Average Error: 1.4 → 1.3
Time: 6.1s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\frac{1}{\frac{\frac{z - a}{z - t}}{y}} + x\]
x + y \cdot \frac{z - t}{z - a}
↓
\frac{1}{\frac{\frac{z - a}{z - t}}{y}} + x
double f(double x, double y, double z, double t, double a) {
        double r625049 = x;
        double r625050 = y;
        double r625051 = z;
        double r625052 = t;
        double r625053 = r625051 - r625052;
        double r625054 = a;
        double r625055 = r625051 - r625054;
        double r625056 = r625053 / r625055;
        double r625057 = r625050 * r625056;
        double r625058 = r625049 + r625057;
        return r625058;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r625059 = 1.0;
        double r625060 = z;
        double r625061 = a;
        double r625062 = r625060 - r625061;
        double r625063 = t;
        double r625064 = r625060 - r625063;
        double r625065 = r625062 / r625064;
        double r625066 = y;
        double r625067 = r625065 / r625066;
        double r625068 = r625059 / r625067;
        double r625069 = x;
        double r625070 = r625068 + r625069;
        return r625070;
}

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-num1.4

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

  5. Applied pow11.4

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

  6. Applied pow11.4

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

  7. Applied pow-prod-down1.4

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

  8. Simplified1.3

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

  10. Applied clear-num1.3

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

  11. Final simplification1.3

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

Reproduce

herbie shell --seed 2020039 
(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)))))