Average Error: 1.4 → 0.6
Time: 19.6s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\frac{y}{\frac{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}}{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}} \cdot \frac{1}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}} + x\]
x + y \cdot \frac{z - t}{z - a}
↓
\frac{y}{\frac{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}}{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}} \cdot \frac{1}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}} + x
double f(double x, double y, double z, double t, double a) {
        double r397404 = x;
        double r397405 = y;
        double r397406 = z;
        double r397407 = t;
        double r397408 = r397406 - r397407;
        double r397409 = a;
        double r397410 = r397406 - r397409;
        double r397411 = r397408 / r397410;
        double r397412 = r397405 * r397411;
        double r397413 = r397404 + r397412;
        return r397413;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r397414 = y;
        double r397415 = z;
        double r397416 = a;
        double r397417 = r397415 - r397416;
        double r397418 = cbrt(r397417);
        double r397419 = r397418 * r397418;
        double r397420 = t;
        double r397421 = r397415 - r397420;
        double r397422 = cbrt(r397421);
        double r397423 = r397422 * r397422;
        double r397424 = r397419 / r397423;
        double r397425 = r397414 / r397424;
        double r397426 = 1.0;
        double r397427 = r397418 / r397422;
        double r397428 = r397426 / r397427;
        double r397429 = r397425 * r397428;
        double r397430 = x;
        double r397431 = r397429 + r397430;
        return r397431;
}

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

Derivation

  1. Initial program 1.4

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

  3. Applied clear-num1.5

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

  5. Applied add-cube-cbrt2.0

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

  6. Applied add-cube-cbrt1.8

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

  7. Applied times-frac1.8

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

  8. Applied add-cube-cbrt1.8

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

  9. Applied times-frac1.8

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

  10. Applied associate-*r*0.6

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

  11. Simplified0.6

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

  12. Final simplification0.6

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

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(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)))))