Average Error: 2.6 → 2.7
Time: 11.8s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\frac{\frac{\sin y}{y}}{z} \cdot x\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\frac{\frac{\sin y}{y}}{z} \cdot x
double f(double x, double y, double z) {
        double r312285 = x;
        double r312286 = y;
        double r312287 = sin(r312286);
        double r312288 = r312287 / r312286;
        double r312289 = r312285 * r312288;
        double r312290 = z;
        double r312291 = r312289 / r312290;
        return r312291;
}
↓
double f(double x, double y, double z) {
        double r312292 = y;
        double r312293 = sin(r312292);
        double r312294 = r312293 / r312292;
        double r312295 = z;
        double r312296 = r312294 / r312295;
        double r312297 = x;
        double r312298 = r312296 * r312297;
        return r312298;
}

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

Original2.6
Target0.3
Herbie2.7
\[\begin{array}{l} \mathbf{if}\;z \lt -4.217372020342714661850238929213415773451 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.446702369113811028051510715777703865332 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Initial program 2.6

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

  3. Applied clear-num2.7

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

  5. Applied clear-num3.1

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

  6. Simplified3.4

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

  7. Final simplification2.7

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

Reproduce

herbie shell --seed 2019304 
(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))