Average Error: 9.4 → 0.1
Time: 4.0s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(1 \cdot \frac{\frac{2}{z} + 2}{t} - 2\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(1 \cdot \frac{\frac{2}{z} + 2}{t} - 2\right)
double f(double x, double y, double z, double t) {
        double r717130 = x;
        double r717131 = y;
        double r717132 = r717130 / r717131;
        double r717133 = 2.0;
        double r717134 = z;
        double r717135 = r717134 * r717133;
        double r717136 = 1.0;
        double r717137 = t;
        double r717138 = r717136 - r717137;
        double r717139 = r717135 * r717138;
        double r717140 = r717133 + r717139;
        double r717141 = r717137 * r717134;
        double r717142 = r717140 / r717141;
        double r717143 = r717132 + r717142;
        return r717143;
}
↓
double f(double x, double y, double z, double t) {
        double r717144 = x;
        double r717145 = y;
        double r717146 = r717144 / r717145;
        double r717147 = 1.0;
        double r717148 = 2.0;
        double r717149 = z;
        double r717150 = r717148 / r717149;
        double r717151 = r717150 + r717148;
        double r717152 = t;
        double r717153 = r717151 / r717152;
        double r717154 = r717147 * r717153;
        double r717155 = r717154 - r717148;
        double r717156 = r717146 + r717155;
        return r717156;
}

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

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

  5. Applied *-un-lft-identity0.1

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

  6. Applied *-un-lft-identity0.1

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

  7. Applied times-frac0.1

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

  8. Applied associate-*l*0.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2020083 
(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))))