Average Error: 9.0 → 0.1
Time: 22.7s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\frac{2}{t} + \frac{\frac{2}{t}}{z}\right) + \left(\frac{x}{y} - 2\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\frac{2}{t} + \frac{\frac{2}{t}}{z}\right) + \left(\frac{x}{y} - 2\right)
double f(double x, double y, double z, double t) {
        double r546848 = x;
        double r546849 = y;
        double r546850 = r546848 / r546849;
        double r546851 = 2.0;
        double r546852 = z;
        double r546853 = r546852 * r546851;
        double r546854 = 1.0;
        double r546855 = t;
        double r546856 = r546854 - r546855;
        double r546857 = r546853 * r546856;
        double r546858 = r546851 + r546857;
        double r546859 = r546855 * r546852;
        double r546860 = r546858 / r546859;
        double r546861 = r546850 + r546860;
        return r546861;
}
↓
double f(double x, double y, double z, double t) {
        double r546862 = 2.0;
        double r546863 = t;
        double r546864 = r546862 / r546863;
        double r546865 = z;
        double r546866 = r546864 / r546865;
        double r546867 = r546864 + r546866;
        double r546868 = x;
        double r546869 = y;
        double r546870 = r546868 / r546869;
        double r546871 = r546870 - r546862;
        double r546872 = r546867 + r546871;
        return r546872;
}

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

Original9.0
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.0

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

  2. Simplified0.1

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

  3. Taylor expanded around 0 0.1

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

  4. Simplified0.1

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

  6. Applied associate-/r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :herbie-target
  (- (/ (+ (/ 2 z) 2) t) (- 2 (/ x y)))

  (+ (/ x y) (/ (+ 2 (* (* z 2) (- 1 t))) (* t z))))