Average Error: 0.1 → 0.1
Time: 4.9s
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 r590122 = x;
        double r590123 = cosh(r590122);
        double r590124 = y;
        double r590125 = sin(r590124);
        double r590126 = r590125 / r590124;
        double r590127 = r590123 * r590126;
        return r590127;
}
↓
double f(double x, double y) {
        double r590128 = x;
        double r590129 = cosh(r590128);
        double r590130 = y;
        double r590131 = sin(r590130);
        double r590132 = r590131 / r590130;
        double r590133 = r590129 * r590132;
        return r590133;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

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. Using strategy rm

  3. Applied clear-num0.2

    \[\leadsto \cosh x \cdot \color{blue}{\frac{1}{\frac{y}{\sin y}}}\]

  4. Taylor expanded around inf 0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020083 +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)))