Average Error: 9.4 → 0.1
Time: 14.3s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\left(\frac{2}{t} - 2\right) + \frac{\frac{2}{z}}{t}\right) + \frac{x}{y}\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\left(\frac{2}{t} - 2\right) + \frac{\frac{2}{z}}{t}\right) + \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r524763 = x;
        double r524764 = y;
        double r524765 = r524763 / r524764;
        double r524766 = 2.0;
        double r524767 = z;
        double r524768 = r524767 * r524766;
        double r524769 = 1.0;
        double r524770 = t;
        double r524771 = r524769 - r524770;
        double r524772 = r524768 * r524771;
        double r524773 = r524766 + r524772;
        double r524774 = r524770 * r524767;
        double r524775 = r524773 / r524774;
        double r524776 = r524765 + r524775;
        return r524776;
}
↓
double f(double x, double y, double z, double t) {
        double r524777 = 2.0;
        double r524778 = t;
        double r524779 = r524777 / r524778;
        double r524780 = r524779 - r524777;
        double r524781 = z;
        double r524782 = r524777 / r524781;
        double r524783 = r524782 / r524778;
        double r524784 = r524780 + r524783;
        double r524785 = x;
        double r524786 = y;
        double r524787 = r524785 / r524786;
        double r524788 = r524784 + r524787;
        return r524788;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original9.4
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.4

    \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]

  2. Taylor expanded around 0 0.1

    \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right) - 2\right)}\]

  3. Simplified0.1

    \[\leadsto \frac{x}{y} + \color{blue}{\left(\frac{\frac{2}{t}}{z} + \left(\frac{2}{t} - 2\right)\right)}\]
  4. Using strategy rm

  5. Applied div-inv0.1

    \[\leadsto \frac{x}{y} + \left(\color{blue}{\frac{2}{t} \cdot \frac{1}{z}} + \left(\frac{2}{t} - 2\right)\right)\]
  6. Using strategy rm

  7. Applied associate-*l/0.1

    \[\leadsto \frac{x}{y} + \left(\color{blue}{\frac{2 \cdot \frac{1}{z}}{t}} + \left(\frac{2}{t} - 2\right)\right)\]

  8. Simplified0.1

    \[\leadsto \frac{x}{y} + \left(\frac{\color{blue}{\frac{2}{z}}}{t} + \left(\frac{2}{t} - 2\right)\right)\]

  9. Final simplification0.1

    \[\leadsto \left(\left(\frac{2}{t} - 2\right) + \frac{\frac{2}{z}}{t}\right) + \frac{x}{y}\]

Reproduce

herbie shell --seed 2019196 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"

  :herbie-target
  (- (/ (+ (/ 2.0 z) 2.0) t) (- 2.0 (/ x y)))

  (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))