Average Error: 8.8 → 0.1
Time: 13.4s
Precision: 64
\[\frac{x}{y} + \frac{2.0 + \left(z \cdot 2.0\right) \cdot \left(1.0 - t\right)}{t \cdot z}\]
↓
\[\left(\left(\frac{\frac{2.0}{z}}{t} - 2.0\right) + \frac{2.0}{t}\right) + \frac{x}{y}\]
\frac{x}{y} + \frac{2.0 + \left(z \cdot 2.0\right) \cdot \left(1.0 - t\right)}{t \cdot z}
↓
\left(\left(\frac{\frac{2.0}{z}}{t} - 2.0\right) + \frac{2.0}{t}\right) + \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r40046662 = x;
        double r40046663 = y;
        double r40046664 = r40046662 / r40046663;
        double r40046665 = 2.0;
        double r40046666 = z;
        double r40046667 = r40046666 * r40046665;
        double r40046668 = 1.0;
        double r40046669 = t;
        double r40046670 = r40046668 - r40046669;
        double r40046671 = r40046667 * r40046670;
        double r40046672 = r40046665 + r40046671;
        double r40046673 = r40046669 * r40046666;
        double r40046674 = r40046672 / r40046673;
        double r40046675 = r40046664 + r40046674;
        return r40046675;
}
↓
double f(double x, double y, double z, double t) {
        double r40046676 = 2.0;
        double r40046677 = z;
        double r40046678 = r40046676 / r40046677;
        double r40046679 = t;
        double r40046680 = r40046678 / r40046679;
        double r40046681 = r40046680 - r40046676;
        double r40046682 = r40046676 / r40046679;
        double r40046683 = r40046681 + r40046682;
        double r40046684 = x;
        double r40046685 = y;
        double r40046686 = r40046684 / r40046685;
        double r40046687 = r40046683 + r40046686;
        return r40046687;
}

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

Original8.8
Target0.1
Herbie0.1
\[\frac{\frac{2.0}{z} + 2.0}{t} - \left(2.0 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 8.8

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

  2. Taylor expanded around 0 0.1

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

  3. Simplified0.1

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

  5. Applied div-inv0.1

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

  7. Applied associate-*l/0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019162 
(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))))