Average Error: 0.1 → 0.1
Time: 9.3s
Precision: 64
\[x \cdot \frac{\sin y}{y}\]
↓
\[\frac{\sin y}{y} \cdot x\]
x \cdot \frac{\sin y}{y}
↓
\frac{\sin y}{y} \cdot x
double f(double x, double y) {
        double r130253 = x;
        double r130254 = y;
        double r130255 = sin(r130254);
        double r130256 = r130255 / r130254;
        double r130257 = r130253 * r130256;
        return r130257;
}
↓
double f(double x, double y) {
        double r130258 = y;
        double r130259 = sin(r130258);
        double r130260 = r130259 / r130258;
        double r130261 = x;
        double r130262 = r130260 * r130261;
        return r130262;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  3. Applied *-commutative0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020042 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))