Average Error: 9.8 → 0.1
Time: 10.0s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\frac{\frac{2}{t}}{z} + \frac{2}{t}\right) - \left(2 - \frac{x}{y}\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\frac{\frac{2}{t}}{z} + \frac{2}{t}\right) - \left(2 - \frac{x}{y}\right)
double f(double x, double y, double z, double t) {
        double r1386736 = x;
        double r1386737 = y;
        double r1386738 = r1386736 / r1386737;
        double r1386739 = 2.0;
        double r1386740 = z;
        double r1386741 = r1386740 * r1386739;
        double r1386742 = 1.0;
        double r1386743 = t;
        double r1386744 = r1386742 - r1386743;
        double r1386745 = r1386741 * r1386744;
        double r1386746 = r1386739 + r1386745;
        double r1386747 = r1386743 * r1386740;
        double r1386748 = r1386746 / r1386747;
        double r1386749 = r1386738 + r1386748;
        return r1386749;
}
↓
double f(double x, double y, double z, double t) {
        double r1386750 = 2.0;
        double r1386751 = t;
        double r1386752 = r1386750 / r1386751;
        double r1386753 = z;
        double r1386754 = r1386752 / r1386753;
        double r1386755 = r1386754 + r1386752;
        double r1386756 = x;
        double r1386757 = y;
        double r1386758 = r1386756 / r1386757;
        double r1386759 = r1386750 - r1386758;
        double r1386760 = r1386755 - r1386759;
        return r1386760;
}

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

Original9.8
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.8

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

  2. Simplified0.1

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

  3. Taylor expanded around 0 0.1

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

  4. Simplified0.1

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

  6. Applied associate-/r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020047 
(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))))