Average Error: 1.4 → 0.9
Time: 8.5s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[x + \left(\left(z - t\right) \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z - a}}\]
x + y \cdot \frac{z - t}{z - a}
↓
x + \left(\left(z - t\right) \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z - a}}
double f(double x, double y, double z, double t, double a) {
        double r848373 = x;
        double r848374 = y;
        double r848375 = z;
        double r848376 = t;
        double r848377 = r848375 - r848376;
        double r848378 = a;
        double r848379 = r848375 - r848378;
        double r848380 = r848377 / r848379;
        double r848381 = r848374 * r848380;
        double r848382 = r848373 + r848381;
        return r848382;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r848383 = x;
        double r848384 = z;
        double r848385 = t;
        double r848386 = r848384 - r848385;
        double r848387 = y;
        double r848388 = cbrt(r848387);
        double r848389 = r848388 * r848388;
        double r848390 = a;
        double r848391 = r848384 - r848390;
        double r848392 = cbrt(r848391);
        double r848393 = r848392 * r848392;
        double r848394 = r848389 / r848393;
        double r848395 = r848386 * r848394;
        double r848396 = r848388 / r848392;
        double r848397 = r848395 * r848396;
        double r848398 = r848383 + r848397;
        return r848398;
}

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
Target1.2
Herbie0.9
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.4

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

  3. Applied *-un-lft-identity1.4

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

  4. Applied associate-*l*1.4

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

  5. Simplified3.1

    \[\leadsto x + 1 \cdot \color{blue}{\left(\left(z - t\right) \cdot \frac{y}{z - a}\right)}\]
  6. Using strategy rm

  7. Applied add-cube-cbrt3.5

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

  8. Applied add-cube-cbrt3.6

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

  9. Applied times-frac3.6

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

  10. Applied associate-*r*0.9

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

  11. Final simplification0.9

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

Reproduce

herbie shell --seed 2020042 
(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)))))