Average Error: 0.1 → 0.2
Time: 5.6s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\sqrt{\cosh x} \cdot \left(\sqrt{\cosh x} \cdot \frac{\sin y}{y}\right)\]
\cosh x \cdot \frac{\sin y}{y}
↓
\sqrt{\cosh x} \cdot \left(\sqrt{\cosh x} \cdot \frac{\sin y}{y}\right)
double f(double x, double y) {
        double r458019 = x;
        double r458020 = cosh(r458019);
        double r458021 = y;
        double r458022 = sin(r458021);
        double r458023 = r458022 / r458021;
        double r458024 = r458020 * r458023;
        return r458024;
}
↓
double f(double x, double y) {
        double r458025 = x;
        double r458026 = cosh(r458025);
        double r458027 = sqrt(r458026);
        double r458028 = y;
        double r458029 = sin(r458028);
        double r458030 = r458029 / r458028;
        double r458031 = r458027 * r458030;
        double r458032 = r458027 * r458031;
        return r458032;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.2
\[\frac{\cosh x \cdot \sin y}{y}\]

Derivation

  1. Initial program 0.1

    \[\cosh x \cdot \frac{\sin y}{y}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.2

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

  4. Applied associate-*l*0.2

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

  5. Final simplification0.2

    \[\leadsto \sqrt{\cosh x} \cdot \left(\sqrt{\cosh x} \cdot \frac{\sin y}{y}\right)\]

Reproduce

herbie shell --seed 2020020 +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)))