Average Error: 0.0 → 0.0
Time: 5.9s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\frac{\sin x}{\frac{y}{\sinh y}}\]
\sin x \cdot \frac{\sinh y}{y}
↓
\frac{\sin x}{\frac{y}{\sinh y}}
double f(double x, double y) {
        double r217144 = x;
        double r217145 = sin(r217144);
        double r217146 = y;
        double r217147 = sinh(r217146);
        double r217148 = r217147 / r217146;
        double r217149 = r217145 * r217148;
        return r217149;
}
↓
double f(double x, double y) {
        double r217150 = x;
        double r217151 = sin(r217150);
        double r217152 = y;
        double r217153 = sinh(r217152);
        double r217154 = r217152 / r217153;
        double r217155 = r217151 / r217154;
        return r217155;
}

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 clear-num0.0

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

  5. Applied *-un-lft-identity0.0

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

  6. Applied associate-*l*0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020081 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))