Average Error: 9.3 → 0.1
Time: 14.4s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\left(\frac{\frac{2}{z}}{t} + \frac{2}{t}\right) - 2\right) + \frac{x}{y}\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\left(\frac{\frac{2}{z}}{t} + \frac{2}{t}\right) - 2\right) + \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r687098 = x;
        double r687099 = y;
        double r687100 = r687098 / r687099;
        double r687101 = 2.0;
        double r687102 = z;
        double r687103 = r687102 * r687101;
        double r687104 = 1.0;
        double r687105 = t;
        double r687106 = r687104 - r687105;
        double r687107 = r687103 * r687106;
        double r687108 = r687101 + r687107;
        double r687109 = r687105 * r687102;
        double r687110 = r687108 / r687109;
        double r687111 = r687100 + r687110;
        return r687111;
}
↓
double f(double x, double y, double z, double t) {
        double r687112 = 2.0;
        double r687113 = z;
        double r687114 = r687112 / r687113;
        double r687115 = t;
        double r687116 = r687114 / r687115;
        double r687117 = r687112 / r687115;
        double r687118 = r687116 + r687117;
        double r687119 = r687118 - r687112;
        double r687120 = x;
        double r687121 = y;
        double r687122 = r687120 / r687121;
        double r687123 = r687119 + r687122;
        return r687123;
}

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. 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

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

  5. Applied associate-+r-0.1

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019194 
(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))))