Average Error: 9.3 → 0.1
Time: 16.0s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\frac{\frac{2}{t}}{z} + \left(\frac{2}{t} - 2\right)\right) + \frac{x}{y}\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\frac{\frac{2}{t}}{z} + \left(\frac{2}{t} - 2\right)\right) + \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r35678023 = x;
        double r35678024 = y;
        double r35678025 = r35678023 / r35678024;
        double r35678026 = 2.0;
        double r35678027 = z;
        double r35678028 = r35678027 * r35678026;
        double r35678029 = 1.0;
        double r35678030 = t;
        double r35678031 = r35678029 - r35678030;
        double r35678032 = r35678028 * r35678031;
        double r35678033 = r35678026 + r35678032;
        double r35678034 = r35678030 * r35678027;
        double r35678035 = r35678033 / r35678034;
        double r35678036 = r35678025 + r35678035;
        return r35678036;
}
↓
double f(double x, double y, double z, double t) {
        double r35678037 = 2.0;
        double r35678038 = t;
        double r35678039 = r35678037 / r35678038;
        double r35678040 = z;
        double r35678041 = r35678039 / r35678040;
        double r35678042 = r35678039 - r35678037;
        double r35678043 = r35678041 + r35678042;
        double r35678044 = x;
        double r35678045 = y;
        double r35678046 = r35678044 / r35678045;
        double r35678047 = r35678043 + r35678046;
        return r35678047;
}

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

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019192 
(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))))