Average Error: 1.4 → 1.4
Time: 4.4s
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 r733266 = x;
        double r733267 = y;
        double r733268 = z;
        double r733269 = t;
        double r733270 = r733268 - r733269;
        double r733271 = a;
        double r733272 = r733268 - r733271;
        double r733273 = r733270 / r733272;
        double r733274 = r733267 * r733273;
        double r733275 = r733266 + r733274;
        return r733275;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r733276 = x;
        double r733277 = y;
        double r733278 = z;
        double r733279 = a;
        double r733280 = r733278 - r733279;
        double r733281 = r733278 / r733280;
        double r733282 = t;
        double r733283 = r733282 / r733280;
        double r733284 = r733281 - r733283;
        double r733285 = r733277 * r733284;
        double r733286 = r733276 + r733285;
        return r733286;
}

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

Derivation

  1. Initial program 1.4

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

  3. Applied div-sub1.4

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

  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2019353 
(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)))))