Average Error: 9.4 → 0.1
Time: 13.7s
Precision: 64
\[\frac{x}{y} + \frac{2.0 + \left(z \cdot 2.0\right) \cdot \left(1.0 - t\right)}{t \cdot z}\]
↓
\[\left(\frac{2.0}{t} + \left(\frac{\frac{2.0}{t}}{z} + \frac{x}{y}\right)\right) - 2.0\]
\frac{x}{y} + \frac{2.0 + \left(z \cdot 2.0\right) \cdot \left(1.0 - t\right)}{t \cdot z}
↓
\left(\frac{2.0}{t} + \left(\frac{\frac{2.0}{t}}{z} + \frac{x}{y}\right)\right) - 2.0
double f(double x, double y, double z, double t) {
        double r43038795 = x;
        double r43038796 = y;
        double r43038797 = r43038795 / r43038796;
        double r43038798 = 2.0;
        double r43038799 = z;
        double r43038800 = r43038799 * r43038798;
        double r43038801 = 1.0;
        double r43038802 = t;
        double r43038803 = r43038801 - r43038802;
        double r43038804 = r43038800 * r43038803;
        double r43038805 = r43038798 + r43038804;
        double r43038806 = r43038802 * r43038799;
        double r43038807 = r43038805 / r43038806;
        double r43038808 = r43038797 + r43038807;
        return r43038808;
}
↓
double f(double x, double y, double z, double t) {
        double r43038809 = 2.0;
        double r43038810 = t;
        double r43038811 = r43038809 / r43038810;
        double r43038812 = z;
        double r43038813 = r43038811 / r43038812;
        double r43038814 = x;
        double r43038815 = y;
        double r43038816 = r43038814 / r43038815;
        double r43038817 = r43038813 + r43038816;
        double r43038818 = r43038811 + r43038817;
        double r43038819 = r43038818 - r43038809;
        return r43038819;
}

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
\[\frac{\frac{2.0}{z} + 2.0}{t} - \left(2.0 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.4

    \[\frac{x}{y} + \frac{2.0 + \left(z \cdot 2.0\right) \cdot \left(1.0 - t\right)}{t \cdot z}\]

  2. Taylor expanded around 0 0.1

    \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2.0 \cdot \frac{1}{t} + 2.0 \cdot \frac{1}{t \cdot z}\right) - 2.0\right)}\]

  3. Simplified0.1

    \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(\frac{\frac{2.0}{z}}{t} + \frac{2.0}{t}\right) - 2.0\right)}\]
  4. Using strategy rm

  5. Applied div-inv0.1

    \[\leadsto \frac{x}{y} + \left(\left(\frac{\frac{2.0}{z}}{t} + \color{blue}{2.0 \cdot \frac{1}{t}}\right) - 2.0\right)\]

  6. Applied div-inv0.1

    \[\leadsto \frac{x}{y} + \left(\left(\color{blue}{\frac{2.0}{z} \cdot \frac{1}{t}} + 2.0 \cdot \frac{1}{t}\right) - 2.0\right)\]

  7. Applied distribute-rgt-out0.1

    \[\leadsto \frac{x}{y} + \left(\color{blue}{\frac{1}{t} \cdot \left(\frac{2.0}{z} + 2.0\right)} - 2.0\right)\]
  8. Using strategy rm

  9. Applied associate-+r-0.1

    \[\leadsto \color{blue}{\left(\frac{x}{y} + \frac{1}{t} \cdot \left(\frac{2.0}{z} + 2.0\right)\right) - 2.0}\]

  10. Simplified0.1

    \[\leadsto \color{blue}{\left(\left(\frac{x}{y} + \frac{\frac{2.0}{t}}{z}\right) + \frac{2.0}{t}\right)} - 2.0\]

  11. Final simplification0.1

    \[\leadsto \left(\frac{2.0}{t} + \left(\frac{\frac{2.0}{t}}{z} + \frac{x}{y}\right)\right) - 2.0\]

Reproduce

herbie shell --seed 2019165 
(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))))