Average Error: 0.0 → 0.0
Time: 28.0s
Precision: 64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\cos x \cdot \frac{\frac{1}{y}}{\frac{1}{\sinh y}}\]
\cos x \cdot \frac{\sinh y}{y}
↓
\cos x \cdot \frac{\frac{1}{y}}{\frac{1}{\sinh y}}
double f(double x, double y) {
        double r149217 = x;
        double r149218 = cos(r149217);
        double r149219 = y;
        double r149220 = sinh(r149219);
        double r149221 = r149220 / r149219;
        double r149222 = r149218 * r149221;
        return r149222;
}
↓
double f(double x, double y) {
        double r149223 = x;
        double r149224 = cos(r149223);
        double r149225 = 1.0;
        double r149226 = y;
        double r149227 = r149225 / r149226;
        double r149228 = sinh(r149226);
        double r149229 = r149225 / r149228;
        double r149230 = r149227 / r149229;
        double r149231 = r149224 * r149230;
        return r149231;
}

Error

Bits error versus x

Bits error versus y

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Results

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Derivation

  1. Initial program 0.0

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

  3. Applied clear-num0.0

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

  5. Applied div-inv0.2

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

  6. Applied associate-/r*0.0

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

  7. Final simplification0.0

    \[\leadsto \cos x \cdot \frac{\frac{1}{y}}{\frac{1}{\sinh y}}\]

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))