Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4

Average Error: 2.2 → 1.2

Time: 23.2s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t) {
        double r417759 = x;
        double r417760 = y;
        double r417761 = r417760 - r417759;
        double r417762 = z;
        double r417763 = t;
        double r417764 = r417762 / r417763;
        double r417765 = r417761 * r417764;
        double r417766 = r417759 + r417765;
        return r417766;
}

↓

double f(double x, double y, double z, double t) {
        double r417767 = x;
        double r417768 = y;
        double r417769 = r417768 - r417767;
        double r417770 = cbrt(r417769);
        double r417771 = r417770 * r417770;
        double r417772 = t;
        double r417773 = cbrt(r417772);
        double r417774 = r417771 / r417773;
        double r417775 = r417770 / r417773;
        double r417776 = z;
        double r417777 = cbrt(r417776);
        double r417778 = r417777 * r417777;
        double r417779 = r417773 * r417773;
        double r417780 = cbrt(r417779);
        double r417781 = r417778 / r417780;
        double r417782 = r417775 * r417781;
        double r417783 = cbrt(r417773);
        double r417784 = r417777 / r417783;
        double r417785 = r417782 * r417784;
        double r417786 = r417774 * r417785;
        double r417787 = r417767 + r417786;
        return r417787;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	2.2
Target	2.4
Herbie	1.2

\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.88671875:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

1. Initial program 2.2

   \[x + \left(y - x\right) \cdot \frac{z}{t}\]
2. Using strategy rm

3. Applied add-cube-cbrt 2.7

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

4. Applied *-un-lft-identity 2.7

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

5. Applied times-frac 2.7

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

6. Applied associate-*r* 4.7

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

7. Simplified 4.7

   \[\leadsto x + \color{blue}{\frac{y - x}{\sqrt[3]{t} \cdot \sqrt[3]{t}}} \cdot \frac{z}{\sqrt[3]{t}}\]
8. Using strategy rm

9. Applied add-cube-cbrt 4.8

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

10. Applied times-frac 4.8

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

11. Applied associate-*l* 1.2

    \[\leadsto x + \color{blue}{\frac{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}{\sqrt[3]{t}} \cdot \left(\frac{\sqrt[3]{y - x}}{\sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}\right)}\]
12. Using strategy rm

13. Applied add-cube-cbrt 1.3

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

14. Applied cbrt-prod 1.3

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

15. Applied add-cube-cbrt 1.3

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

16. Applied times-frac 1.3

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

17. Applied associate-*r* 1.2

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

18. Final simplification 1.2

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

Reproduce

herbie shell --seed 2019323 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.887) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) -0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))

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