Average Error: 10.1 → 0.1
Time: 13.7s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\left(\frac{2}{t} - 2\right) + \frac{\frac{2}{z}}{t}\right) + \frac{x}{y}\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\left(\frac{2}{t} - 2\right) + \frac{\frac{2}{z}}{t}\right) + \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r420949 = x;
        double r420950 = y;
        double r420951 = r420949 / r420950;
        double r420952 = 2.0;
        double r420953 = z;
        double r420954 = r420953 * r420952;
        double r420955 = 1.0;
        double r420956 = t;
        double r420957 = r420955 - r420956;
        double r420958 = r420954 * r420957;
        double r420959 = r420952 + r420958;
        double r420960 = r420956 * r420953;
        double r420961 = r420959 / r420960;
        double r420962 = r420951 + r420961;
        return r420962;
}
↓
double f(double x, double y, double z, double t) {
        double r420963 = 2.0;
        double r420964 = t;
        double r420965 = r420963 / r420964;
        double r420966 = r420965 - r420963;
        double r420967 = z;
        double r420968 = r420963 / r420967;
        double r420969 = r420968 / r420964;
        double r420970 = r420966 + r420969;
        double r420971 = x;
        double r420972 = y;
        double r420973 = r420971 / r420972;
        double r420974 = r420970 + r420973;
        return r420974;
}

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

Original10.1
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 10.1

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

  2. Simplified10.1

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

  3. Taylor expanded around 0 0.1

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

  4. Simplified0.1

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

  6. Applied div-inv0.1

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

  8. Applied associate-*l/0.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 
(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))))