Average Error: 0.1 → 0.1
Time: 22.1s
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 r28400100 = x;
        double r28400101 = cosh(r28400100);
        double r28400102 = y;
        double r28400103 = sin(r28400102);
        double r28400104 = r28400103 / r28400102;
        double r28400105 = r28400101 * r28400104;
        return r28400105;
}
↓
double f(double x, double y) {
        double r28400106 = x;
        double r28400107 = cosh(r28400106);
        double r28400108 = y;
        double r28400109 = sin(r28400108);
        double r28400110 = r28400109 / r28400108;
        double r28400111 = r28400107 * r28400110;
        return r28400111;
}

Error

Bits error versus x

Bits error versus y

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Results

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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 2019164 
(FPCore (x y)
  :name "Linear.Quaternion:$csinh from linear-1.19.1.3"

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

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