Average Error: 1.4 → 1.0
Time: 12.1s
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 r411826 = x;
        double r411827 = y;
        double r411828 = z;
        double r411829 = t;
        double r411830 = r411828 - r411829;
        double r411831 = a;
        double r411832 = r411828 - r411831;
        double r411833 = r411830 / r411832;
        double r411834 = r411827 * r411833;
        double r411835 = r411826 + r411834;
        return r411835;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r411836 = x;
        double r411837 = z;
        double r411838 = t;
        double r411839 = r411837 - r411838;
        double r411840 = y;
        double r411841 = cbrt(r411840);
        double r411842 = r411841 * r411841;
        double r411843 = a;
        double r411844 = r411837 - r411843;
        double r411845 = cbrt(r411844);
        double r411846 = r411845 * r411845;
        double r411847 = r411842 / r411846;
        double r411848 = r411839 * r411847;
        double r411849 = r411841 / r411845;
        double r411850 = r411848 * r411849;
        double r411851 = r411836 + r411850;
        return r411851;
}

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
Herbie1.0
\[x + \frac{y}{\frac{z - a}{z - t}}\]

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. Simplified3.0

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

  7. Applied add-cube-cbrt3.4

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

  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*1.0

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

  11. Final simplification1.0

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

Reproduce

herbie shell --seed 2019303 
(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)))))