Average Error: 0.1 → 0.1
Time: 12.5s
Precision: 64
\[x \cdot \frac{\sin y}{y}\]
↓
\[\frac{x}{\frac{y}{\sin y}}\]
x \cdot \frac{\sin y}{y}
↓
\frac{x}{\frac{y}{\sin y}}
double f(double x, double y) {
        double r130805 = x;
        double r130806 = y;
        double r130807 = sin(r130806);
        double r130808 = r130807 / r130806;
        double r130809 = r130805 * r130808;
        return r130809;
}
↓
double f(double x, double y) {
        double r130810 = x;
        double r130811 = y;
        double r130812 = sin(r130811);
        double r130813 = r130811 / r130812;
        double r130814 = r130810 / r130813;
        return r130814;
}

Error

Bits error versus x

Bits error versus y

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Results

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Derivation

  1. Initial program 0.1

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

  2. Simplified0.1

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

  4. Applied clear-num0.2

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

  6. Applied *-un-lft-identity0.2

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

  7. Applied *-un-lft-identity0.2

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

  8. Applied times-frac0.2

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

  9. Applied associate-*l*0.2

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

  10. Simplified0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  (* x (/ (sin y) y)))