Average Error: 9.3 → 0.1
Time: 5.6s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\frac{\frac{2}{z} + 2}{t} + \frac{x}{y}\right) - 2\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\frac{\frac{2}{z} + 2}{t} + \frac{x}{y}\right) - 2
double f(double x, double y, double z, double t) {
        double r734032 = x;
        double r734033 = y;
        double r734034 = r734032 / r734033;
        double r734035 = 2.0;
        double r734036 = z;
        double r734037 = r734036 * r734035;
        double r734038 = 1.0;
        double r734039 = t;
        double r734040 = r734038 - r734039;
        double r734041 = r734037 * r734040;
        double r734042 = r734035 + r734041;
        double r734043 = r734039 * r734036;
        double r734044 = r734042 / r734043;
        double r734045 = r734034 + r734044;
        return r734045;
}
↓
double f(double x, double y, double z, double t) {
        double r734046 = 2.0;
        double r734047 = z;
        double r734048 = r734046 / r734047;
        double r734049 = r734048 + r734046;
        double r734050 = t;
        double r734051 = r734049 / r734050;
        double r734052 = x;
        double r734053 = y;
        double r734054 = r734052 / r734053;
        double r734055 = r734051 + r734054;
        double r734056 = r734055 - r734046;
        return r734056;
}

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

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

  3. Simplified0.1

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

  5. Applied sub-neg0.1

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

  6. Applied associate-+r+0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 1978988140 
(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))))