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 r641267 = x;
        double r641268 = y;
        double r641269 = sin(r641268);
        double r641270 = r641269 / r641268;
        double r641271 = r641267 * r641270;
        double r641272 = z;
        double r641273 = r641271 / r641272;
        return r641273;
}
↓
double f(double x, double y, double z) {
        double r641274 = x;
        double r641275 = z;
        double r641276 = r641274 / r641275;
        double r641277 = y;
        double r641278 = sin(r641277);
        double r641279 = r641277 / r641278;
        double r641280 = r641276 / r641279;
        return r641280;
}

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))