Average Error: 2.8 → 1.7
Time: 13.6s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot \frac{\sin y}{y} \le 2.083597813045566445531085328327042967006 \cdot 10^{-202}:\\ \;\;\;\;x \cdot \frac{\frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(\sin y \cdot \frac{1}{y}\right)}{z}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot \frac{\sin y}{y} \le 2.083597813045566445531085328327042967006 \cdot 10^{-202}:\\
\;\;\;\;x \cdot \frac{\frac{1}{\frac{y}{\sin y}}}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r311993 = x;
        double r311994 = y;
        double r311995 = sin(r311994);
        double r311996 = r311995 / r311994;
        double r311997 = r311993 * r311996;
        double r311998 = z;
        double r311999 = r311997 / r311998;
        return r311999;
}
↓
double f(double x, double y, double z) {
        double r312000 = x;
        double r312001 = y;
        double r312002 = sin(r312001);
        double r312003 = r312002 / r312001;
        double r312004 = r312000 * r312003;
        double r312005 = 2.0835978130455664e-202;
        bool r312006 = r312004 <= r312005;
        double r312007 = 1.0;
        double r312008 = r312001 / r312002;
        double r312009 = r312007 / r312008;
        double r312010 = z;
        double r312011 = r312009 / r312010;
        double r312012 = r312000 * r312011;
        double r312013 = r312007 / r312001;
        double r312014 = r312002 * r312013;
        double r312015 = r312000 * r312014;
        double r312016 = r312015 / r312010;
        double r312017 = r312006 ? r312012 : r312016;
        return r312017;
}

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

Original2.8
Target0.3
Herbie1.7
\[\begin{array}{l} \mathbf{if}\;z \lt -4.217372020342714661850238929213415773451 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.446702369113811028051510715777703865332 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* x (/ (sin y) y)) < 2.0835978130455664e-202

    1. Initial program 4.2

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

    3. Applied *-un-lft-identity4.2

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

    4. Applied times-frac2.4

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

    5. Simplified2.4

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

    7. Applied clear-num2.4

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

    if 2.0835978130455664e-202 < (* x (/ (sin y) y))

    1. Initial program 0.2

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

    3. Applied div-inv0.2

      \[\leadsto \frac{x \cdot \color{blue}{\left(\sin y \cdot \frac{1}{y}\right)}}{z}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \frac{\sin y}{y} \le 2.083597813045566445531085328327042967006 \cdot 10^{-202}:\\ \;\;\;\;x \cdot \frac{\frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(\sin y \cdot \frac{1}{y}\right)}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019208 
(FPCore (x y z)
  :name "Linear.Quaternion:$ctanh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< z -4.21737202034271466e-29) (/ (* x (/ 1 (/ y (sin y)))) z) (if (< z 4.44670236911381103e64) (/ x (* z (/ y (sin y)))) (/ (* x (/ 1 (/ y (sin y)))) z)))

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