Average Error: 1.4 → 1.4
Time: 4.3s
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 r620262 = x;
        double r620263 = y;
        double r620264 = z;
        double r620265 = t;
        double r620266 = r620264 - r620265;
        double r620267 = a;
        double r620268 = r620264 - r620267;
        double r620269 = r620266 / r620268;
        double r620270 = r620263 * r620269;
        double r620271 = r620262 + r620270;
        return r620271;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r620272 = x;
        double r620273 = y;
        double r620274 = z;
        double r620275 = a;
        double r620276 = r620274 - r620275;
        double r620277 = r620274 / r620276;
        double r620278 = t;
        double r620279 = r620278 / r620276;
        double r620280 = r620277 - r620279;
        double r620281 = r620273 * r620280;
        double r620282 = r620272 + r620281;
        return r620282;
}

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)))))