Average Error: 9.4 → 0.1
Time: 13.1s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(\left(\frac{\frac{2}{t}}{z} + \frac{2}{t}\right) - 2\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(\left(\frac{\frac{2}{t}}{z} + \frac{2}{t}\right) - 2\right)
double f(double x, double y, double z, double t) {
        double r618152 = x;
        double r618153 = y;
        double r618154 = r618152 / r618153;
        double r618155 = 2.0;
        double r618156 = z;
        double r618157 = r618156 * r618155;
        double r618158 = 1.0;
        double r618159 = t;
        double r618160 = r618158 - r618159;
        double r618161 = r618157 * r618160;
        double r618162 = r618155 + r618161;
        double r618163 = r618159 * r618156;
        double r618164 = r618162 / r618163;
        double r618165 = r618154 + r618164;
        return r618165;
}
↓
double f(double x, double y, double z, double t) {
        double r618166 = x;
        double r618167 = y;
        double r618168 = r618166 / r618167;
        double r618169 = 2.0;
        double r618170 = t;
        double r618171 = r618169 / r618170;
        double r618172 = z;
        double r618173 = r618171 / r618172;
        double r618174 = r618173 + r618171;
        double r618175 = r618174 - r618169;
        double r618176 = r618168 + r618175;
        return r618176;
}

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

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

  3. Simplified0.1

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

  5. Applied associate-/r*0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019235 
(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))))