Average Error: 9.3 → 0.1
Time: 10.9s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\frac{2}{t} + \frac{\frac{2}{t}}{z}\right) - \left(2 - \frac{x}{y}\right)\]
\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(2 - \frac{x}{y}\right)
double f(double x, double y, double z, double t) {
        double r526121 = x;
        double r526122 = y;
        double r526123 = r526121 / r526122;
        double r526124 = 2.0;
        double r526125 = z;
        double r526126 = r526125 * r526124;
        double r526127 = 1.0;
        double r526128 = t;
        double r526129 = r526127 - r526128;
        double r526130 = r526126 * r526129;
        double r526131 = r526124 + r526130;
        double r526132 = r526128 * r526125;
        double r526133 = r526131 / r526132;
        double r526134 = r526123 + r526133;
        return r526134;
}
↓
double f(double x, double y, double z, double t) {
        double r526135 = 2.0;
        double r526136 = t;
        double r526137 = r526135 / r526136;
        double r526138 = z;
        double r526139 = r526137 / r526138;
        double r526140 = r526137 + r526139;
        double r526141 = x;
        double r526142 = y;
        double r526143 = r526141 / r526142;
        double r526144 = r526135 - r526143;
        double r526145 = r526140 - r526144;
        return r526145;
}

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

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

  3. Taylor expanded around 0 0.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020042 
(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))))