Average Error: 2.7 → 3.0
Time: 12.0s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\frac{\frac{x}{z}}{\frac{y}{\sin y}}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\frac{\frac{x}{z}}{\frac{y}{\sin y}}
double f(double x, double y, double z) {
        double r638439 = x;
        double r638440 = y;
        double r638441 = sin(r638440);
        double r638442 = r638441 / r638440;
        double r638443 = r638439 * r638442;
        double r638444 = z;
        double r638445 = r638443 / r638444;
        return r638445;
}
↓
double f(double x, double y, double z) {
        double r638446 = x;
        double r638447 = z;
        double r638448 = r638446 / r638447;
        double r638449 = y;
        double r638450 = sin(r638449);
        double r638451 = r638449 / r638450;
        double r638452 = r638448 / r638451;
        return r638452;
}

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
Herbie3.0
\[\begin{array}{l} \mathbf{if}\;z \lt -4.21737202034271466 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Initial program 2.7

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

  3. Applied associate-/l*3.0

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

  4. Simplified3.0

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

  6. Applied associate-/r*3.0

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

  7. Final simplification3.0

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

Reproduce

herbie shell --seed 2020042 +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))