Average Error: 1.2 → 2.5
Time: 4.3s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[x + y \cdot \left(\sqrt[3]{{\left(\frac{z}{z - a}\right)}^{3}} - \frac{t}{z - a}\right)\]
x + y \cdot \frac{z - t}{z - a}
↓
x + y \cdot \left(\sqrt[3]{{\left(\frac{z}{z - a}\right)}^{3}} - \frac{t}{z - a}\right)
double f(double x, double y, double z, double t, double a) {
        double r642358 = x;
        double r642359 = y;
        double r642360 = z;
        double r642361 = t;
        double r642362 = r642360 - r642361;
        double r642363 = a;
        double r642364 = r642360 - r642363;
        double r642365 = r642362 / r642364;
        double r642366 = r642359 * r642365;
        double r642367 = r642358 + r642366;
        return r642367;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r642368 = x;
        double r642369 = y;
        double r642370 = z;
        double r642371 = a;
        double r642372 = r642370 - r642371;
        double r642373 = r642370 / r642372;
        double r642374 = 3.0;
        double r642375 = pow(r642373, r642374);
        double r642376 = cbrt(r642375);
        double r642377 = t;
        double r642378 = r642377 / r642372;
        double r642379 = r642376 - r642378;
        double r642380 = r642369 * r642379;
        double r642381 = r642368 + r642380;
        return r642381;
}

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

Original1.2
Target1.1
Herbie2.5
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.2

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

  3. Applied div-sub1.2

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

  5. Applied add-cbrt-cube16.0

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

  6. Applied add-cbrt-cube29.7

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

  7. Applied cbrt-undiv29.8

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

  8. Simplified2.5

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

  9. Final simplification2.5

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

Reproduce

herbie shell --seed 2020034 
(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)))))