Average Error: 11.3 → 0.6
Time: 4.1s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}} \cdot \frac{y}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}} \cdot \frac{y}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}}
double f(double x, double y, double z, double t, double a) {
        double r628313 = x;
        double r628314 = y;
        double r628315 = z;
        double r628316 = t;
        double r628317 = r628315 - r628316;
        double r628318 = r628314 * r628317;
        double r628319 = a;
        double r628320 = r628315 - r628319;
        double r628321 = r628318 / r628320;
        double r628322 = r628313 + r628321;
        return r628322;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r628323 = x;
        double r628324 = z;
        double r628325 = t;
        double r628326 = r628324 - r628325;
        double r628327 = cbrt(r628326);
        double r628328 = r628327 * r628327;
        double r628329 = a;
        double r628330 = r628324 - r628329;
        double r628331 = cbrt(r628330);
        double r628332 = r628331 * r628331;
        double r628333 = r628328 / r628332;
        double r628334 = y;
        double r628335 = r628331 / r628327;
        double r628336 = r628334 / r628335;
        double r628337 = r628333 * r628336;
        double r628338 = r628323 + r628337;
        return r628338;
}

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

Original11.3
Target1.4
Herbie0.6
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 11.3

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

  3. Applied associate-/l*1.4

    \[\leadsto x + \color{blue}{\frac{y}{\frac{z - a}{z - t}}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt1.9

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

  6. Applied add-cube-cbrt1.8

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

  7. Applied times-frac1.8

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

  8. Applied *-un-lft-identity1.8

    \[\leadsto x + \frac{\color{blue}{1 \cdot y}}{\frac{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}}{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}} \cdot \frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}}\]

  9. Applied times-frac0.6

    \[\leadsto x + \color{blue}{\frac{1}{\frac{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}}{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}} \cdot \frac{y}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}}}\]

  10. Simplified0.6

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

  11. Final simplification0.6

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

Reproduce

herbie shell --seed 2020060 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

  (+ x (/ (* y (- z t)) (- z a))))