Average Error: 2.7 → 0.2
Time: 5.1s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot \frac{\sin y}{y} \le -4.5545988867587666 \cdot 10^{-295}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;x \cdot \frac{\sin y}{y} \le 7.56936427636939772 \cdot 10^{-202}:\\ \;\;\;\;x \cdot \frac{\frac{\sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1}}{\frac{\frac{1}{\sin y}}{\frac{\sqrt[3]{1}}{y}}}}{z}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot \frac{\sin y}{y} \le -4.5545988867587666 \cdot 10^{-295}:\\
\;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\

\mathbf{elif}\;x \cdot \frac{\sin y}{y} \le 7.56936427636939772 \cdot 10^{-202}:\\
\;\;\;\;x \cdot \frac{\frac{\sin y}{y}}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot \frac{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1}}{\frac{\frac{1}{\sin y}}{\frac{\sqrt[3]{1}}{y}}}}{z}\\

\end{array}
double f(double x, double y, double z) {
        double r425492 = x;
        double r425493 = y;
        double r425494 = sin(r425493);
        double r425495 = r425494 / r425493;
        double r425496 = r425492 * r425495;
        double r425497 = z;
        double r425498 = r425496 / r425497;
        return r425498;
}
↓
double f(double x, double y, double z) {
        double r425499 = x;
        double r425500 = y;
        double r425501 = sin(r425500);
        double r425502 = r425501 / r425500;
        double r425503 = r425499 * r425502;
        double r425504 = -4.554598886758767e-295;
        bool r425505 = r425503 <= r425504;
        double r425506 = 1.0;
        double r425507 = r425500 / r425501;
        double r425508 = r425506 / r425507;
        double r425509 = r425499 * r425508;
        double r425510 = z;
        double r425511 = r425509 / r425510;
        double r425512 = 7.569364276369398e-202;
        bool r425513 = r425503 <= r425512;
        double r425514 = r425502 / r425510;
        double r425515 = r425499 * r425514;
        double r425516 = cbrt(r425506);
        double r425517 = r425516 * r425516;
        double r425518 = r425517 / r425506;
        double r425519 = r425506 / r425501;
        double r425520 = r425516 / r425500;
        double r425521 = r425519 / r425520;
        double r425522 = r425518 / r425521;
        double r425523 = r425499 * r425522;
        double r425524 = r425523 / r425510;
        double r425525 = r425513 ? r425515 : r425524;
        double r425526 = r425505 ? r425511 : r425525;
        return r425526;
}

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

Original2.7
Target0.3
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;z \lt -4.21737202034271466 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* x (/ (sin y) y)) < -4.554598886758767e-295

    1. Initial program 0.2

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

    3. Applied clear-num0.2

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

    if -4.554598886758767e-295 < (* x (/ (sin y) y)) < 7.569364276369398e-202

    1. Initial program 10.7

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

    3. Applied *-un-lft-identity10.7

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

    4. Applied times-frac0.3

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

    5. Simplified0.3

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

    if 7.569364276369398e-202 < (* x (/ (sin y) y))

    1. Initial program 0.2

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

    3. Applied clear-num0.2

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

    5. Applied div-inv0.3

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

    6. Applied associate-/r*0.2

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

    8. Applied *-un-lft-identity0.2

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

    9. Applied add-cube-cbrt0.2

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

    10. Applied times-frac0.2

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

    11. Applied associate-/l*0.3

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \frac{\sin y}{y} \le -4.5545988867587666 \cdot 10^{-295}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;x \cdot \frac{\sin y}{y} \le 7.56936427636939772 \cdot 10^{-202}:\\ \;\;\;\;x \cdot \frac{\frac{\sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1}}{\frac{\frac{1}{\sin y}}{\frac{\sqrt[3]{1}}{y}}}}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020021 
(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))