Average Error: 7.3 → 0.3
Time: 14.8s
Precision: 64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.0432260555262782 \cdot 10^{-16}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{z}}{x}\\ \mathbf{elif}\;y \le 2922533292505.41:\\ \;\;\;\;\frac{\frac{y}{x} \cdot \cosh x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{z}}{x}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.0432260555262782 \cdot 10^{-16}:\\
\;\;\;\;\frac{\frac{\cosh x \cdot y}{z}}{x}\\

\mathbf{elif}\;y \le 2922533292505.41:\\
\;\;\;\;\frac{\frac{y}{x} \cdot \cosh x}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r10982124 = x;
        double r10982125 = cosh(r10982124);
        double r10982126 = y;
        double r10982127 = r10982126 / r10982124;
        double r10982128 = r10982125 * r10982127;
        double r10982129 = z;
        double r10982130 = r10982128 / r10982129;
        return r10982130;
}
↓
double f(double x, double y, double z) {
        double r10982131 = y;
        double r10982132 = -1.0432260555262782e-16;
        bool r10982133 = r10982131 <= r10982132;
        double r10982134 = x;
        double r10982135 = cosh(r10982134);
        double r10982136 = r10982135 * r10982131;
        double r10982137 = z;
        double r10982138 = r10982136 / r10982137;
        double r10982139 = r10982138 / r10982134;
        double r10982140 = 2922533292505.41;
        bool r10982141 = r10982131 <= r10982140;
        double r10982142 = r10982131 / r10982134;
        double r10982143 = r10982142 * r10982135;
        double r10982144 = r10982143 / r10982137;
        double r10982145 = r10982141 ? r10982144 : r10982139;
        double r10982146 = r10982133 ? r10982139 : r10982145;
        return r10982146;
}

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

Derivation

  1. Split input into 2 regimes

  2. if y < -1.0432260555262782e-16 or 2922533292505.41 < y

    1. Initial program 20.1

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

    3. Applied associate-*r/20.1

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

    4. Applied associate-/l/0.3

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

    6. Applied associate-/r*0.3

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

    if -1.0432260555262782e-16 < y < 2922533292505.41

    1. Initial program 0.3

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.0432260555262782 \cdot 10^{-16}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{z}}{x}\\ \mathbf{elif}\;y \le 2922533292505.41:\\ \;\;\;\;\frac{\frac{y}{x} \cdot \cosh x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{z}}{x}\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(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))