Average Error: 9.4 → 0.1
Time: 15.8s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(\left(\frac{2}{t} + \frac{\frac{2}{t}}{z}\right) - 2\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(\left(\frac{2}{t} + \frac{\frac{2}{t}}{z}\right) - 2\right)
double f(double x, double y, double z, double t) {
        double r975045 = x;
        double r975046 = y;
        double r975047 = r975045 / r975046;
        double r975048 = 2.0;
        double r975049 = z;
        double r975050 = r975049 * r975048;
        double r975051 = 1.0;
        double r975052 = t;
        double r975053 = r975051 - r975052;
        double r975054 = r975050 * r975053;
        double r975055 = r975048 + r975054;
        double r975056 = r975052 * r975049;
        double r975057 = r975055 / r975056;
        double r975058 = r975047 + r975057;
        return r975058;
}
↓
double f(double x, double y, double z, double t) {
        double r975059 = x;
        double r975060 = y;
        double r975061 = r975059 / r975060;
        double r975062 = 2.0;
        double r975063 = t;
        double r975064 = r975062 / r975063;
        double r975065 = z;
        double r975066 = r975064 / r975065;
        double r975067 = r975064 + r975066;
        double r975068 = r975067 - r975062;
        double r975069 = r975061 + r975068;
        return r975069;
}

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

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

  5. Applied associate-/r*0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020046 
(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))))