Average Error: 7.5 → 7.6
Time: 10.9s
Precision: 64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\frac{\cosh x}{z} \cdot \frac{y}{x}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\frac{\cosh x}{z} \cdot \frac{y}{x}
double f(double x, double y, double z) {
        double r373275 = x;
        double r373276 = cosh(r373275);
        double r373277 = y;
        double r373278 = r373277 / r373275;
        double r373279 = r373276 * r373278;
        double r373280 = z;
        double r373281 = r373279 / r373280;
        return r373281;
}
↓
double f(double x, double y, double z) {
        double r373282 = x;
        double r373283 = cosh(r373282);
        double r373284 = z;
        double r373285 = r373283 / r373284;
        double r373286 = y;
        double r373287 = r373286 / r373282;
        double r373288 = r373285 * r373287;
        return r373288;
}

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

Original7.5
Target0.4
Herbie7.6
\[\begin{array}{l} \mathbf{if}\;y \lt -4.618902267687041990497740832940559043667 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{elif}\;y \lt 1.038530535935153018369520384190862667426 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -0.0013835500119336905

    1. Initial program 20.7

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

    3. Applied associate-*r/20.7

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

    4. Applied associate-/l/0.5

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

    6. Applied associate-/r*0.5

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

    if -0.0013835500119336905 < y < 1.1100678389608288e+19

    1. Initial program 0.3

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

    3. Applied associate-*r/0.3

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

    4. Applied associate-/l/10.8

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

    6. Applied times-frac0.4

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

    if 1.1100678389608288e+19 < y

    1. Initial program 22.5

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

    3. Applied associate-*r/22.5

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

    4. Applied associate-/l/0.3

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

    6. Applied associate-/r*0.3

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

    8. Applied div-inv0.4

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

  4. Final simplification7.6

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

Reproduce

herbie shell --seed 2019291 
(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))