Average Error: 2.7 → 1.6
Time: 10.4s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot \frac{\sin y}{y} \le 0.0:\\ \;\;\;\;x \cdot \frac{\frac{\sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{x}{\frac{y}{\sin y}}}{-z}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot \frac{\sin y}{y} \le 0.0:\\
\;\;\;\;x \cdot \frac{\frac{\sin y}{y}}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r566265 = x;
        double r566266 = y;
        double r566267 = sin(r566266);
        double r566268 = r566267 / r566266;
        double r566269 = r566265 * r566268;
        double r566270 = z;
        double r566271 = r566269 / r566270;
        return r566271;
}
↓
double f(double x, double y, double z) {
        double r566272 = x;
        double r566273 = y;
        double r566274 = sin(r566273);
        double r566275 = r566274 / r566273;
        double r566276 = r566272 * r566275;
        double r566277 = 0.0;
        bool r566278 = r566276 <= r566277;
        double r566279 = z;
        double r566280 = r566275 / r566279;
        double r566281 = r566272 * r566280;
        double r566282 = r566273 / r566274;
        double r566283 = r566272 / r566282;
        double r566284 = -r566283;
        double r566285 = -r566279;
        double r566286 = r566284 / r566285;
        double r566287 = r566278 ? r566281 : r566286;
        return r566287;
}

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
Herbie1.6
\[\begin{array}{l} \mathbf{if}\;z \lt -4.217372020342714661850238929213415773451 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.446702369113811028051510715777703865332 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* x (/ (sin y) y)) < 0.0

    1. Initial program 2.6

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

    3. Applied *-un-lft-identity2.6

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

    4. Applied times-frac2.8

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

    5. Simplified2.8

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

    if 0.0 < (* x (/ (sin y) y))

    1. Initial program 2.9

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

    3. Applied clear-num2.9

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

    5. Applied frac-2neg2.9

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

    6. Simplified2.9

      \[\leadsto \frac{\color{blue}{-\frac{x}{\frac{y}{\sin y}}}}{-z}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \frac{\sin y}{y} \le 0.0:\\ \;\;\;\;x \cdot \frac{\frac{\sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{x}{\frac{y}{\sin y}}}{-z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019351 +o rules:numerics
(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))