Average Error: 0.0 → 0.0
Time: 25.1s
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 r154025 = x;
        double r154026 = cos(r154025);
        double r154027 = y;
        double r154028 = sinh(r154027);
        double r154029 = r154028 / r154027;
        double r154030 = r154026 * r154029;
        return r154030;
}
↓
double f(double x, double y) {
        double r154031 = x;
        double r154032 = cos(r154031);
        double r154033 = y;
        double r154034 = sinh(r154033);
        double r154035 = r154034 / r154033;
        double r154036 = sqrt(r154035);
        double r154037 = r154036 * r154036;
        double r154038 = r154032 * r154037;
        return r154038;
}

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 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 2020047 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))