Average Error: 6.2 → 2.5
Time: 3.8s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[x + \frac{y}{a} \cdot \left(z - t\right)\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
x + \frac{y}{a} \cdot \left(z - t\right)
double f(double x, double y, double z, double t, double a) {
        double r237895 = x;
        double r237896 = y;
        double r237897 = z;
        double r237898 = t;
        double r237899 = r237897 - r237898;
        double r237900 = r237896 * r237899;
        double r237901 = a;
        double r237902 = r237900 / r237901;
        double r237903 = r237895 + r237902;
        return r237903;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r237904 = x;
        double r237905 = y;
        double r237906 = a;
        double r237907 = r237905 / r237906;
        double r237908 = z;
        double r237909 = t;
        double r237910 = r237908 - r237909;
        double r237911 = r237907 * r237910;
        double r237912 = r237904 + r237911;
        return r237912;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.2
Target0.7
Herbie2.5
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Initial program 6.2

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

  3. Applied clear-num6.3

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

  5. Applied associate-/r*2.5

    \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{a}{y}}{z - t}}}\]
  6. Using strategy rm

  7. Applied div-inv2.5

    \[\leadsto x + \frac{1}{\color{blue}{\frac{a}{y} \cdot \frac{1}{z - t}}}\]

  8. Applied add-cube-cbrt2.5

    \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\frac{a}{y} \cdot \frac{1}{z - t}}\]

  9. Applied times-frac2.7

    \[\leadsto x + \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{a}{y}} \cdot \frac{\sqrt[3]{1}}{\frac{1}{z - t}}}\]

  10. Simplified2.6

    \[\leadsto x + \color{blue}{\frac{y}{a}} \cdot \frac{\sqrt[3]{1}}{\frac{1}{z - t}}\]

  11. Simplified2.5

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

  12. Final simplification2.5

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

Reproduce

herbie shell --seed 2020035 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (+ x (/ 1 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (+ x (/ (* y (- z t)) a)) (+ x (/ y (/ a (- z t))))))

  (+ x (/ (* y (- z t)) a)))