Average Error: 1.2 → 1.1
Time: 5.1s
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 r583615 = x;
        double r583616 = y;
        double r583617 = z;
        double r583618 = t;
        double r583619 = r583617 - r583618;
        double r583620 = a;
        double r583621 = r583617 - r583620;
        double r583622 = r583619 / r583621;
        double r583623 = r583616 * r583622;
        double r583624 = r583615 + r583623;
        return r583624;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r583625 = y;
        double r583626 = z;
        double r583627 = a;
        double r583628 = r583626 - r583627;
        double r583629 = t;
        double r583630 = r583626 - r583629;
        double r583631 = r583628 / r583630;
        double r583632 = r583625 / r583631;
        double r583633 = x;
        double r583634 = r583632 + r583633;
        return r583634;
}

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

Original1.2
Target1.1
Herbie1.1
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.2

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

  3. Applied clear-num1.2

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

  5. Applied *-un-lft-identity1.2

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

  6. Applied associate-*l*1.2

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

  7. Simplified1.1

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

  8. Final simplification1.1

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

Reproduce

herbie shell --seed 2020081 
(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)))))