Average Error: 8.9 → 0.1
Time: 15.9s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\frac{2}{t} + \left(\frac{\frac{2}{t}}{z} - 2\right)\right) + \frac{x}{y}\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\frac{2}{t} + \left(\frac{\frac{2}{t}}{z} - 2\right)\right) + \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r23532759 = x;
        double r23532760 = y;
        double r23532761 = r23532759 / r23532760;
        double r23532762 = 2.0;
        double r23532763 = z;
        double r23532764 = r23532763 * r23532762;
        double r23532765 = 1.0;
        double r23532766 = t;
        double r23532767 = r23532765 - r23532766;
        double r23532768 = r23532764 * r23532767;
        double r23532769 = r23532762 + r23532768;
        double r23532770 = r23532766 * r23532763;
        double r23532771 = r23532769 / r23532770;
        double r23532772 = r23532761 + r23532771;
        return r23532772;
}
↓
double f(double x, double y, double z, double t) {
        double r23532773 = 2.0;
        double r23532774 = t;
        double r23532775 = r23532773 / r23532774;
        double r23532776 = z;
        double r23532777 = r23532775 / r23532776;
        double r23532778 = r23532777 - r23532773;
        double r23532779 = r23532775 + r23532778;
        double r23532780 = x;
        double r23532781 = y;
        double r23532782 = r23532780 / r23532781;
        double r23532783 = r23532779 + r23532782;
        return r23532783;
}

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

Original8.9
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 8.9

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

  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

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019171 
(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))))