Average Error: 7.7 → 0.4
Time: 12.2s
Precision: 64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.150123078305551352915999172151981233547 \cdot 10^{-8} \lor \neg \left(z \le 1.096497473325428813191452397318998843153 \cdot 10^{72}\right):\\ \;\;\;\;\frac{\cosh x \cdot y}{z \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{z}}{x}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.150123078305551352915999172151981233547 \cdot 10^{-8} \lor \neg \left(z \le 1.096497473325428813191452397318998843153 \cdot 10^{72}\right):\\
\;\;\;\;\frac{\cosh x \cdot y}{z \cdot x}\\

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

\end{array}
double f(double x, double y, double z) {
        double r389222 = x;
        double r389223 = cosh(r389222);
        double r389224 = y;
        double r389225 = r389224 / r389222;
        double r389226 = r389223 * r389225;
        double r389227 = z;
        double r389228 = r389226 / r389227;
        return r389228;
}
↓
double f(double x, double y, double z) {
        double r389229 = z;
        double r389230 = -1.1501230783055514e-08;
        bool r389231 = r389229 <= r389230;
        double r389232 = 1.0964974733254288e+72;
        bool r389233 = r389229 <= r389232;
        double r389234 = !r389233;
        bool r389235 = r389231 || r389234;
        double r389236 = x;
        double r389237 = cosh(r389236);
        double r389238 = y;
        double r389239 = r389237 * r389238;
        double r389240 = r389229 * r389236;
        double r389241 = r389239 / r389240;
        double r389242 = r389239 / r389229;
        double r389243 = r389242 / r389236;
        double r389244 = r389235 ? r389241 : r389243;
        return r389244;
}

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
Target0.4
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;y \lt -4.618902267687041990497740832940559043667 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{elif}\;y \lt 1.038530535935153018369520384190862667426 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.1501230783055514e-08 or 1.0964974733254288e+72 < z

    1. Initial program 12.5

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

    3. Applied associate-*r/12.5

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

    4. Applied associate-/l/0.3

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

    if -1.1501230783055514e-08 < z < 1.0964974733254288e+72

    1. Initial program 0.8

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

    3. Applied associate-*r/0.8

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

    4. Applied associate-/l/17.0

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

    6. Applied associate-/r*0.6

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.150123078305551352915999172151981233547 \cdot 10^{-8} \lor \neg \left(z \le 1.096497473325428813191452397318998843153 \cdot 10^{72}\right):\\ \;\;\;\;\frac{\cosh x \cdot y}{z \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{z}}{x}\\ \end{array}\]

Reproduce

herbie shell --seed 2019212 +o rules:numerics
(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))