Average Error: 2.6 → 3.4
Time: 19.3s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\frac{1}{\frac{\frac{z}{x}}{\frac{\sin y}{y}}}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\frac{1}{\frac{\frac{z}{x}}{\frac{\sin y}{y}}}
double f(double x, double y, double z) {
        double r384563 = x;
        double r384564 = y;
        double r384565 = sin(r384564);
        double r384566 = r384565 / r384564;
        double r384567 = r384563 * r384566;
        double r384568 = z;
        double r384569 = r384567 / r384568;
        return r384569;
}
↓
double f(double x, double y, double z) {
        double r384570 = 1.0;
        double r384571 = z;
        double r384572 = x;
        double r384573 = r384571 / r384572;
        double r384574 = y;
        double r384575 = sin(r384574);
        double r384576 = r384575 / r384574;
        double r384577 = r384573 / r384576;
        double r384578 = r384570 / r384577;
        return r384578;
}

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
Herbie3.4
\[\begin{array}{l} \mathbf{if}\;z \lt -4.217372020342714661850238929213415773451 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.446702369113811028051510715777703865332 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Initial program 2.6

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

  3. Applied div-inv2.7

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

  5. Applied clear-num3.1

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

  6. Simplified3.4

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

  7. Final simplification3.4

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

Reproduce

herbie shell --seed 2019304 +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))