Average Error: 9.1 → 0.1
Time: 18.4s
Precision: 64
\[\frac{x}{y} + \frac{2.0 + \left(z \cdot 2.0\right) \cdot \left(1.0 - t\right)}{t \cdot z}\]
↓
\[\left(\left(\frac{2.0}{t} + \frac{\frac{2.0}{t}}{z}\right) + \frac{x}{y}\right) - 2.0\]
\frac{x}{y} + \frac{2.0 + \left(z \cdot 2.0\right) \cdot \left(1.0 - t\right)}{t \cdot z}
↓
\left(\left(\frac{2.0}{t} + \frac{\frac{2.0}{t}}{z}\right) + \frac{x}{y}\right) - 2.0
double f(double x, double y, double z, double t) {
        double r36484687 = x;
        double r36484688 = y;
        double r36484689 = r36484687 / r36484688;
        double r36484690 = 2.0;
        double r36484691 = z;
        double r36484692 = r36484691 * r36484690;
        double r36484693 = 1.0;
        double r36484694 = t;
        double r36484695 = r36484693 - r36484694;
        double r36484696 = r36484692 * r36484695;
        double r36484697 = r36484690 + r36484696;
        double r36484698 = r36484694 * r36484691;
        double r36484699 = r36484697 / r36484698;
        double r36484700 = r36484689 + r36484699;
        return r36484700;
}
↓
double f(double x, double y, double z, double t) {
        double r36484701 = 2.0;
        double r36484702 = t;
        double r36484703 = r36484701 / r36484702;
        double r36484704 = z;
        double r36484705 = r36484703 / r36484704;
        double r36484706 = r36484703 + r36484705;
        double r36484707 = x;
        double r36484708 = y;
        double r36484709 = r36484707 / r36484708;
        double r36484710 = r36484706 + r36484709;
        double r36484711 = r36484710 - r36484701;
        return r36484711;
}

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
\[\frac{\frac{2.0}{z} + 2.0}{t} - \left(2.0 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.1

    \[\frac{x}{y} + \frac{2.0 + \left(z \cdot 2.0\right) \cdot \left(1.0 - t\right)}{t \cdot z}\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{2.0}{t}, \frac{\mathsf{fma}\left(z, 1.0, 1\right)}{z}, \frac{x}{y}\right) - 2.0}\]

  3. Taylor expanded around 0 0.1

    \[\leadsto \color{blue}{\left(\frac{x}{y} + \left(2.0 \cdot \frac{1}{t} + 2.0 \cdot \frac{1}{t \cdot z}\right)\right)} - 2.0\]

  4. Simplified0.1

    \[\leadsto \color{blue}{\left(\left(\frac{2.0}{t} + \frac{\frac{2.0}{t}}{z}\right) + \frac{x}{y}\right)} - 2.0\]

  5. Final simplification0.1

    \[\leadsto \left(\left(\frac{2.0}{t} + \frac{\frac{2.0}{t}}{z}\right) + \frac{x}{y}\right) - 2.0\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(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))))