Average Error: 0.1 → 0.1
Time: 3.5s
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 r115498 = x;
        double r115499 = y;
        double r115500 = sin(r115499);
        double r115501 = r115500 / r115499;
        double r115502 = r115498 * r115501;
        return r115502;
}
↓
double f(double x, double y) {
        double r115503 = y;
        double r115504 = sin(r115503);
        double r115505 = r115504 / r115503;
        double r115506 = x;
        double r115507 = r115505 * r115506;
        return r115507;
}

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 2020062 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))