Average Error: 3.0 → 0.8
Time: 4.4s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.1728892342568057 \cdot 10^{-27}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{y} \cdot \sin y\right)}{z}\\ \mathbf{elif}\;z \le 1.32101974044890363 \cdot 10^{187}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{x}{\frac{y}{\sin y}}\right)}^{1} \cdot \frac{1}{z}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.1728892342568057 \cdot 10^{-27}:\\
\;\;\;\;\frac{x \cdot \left(\frac{1}{y} \cdot \sin y\right)}{z}\\

\mathbf{elif}\;z \le 1.32101974044890363 \cdot 10^{187}:\\
\;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\

\mathbf{else}:\\
\;\;\;\;{\left(\frac{x}{\frac{y}{\sin y}}\right)}^{1} \cdot \frac{1}{z}\\

\end{array}
double f(double x, double y, double z) {
        double r519105 = x;
        double r519106 = y;
        double r519107 = sin(r519106);
        double r519108 = r519107 / r519106;
        double r519109 = r519105 * r519108;
        double r519110 = z;
        double r519111 = r519109 / r519110;
        return r519111;
}
↓
double f(double x, double y, double z) {
        double r519112 = z;
        double r519113 = -1.1728892342568057e-27;
        bool r519114 = r519112 <= r519113;
        double r519115 = x;
        double r519116 = 1.0;
        double r519117 = y;
        double r519118 = r519116 / r519117;
        double r519119 = sin(r519117);
        double r519120 = r519118 * r519119;
        double r519121 = r519115 * r519120;
        double r519122 = r519121 / r519112;
        double r519123 = 1.3210197404489036e+187;
        bool r519124 = r519112 <= r519123;
        double r519125 = r519117 / r519119;
        double r519126 = r519112 * r519125;
        double r519127 = r519115 / r519126;
        double r519128 = r519115 / r519125;
        double r519129 = pow(r519128, r519116);
        double r519130 = r519116 / r519112;
        double r519131 = r519129 * r519130;
        double r519132 = r519124 ? r519127 : r519131;
        double r519133 = r519114 ? r519122 : r519132;
        return r519133;
}

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

Original3.0
Target0.3
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;z \lt -4.21737202034271466 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if z < -1.1728892342568057e-27

    1. Initial program 0.2

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

    3. Applied clear-num0.3

      \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{\frac{y}{\sin y}}}}{z}\]
    4. Using strategy rm

    5. Applied div-inv0.4

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

    6. Applied add-cube-cbrt0.4

      \[\leadsto \frac{x \cdot \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{y \cdot \frac{1}{\sin y}}}{z}\]

    7. Applied times-frac0.3

      \[\leadsto \frac{x \cdot \color{blue}{\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{y} \cdot \frac{\sqrt[3]{1}}{\frac{1}{\sin y}}\right)}}{z}\]

    8. Simplified0.3

      \[\leadsto \frac{x \cdot \left(\color{blue}{\frac{1}{y}} \cdot \frac{\sqrt[3]{1}}{\frac{1}{\sin y}}\right)}{z}\]

    9. Simplified0.3

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

    if -1.1728892342568057e-27 < z < 1.3210197404489036e+187

    1. Initial program 4.8

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

    3. Applied clear-num4.9

      \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{\frac{y}{\sin y}}}}{z}\]
    4. Using strategy rm

    5. Applied associate-/l*1.2

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

    6. Simplified1.1

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

    if 1.3210197404489036e+187 < z

    1. Initial program 0.1

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

    3. Applied clear-num0.1

      \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{\frac{y}{\sin y}}}}{z}\]
    4. Using strategy rm

    5. Applied pow10.1

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

    6. Applied pow10.1

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

    7. Applied pow-prod-down0.1

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

    8. Simplified0.1

      \[\leadsto \frac{{\color{blue}{\left(\frac{x}{\frac{y}{\sin y}}\right)}}^{1}}{z}\]
    9. Using strategy rm

    10. Applied div-inv0.2

      \[\leadsto \color{blue}{{\left(\frac{x}{\frac{y}{\sin y}}\right)}^{1} \cdot \frac{1}{z}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.1728892342568057 \cdot 10^{-27}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{y} \cdot \sin y\right)}{z}\\ \mathbf{elif}\;z \le 1.32101974044890363 \cdot 10^{187}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{x}{\frac{y}{\sin y}}\right)}^{1} \cdot \frac{1}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020062 
(FPCore (x y z)
  :name "Linear.Quaternion:$ctanh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< z -4.2173720203427147e-29) (/ (* x (/ 1 (/ y (sin y)))) z) (if (< z 4.446702369113811e+64) (/ x (* z (/ y (sin y)))) (/ (* x (/ 1 (/ y (sin y)))) z)))

  (/ (* x (/ (sin y) y)) z))