Average Error: 1.3 → 1.6
Time: 11.2s
Precision: 64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[x + y \cdot \left(\frac{z}{a - t} - \frac{\frac{t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}}{\sqrt[3]{a - t}}\right)\]
x + y \cdot \frac{z - t}{a - t}
↓
x + y \cdot \left(\frac{z}{a - t} - \frac{\frac{t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}}{\sqrt[3]{a - t}}\right)
double f(double x, double y, double z, double t, double a) {
        double r705680 = x;
        double r705681 = y;
        double r705682 = z;
        double r705683 = t;
        double r705684 = r705682 - r705683;
        double r705685 = a;
        double r705686 = r705685 - r705683;
        double r705687 = r705684 / r705686;
        double r705688 = r705681 * r705687;
        double r705689 = r705680 + r705688;
        return r705689;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r705690 = x;
        double r705691 = y;
        double r705692 = z;
        double r705693 = a;
        double r705694 = t;
        double r705695 = r705693 - r705694;
        double r705696 = r705692 / r705695;
        double r705697 = cbrt(r705695);
        double r705698 = r705697 * r705697;
        double r705699 = r705694 / r705698;
        double r705700 = r705699 / r705697;
        double r705701 = r705696 - r705700;
        double r705702 = r705691 * r705701;
        double r705703 = r705690 + r705702;
        return r705703;
}

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
Target0.4
Herbie1.6
\[\begin{array}{l} \mathbf{if}\;y \lt -8.50808486055124107 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Initial program 1.3

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

  3. Applied div-sub1.3

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

  5. Applied add-cube-cbrt1.6

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

  6. Applied associate-/r*1.6

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

  7. Final simplification1.6

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

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, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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