Average Error: 0.0 → 0.0
Time: 18.4s
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 r167836 = x;
        double r167837 = cos(r167836);
        double r167838 = y;
        double r167839 = sinh(r167838);
        double r167840 = r167839 / r167838;
        double r167841 = r167837 * r167840;
        return r167841;
}
↓
double f(double x, double y) {
        double r167842 = x;
        double r167843 = cos(r167842);
        double r167844 = 1.0;
        double r167845 = y;
        double r167846 = r167844 / r167845;
        double r167847 = sinh(r167845);
        double r167848 = r167844 / r167847;
        double r167849 = r167846 / r167848;
        double r167850 = r167843 * r167849;
        return r167850;
}

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 0.0

    \[\cos x \cdot \frac{\sinh y}{y}\]
  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)))