Average Error: 9.1 → 0.1
Time: 12.4s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(\left(\frac{\frac{2}{z}}{t} + \frac{2}{t}\right) - 2\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(\left(\frac{\frac{2}{z}}{t} + \frac{2}{t}\right) - 2\right)
double f(double x, double y, double z, double t) {
        double r570948 = x;
        double r570949 = y;
        double r570950 = r570948 / r570949;
        double r570951 = 2.0;
        double r570952 = z;
        double r570953 = r570952 * r570951;
        double r570954 = 1.0;
        double r570955 = t;
        double r570956 = r570954 - r570955;
        double r570957 = r570953 * r570956;
        double r570958 = r570951 + r570957;
        double r570959 = r570955 * r570952;
        double r570960 = r570958 / r570959;
        double r570961 = r570950 + r570960;
        return r570961;
}
↓
double f(double x, double y, double z, double t) {
        double r570962 = x;
        double r570963 = y;
        double r570964 = r570962 / r570963;
        double r570965 = 2.0;
        double r570966 = z;
        double r570967 = r570965 / r570966;
        double r570968 = t;
        double r570969 = r570967 / r570968;
        double r570970 = r570965 / r570968;
        double r570971 = r570969 + r570970;
        double r570972 = r570971 - r570965;
        double r570973 = r570964 + r570972;
        return r570973;
}

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

Original9.1
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.1

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

  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

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

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

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

  6. Applied times-frac0.1

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

  8. Applied associate-*l/0.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019209 
(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))))