Average Error: 0.1 → 0.1
Time: 7.8s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\cosh x \cdot \frac{\sin y}{y}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\cosh x \cdot \frac{\sin y}{y}
double f(double x, double y) {
        double r531016 = x;
        double r531017 = cosh(r531016);
        double r531018 = y;
        double r531019 = sin(r531018);
        double r531020 = r531019 / r531018;
        double r531021 = r531017 * r531020;
        return r531021;
}
↓
double f(double x, double y) {
        double r531022 = x;
        double r531023 = cosh(r531022);
        double r531024 = y;
        double r531025 = sin(r531024);
        double r531026 = r531025 / r531024;
        double r531027 = r531023 * r531026;
        return r531027;
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.1
\[\frac{\cosh x \cdot \sin y}{y}\]

Derivation

  1. Initial program 0.1

    \[\cosh x \cdot \frac{\sin y}{y}\]

  2. Final simplification0.1

    \[\leadsto \cosh x \cdot \frac{\sin y}{y}\]

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csinh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (/ (* (cosh x) (sin y)) y)

  (* (cosh x) (/ (sin y) y)))