Average Error: 9.5 → 0.1
Time: 20.4s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\left(\frac{2}{z \cdot t} - 2\right) + \frac{2}{t}\right) + \frac{x}{y}\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\left(\frac{2}{z \cdot t} - 2\right) + \frac{2}{t}\right) + \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r36364679 = x;
        double r36364680 = y;
        double r36364681 = r36364679 / r36364680;
        double r36364682 = 2.0;
        double r36364683 = z;
        double r36364684 = r36364683 * r36364682;
        double r36364685 = 1.0;
        double r36364686 = t;
        double r36364687 = r36364685 - r36364686;
        double r36364688 = r36364684 * r36364687;
        double r36364689 = r36364682 + r36364688;
        double r36364690 = r36364686 * r36364683;
        double r36364691 = r36364689 / r36364690;
        double r36364692 = r36364681 + r36364691;
        return r36364692;
}
↓
double f(double x, double y, double z, double t) {
        double r36364693 = 2.0;
        double r36364694 = z;
        double r36364695 = t;
        double r36364696 = r36364694 * r36364695;
        double r36364697 = r36364693 / r36364696;
        double r36364698 = r36364697 - r36364693;
        double r36364699 = r36364693 / r36364695;
        double r36364700 = r36364698 + r36364699;
        double r36364701 = x;
        double r36364702 = y;
        double r36364703 = r36364701 / r36364702;
        double r36364704 = r36364700 + r36364703;
        return r36364704;
}

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

Original9.5
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.5

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

  2. Taylor expanded around 0 0.1

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

  3. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019169 
(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))))