Average Error: 1.3 → 0.5
Time: 14.1s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[x + \frac{y}{\frac{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}}{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}} \cdot \frac{\sqrt[3]{1}}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}}\]
x + y \cdot \frac{z - t}{z - a}
↓
x + \frac{y}{\frac{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}}{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}} \cdot \frac{\sqrt[3]{1}}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}}
double f(double x, double y, double z, double t, double a) {
        double r414500 = x;
        double r414501 = y;
        double r414502 = z;
        double r414503 = t;
        double r414504 = r414502 - r414503;
        double r414505 = a;
        double r414506 = r414502 - r414505;
        double r414507 = r414504 / r414506;
        double r414508 = r414501 * r414507;
        double r414509 = r414500 + r414508;
        return r414509;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r414510 = x;
        double r414511 = y;
        double r414512 = z;
        double r414513 = a;
        double r414514 = r414512 - r414513;
        double r414515 = cbrt(r414514);
        double r414516 = r414515 * r414515;
        double r414517 = t;
        double r414518 = r414512 - r414517;
        double r414519 = cbrt(r414518);
        double r414520 = r414519 * r414519;
        double r414521 = r414516 / r414520;
        double r414522 = r414511 / r414521;
        double r414523 = 1.0;
        double r414524 = cbrt(r414523);
        double r414525 = r414515 / r414519;
        double r414526 = r414524 / r414525;
        double r414527 = r414522 * r414526;
        double r414528 = r414510 + r414527;
        return r414528;
}

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

Original1.3
Target1.2
Herbie0.5
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.3

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

  3. Applied clear-num1.3

    \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{z - a}{z - t}}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt1.9

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

  6. Applied add-cube-cbrt1.7

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

  7. Applied times-frac1.7

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

  8. Applied add-cube-cbrt1.7

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

  9. Applied times-frac1.7

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

  10. Applied associate-*r*0.5

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

  11. Simplified0.5

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

  12. Final simplification0.5

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

Reproduce

herbie shell --seed 2019298 
(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)))))