \cdot 10^{50} \lor \neg \left(z \le 4.55122421414426669 \cdot 10^{48}\right):\\ \;\;\;\;\frac{\cosh x \cdot y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{z}}{x}\\ \end{array}\]

Reproduce

herbie shell --seed 2020100 
(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 1.0385305359351529e-39) (/ (/ (* (cosh x) y) x) z) (* (/ (/ y z) x) (cosh x))))

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