Average Error: 1.5 → 1.5
Time: 5.7s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[x + y \cdot \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\]
x + y \cdot \frac{z - t}{z - a}
↓
x + y \cdot \left(\frac{z}{z - a} - \frac{t}{z - a}\right)
double f(double x, double y, double z, double t, double a) {
        double r699572 = x;
        double r699573 = y;
        double r699574 = z;
        double r699575 = t;
        double r699576 = r699574 - r699575;
        double r699577 = a;
        double r699578 = r699574 - r699577;
        double r699579 = r699576 / r699578;
        double r699580 = r699573 * r699579;
        double r699581 = r699572 + r699580;
        return r699581;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r699582 = x;
        double r699583 = y;
        double r699584 = z;
        double r699585 = a;
        double r699586 = r699584 - r699585;
        double r699587 = r699584 / r699586;
        double r699588 = t;
        double r699589 = r699588 / r699586;
        double r699590 = r699587 - r699589;
        double r699591 = r699583 * r699590;
        double r699592 = r699582 + r699591;
        return r699592;
}

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

Original1.5
Target1.4
Herbie1.5
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.5

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

  3. Applied div-sub1.5

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

  4. Final simplification1.5

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

Reproduce

herbie shell --seed 2020060 
(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)))))