Average Error: 0.0 → 0.0
Time: 14.9s
Precision: 64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\sqrt{\frac{\sinh y}{y}} \cdot \left(\sqrt{\frac{\sinh y}{y}} \cdot \cos x\right)\]
\cos x \cdot \frac{\sinh y}{y}
↓
\sqrt{\frac{\sinh y}{y}} \cdot \left(\sqrt{\frac{\sinh y}{y}} \cdot \cos x\right)
double f(double x, double y) {
        double r6400507 = x;
        double r6400508 = cos(r6400507);
        double r6400509 = y;
        double r6400510 = sinh(r6400509);
        double r6400511 = r6400510 / r6400509;
        double r6400512 = r6400508 * r6400511;
        return r6400512;
}
↓
double f(double x, double y) {
        double r6400513 = y;
        double r6400514 = sinh(r6400513);
        double r6400515 = r6400514 / r6400513;
        double r6400516 = sqrt(r6400515);
        double r6400517 = x;
        double r6400518 = cos(r6400517);
        double r6400519 = r6400516 * r6400518;
        double r6400520 = r6400516 * r6400519;
        return r6400520;
}

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. Applied associate-*r*0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  (* (cos x) (/ (sinh y) y)))