Average Error: 1.4 → 1.3
Time: 9.0s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\frac{y}{\frac{z - a}{z - t}} + x\]
x + y \cdot \frac{z - t}{z - a}
↓
\frac{y}{\frac{z - a}{z - t}} + x
double f(double x, double y, double z, double t, double a) {
        double r529842 = x;
        double r529843 = y;
        double r529844 = z;
        double r529845 = t;
        double r529846 = r529844 - r529845;
        double r529847 = a;
        double r529848 = r529844 - r529847;
        double r529849 = r529846 / r529848;
        double r529850 = r529843 * r529849;
        double r529851 = r529842 + r529850;
        return r529851;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r529852 = y;
        double r529853 = z;
        double r529854 = a;
        double r529855 = r529853 - r529854;
        double r529856 = t;
        double r529857 = r529853 - r529856;
        double r529858 = r529855 / r529857;
        double r529859 = r529852 / r529858;
        double r529860 = x;
        double r529861 = r529859 + r529860;
        return r529861;
}

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

Original1.4
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.4

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

  3. Applied clear-num1.5

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

  5. Applied pow11.5

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

  6. Applied pow11.5

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

  7. Applied pow-prod-down1.5

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

  8. Simplified1.3

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

  9. Final simplification1.3

    \[\leadsto \frac{y}{\frac{z - a}{z - t}} + x\]

Reproduce

herbie shell --seed 2020045 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

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