Average Error: 0.3 → 0.2
Time: 16.2s
Precision: 64
\[\left(1 \lt x \land x + 1 \lt y\right) \land \left(0 \lt z \land z \lt 2\right)\]
\[\frac{\frac{x}{y}}{z}\]
\[\frac{x}{y \cdot z}\]
\frac{\frac{x}{y}}{z}
\frac{x}{y \cdot z}
double f(double x, double y, double z) {
        double r23364907 = x;
        double r23364908 = y;
        double r23364909 = r23364907 / r23364908;
        double r23364910 = z;
        double r23364911 = r23364909 / r23364910;
        return r23364911;
}

double f(double x, double y, double z) {
        double r23364912 = x;
        double r23364913 = y;
        double r23364914 = z;
        double r23364915 = r23364913 * r23364914;
        double r23364916 = r23364912 / r23364915;
        return r23364916;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.3

    \[\frac{\frac{x}{y}}{z}\]
  2. Taylor expanded around inf 0.2

    \[\leadsto \color{blue}{\frac{x}{z \cdot y}}\]
  3. Final simplification0.2

    \[\leadsto \frac{x}{y \cdot z}\]

Reproduce

herbie shell --seed 1 
(FPCore (x y z)
  :name "(x/y)/z"
  :pre (and (and (< 1 x) (< (+ x 1) y)) (and (< 0 z) (< z 2)))
  (/ (/ x y) z))