Average Error: 2.7 → 1.7
Time: 15.1s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot \frac{\sin y}{y} \le -1.371660816435320975638711159936380278311 \cdot 10^{-137}:\\ \;\;\;\;\frac{x \cdot \left(\sin y \cdot \frac{1}{y}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot \frac{\sin y}{y} \le -1.371660816435320975638711159936380278311 \cdot 10^{-137}:\\
\;\;\;\;\frac{x \cdot \left(\sin y \cdot \frac{1}{y}\right)}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\

\end{array}
double f(double x, double y, double z) {
        double r261635 = x;
        double r261636 = y;
        double r261637 = sin(r261636);
        double r261638 = r261637 / r261636;
        double r261639 = r261635 * r261638;
        double r261640 = z;
        double r261641 = r261639 / r261640;
        return r261641;
}
↓
double f(double x, double y, double z) {
        double r261642 = x;
        double r261643 = y;
        double r261644 = sin(r261643);
        double r261645 = r261644 / r261643;
        double r261646 = r261642 * r261645;
        double r261647 = -1.371660816435321e-137;
        bool r261648 = r261646 <= r261647;
        double r261649 = 1.0;
        double r261650 = r261649 / r261643;
        double r261651 = r261644 * r261650;
        double r261652 = r261642 * r261651;
        double r261653 = z;
        double r261654 = r261652 / r261653;
        double r261655 = r261653 / r261645;
        double r261656 = r261642 / r261655;
        double r261657 = r261648 ? r261654 : r261656;
        return r261657;
}

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
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)) < -1.371660816435321e-137

    1. Initial program 0.2

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

    3. Applied div-inv0.3

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

    if -1.371660816435321e-137 < (* x (/ (sin y) y))

    1. Initial program 3.6

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

    3. Applied associate-/l*2.2

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

    5. Applied pow12.2

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

  4. Final simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \frac{\sin y}{y} \le -1.371660816435320975638711159936380278311 \cdot 10^{-137}:\\ \;\;\;\;\frac{x \cdot \left(\sin y \cdot \frac{1}{y}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019212 +o rules:numerics
(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))