Average Error: 0.0 → 0.0
Time: 25.0s
Precision: 64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\cos x \cdot \left(\sqrt{\frac{\sinh y}{y}} \cdot \sqrt{\frac{\sinh y}{y}}\right)\]
\cos x \cdot \frac{\sinh y}{y}
↓
\cos x \cdot \left(\sqrt{\frac{\sinh y}{y}} \cdot \sqrt{\frac{\sinh y}{y}}\right)
double f(double x, double y) {
        double r94026 = x;
        double r94027 = cos(r94026);
        double r94028 = y;
        double r94029 = sinh(r94028);
        double r94030 = r94029 / r94028;
        double r94031 = r94027 * r94030;
        return r94031;
}
↓
double f(double x, double y) {
        double r94032 = x;
        double r94033 = cos(r94032);
        double r94034 = y;
        double r94035 = sinh(r94034);
        double r94036 = r94035 / r94034;
        double r94037 = sqrt(r94036);
        double r94038 = r94037 * r94037;
        double r94039 = r94033 * r94038;
        return r94039;
}

Error

Bits error versus x

Bits error versus y

Try it out

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 add-sqr-sqrt0.0

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

  4. Final simplification0.0

    \[\leadsto \cos x \cdot \left(\sqrt{\frac{\sinh y}{y}} \cdot \sqrt{\frac{\sinh y}{y}}\right)\]

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))