Average Error: 0.0 → 0.0
Time: 34.7s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\frac{\sinh y}{y} \cdot \sin x\]
\sin x \cdot \frac{\sinh y}{y}
↓
\frac{\sinh y}{y} \cdot \sin x
double f(double x, double y) {
        double r168173 = x;
        double r168174 = sin(r168173);
        double r168175 = y;
        double r168176 = sinh(r168175);
        double r168177 = r168176 / r168175;
        double r168178 = r168174 * r168177;
        return r168178;
}
↓
double f(double x, double y) {
        double r168179 = y;
        double r168180 = sinh(r168179);
        double r168181 = r168180 / r168179;
        double r168182 = x;
        double r168183 = sin(r168182);
        double r168184 = r168181 * r168183;
        return r168184;
}

Error

Bits error versus x

Bits error versus y

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Results

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Derivation

  1. Initial program 0.0

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

  3. Applied *-commutative0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))