Average Error: 1.5 → 1.5
Time: 4.8s
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 r647445 = x;
        double r647446 = y;
        double r647447 = z;
        double r647448 = t;
        double r647449 = r647447 - r647448;
        double r647450 = a;
        double r647451 = r647447 - r647450;
        double r647452 = r647449 / r647451;
        double r647453 = r647446 * r647452;
        double r647454 = r647445 + r647453;
        return r647454;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r647455 = x;
        double r647456 = y;
        double r647457 = z;
        double r647458 = a;
        double r647459 = r647457 - r647458;
        double r647460 = r647457 / r647459;
        double r647461 = t;
        double r647462 = r647461 / r647459;
        double r647463 = r647460 - r647462;
        double r647464 = r647456 * r647463;
        double r647465 = r647455 + r647464;
        return r647465;
}

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)))))