Average Error: 9.3 → 0.1
Time: 22.6s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{\left(1 - t\right) \cdot 2 + \frac{2}{z}}{t} + \frac{x}{y}\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{\left(1 - t\right) \cdot 2 + \frac{2}{z}}{t} + \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r546138 = x;
        double r546139 = y;
        double r546140 = r546138 / r546139;
        double r546141 = 2.0;
        double r546142 = z;
        double r546143 = r546142 * r546141;
        double r546144 = 1.0;
        double r546145 = t;
        double r546146 = r546144 - r546145;
        double r546147 = r546143 * r546146;
        double r546148 = r546141 + r546147;
        double r546149 = r546145 * r546142;
        double r546150 = r546148 / r546149;
        double r546151 = r546140 + r546150;
        return r546151;
}
↓
double f(double x, double y, double z, double t) {
        double r546152 = 1.0;
        double r546153 = t;
        double r546154 = r546152 - r546153;
        double r546155 = 2.0;
        double r546156 = r546154 * r546155;
        double r546157 = z;
        double r546158 = r546155 / r546157;
        double r546159 = r546156 + r546158;
        double r546160 = r546159 / r546153;
        double r546161 = x;
        double r546162 = y;
        double r546163 = r546161 / r546162;
        double r546164 = r546160 + r546163;
        return r546164;
}

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

Original9.3
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.3

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019325 
(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))))