Average Error: 1.7 → 0.5
Time: 17.6s
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 r383287 = x;
        double r383288 = y;
        double r383289 = z;
        double r383290 = t;
        double r383291 = r383289 - r383290;
        double r383292 = a;
        double r383293 = r383289 - r383292;
        double r383294 = r383291 / r383293;
        double r383295 = r383288 * r383294;
        double r383296 = r383287 + r383295;
        return r383296;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r383297 = x;
        double r383298 = y;
        double r383299 = z;
        double r383300 = t;
        double r383301 = r383299 - r383300;
        double r383302 = cbrt(r383301);
        double r383303 = r383302 * r383302;
        double r383304 = a;
        double r383305 = r383299 - r383304;
        double r383306 = cbrt(r383305);
        double r383307 = r383306 * r383306;
        double r383308 = r383303 / r383307;
        double r383309 = r383298 * r383308;
        double r383310 = r383302 / r383306;
        double r383311 = r383309 * r383310;
        double r383312 = r383297 + r383311;
        return r383312;
}

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)))))