Average Error: 9.4 → 0.1
Time: 28.2s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\frac{2}{t} + \left(\frac{\frac{2}{z}}{t} - 2\right)\right) + \frac{x}{y}\]
\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}{z}}{t} - 2\right)\right) + \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r40327072 = x;
        double r40327073 = y;
        double r40327074 = r40327072 / r40327073;
        double r40327075 = 2.0;
        double r40327076 = z;
        double r40327077 = r40327076 * r40327075;
        double r40327078 = 1.0;
        double r40327079 = t;
        double r40327080 = r40327078 - r40327079;
        double r40327081 = r40327077 * r40327080;
        double r40327082 = r40327075 + r40327081;
        double r40327083 = r40327079 * r40327076;
        double r40327084 = r40327082 / r40327083;
        double r40327085 = r40327074 + r40327084;
        return r40327085;
}
↓
double f(double x, double y, double z, double t) {
        double r40327086 = 2.0;
        double r40327087 = t;
        double r40327088 = r40327086 / r40327087;
        double r40327089 = z;
        double r40327090 = r40327086 / r40327089;
        double r40327091 = r40327090 / r40327087;
        double r40327092 = r40327091 - r40327086;
        double r40327093 = r40327088 + r40327092;
        double r40327094 = x;
        double r40327095 = y;
        double r40327096 = r40327094 / r40327095;
        double r40327097 = r40327093 + r40327096;
        return r40327097;
}

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

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

  4. Taylor expanded around 0 0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019168 
(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))))