Average Error: 1.2 → 1.1
Time: 5.0s
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 r684410 = x;
        double r684411 = y;
        double r684412 = z;
        double r684413 = t;
        double r684414 = r684412 - r684413;
        double r684415 = a;
        double r684416 = r684412 - r684415;
        double r684417 = r684414 / r684416;
        double r684418 = r684411 * r684417;
        double r684419 = r684410 + r684418;
        return r684419;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r684420 = y;
        double r684421 = z;
        double r684422 = a;
        double r684423 = r684421 - r684422;
        double r684424 = t;
        double r684425 = r684421 - r684424;
        double r684426 = r684423 / r684425;
        double r684427 = r684420 / r684426;
        double r684428 = x;
        double r684429 = r684427 + r684428;
        return r684429;
}

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 pow11.2

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

  6. Applied pow11.2

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

  7. Applied pow-prod-down1.2

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

  8. Simplified1.1

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

  9. Final simplification1.1

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

Reproduce

herbie shell --seed 2020020 
(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)))))