Average Error: 9.3 → 0.1
Time: 16.6s
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 r545051 = x;
        double r545052 = y;
        double r545053 = r545051 / r545052;
        double r545054 = 2.0;
        double r545055 = z;
        double r545056 = r545055 * r545054;
        double r545057 = 1.0;
        double r545058 = t;
        double r545059 = r545057 - r545058;
        double r545060 = r545056 * r545059;
        double r545061 = r545054 + r545060;
        double r545062 = r545058 * r545055;
        double r545063 = r545061 / r545062;
        double r545064 = r545053 + r545063;
        return r545064;
}
↓
double f(double x, double y, double z, double t) {
        double r545065 = 2.0;
        double r545066 = t;
        double r545067 = r545065 / r545066;
        double r545068 = z;
        double r545069 = r545067 / r545068;
        double r545070 = r545067 - r545065;
        double r545071 = r545069 + r545070;
        double r545072 = x;
        double r545073 = y;
        double r545074 = r545072 / r545073;
        double r545075 = r545071 + r545074;
        return r545075;
}

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

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

  3. Taylor expanded around 0 0.1

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

  4. Simplified0.1

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

  6. Applied associate-/r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019326 
(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))))