Average Error: 1.7 → 0.5
Time: 17.7s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[x + \left(y \cdot \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}}\right) \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{z - a}}\]
x + y \cdot \frac{z - t}{z - a}
↓
x + \left(y \cdot \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}}\right) \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{z - a}}
double f(double x, double y, double z, double t, double a) {
        double r350294 = x;
        double r350295 = y;
        double r350296 = z;
        double r350297 = t;
        double r350298 = r350296 - r350297;
        double r350299 = a;
        double r350300 = r350296 - r350299;
        double r350301 = r350298 / r350300;
        double r350302 = r350295 * r350301;
        double r350303 = r350294 + r350302;
        return r350303;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r350304 = x;
        double r350305 = y;
        double r350306 = z;
        double r350307 = t;
        double r350308 = r350306 - r350307;
        double r350309 = cbrt(r350308);
        double r350310 = r350309 * r350309;
        double r350311 = a;
        double r350312 = r350306 - r350311;
        double r350313 = cbrt(r350312);
        double r350314 = r350313 * r350313;
        double r350315 = r350310 / r350314;
        double r350316 = r350305 * r350315;
        double r350317 = r350309 / r350313;
        double r350318 = r350316 * r350317;
        double r350319 = r350304 + r350318;
        return r350319;
}

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

Original1.7
Target1.5
Herbie0.5
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.7

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

  3. Applied add-cube-cbrt2.2

    \[\leadsto x + y \cdot \frac{z - t}{\color{blue}{\left(\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}\right) \cdot \sqrt[3]{z - a}}}\]

  4. Applied add-cube-cbrt2.0

    \[\leadsto x + y \cdot \frac{\color{blue}{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \sqrt[3]{z - t}}}{\left(\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}\right) \cdot \sqrt[3]{z - a}}\]

  5. Applied times-frac2.0

    \[\leadsto x + y \cdot \color{blue}{\left(\frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}} \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{z - a}}\right)}\]

  6. Applied associate-*r*0.5

    \[\leadsto x + \color{blue}{\left(y \cdot \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}}\right) \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{z - a}}}\]

  7. Final simplification0.5

    \[\leadsto x + \left(y \cdot \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}}\right) \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{z - a}}\]

Reproduce

herbie shell --seed 2019323 
(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)))))