Average Error: 0.1 → 0.2
Time: 5.3s
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 r555144 = x;
        double r555145 = cosh(r555144);
        double r555146 = y;
        double r555147 = sin(r555146);
        double r555148 = r555147 / r555146;
        double r555149 = r555145 * r555148;
        return r555149;
}
↓
double f(double x, double y) {
        double r555150 = x;
        double r555151 = cosh(r555150);
        double r555152 = sqrt(r555151);
        double r555153 = y;
        double r555154 = sin(r555153);
        double r555155 = r555154 / r555153;
        double r555156 = r555152 * r555155;
        double r555157 = r555152 * r555156;
        return r555157;
}

Error

Bits error versus x

Bits error versus y

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Results

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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 
(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)))