Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A

Average Error: 10.7 → 0.9

Time: 19.6s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a) {
        double r36283865 = x;
        double r36283866 = y;
        double r36283867 = z;
        double r36283868 = r36283866 - r36283867;
        double r36283869 = t;
        double r36283870 = r36283868 * r36283869;
        double r36283871 = a;
        double r36283872 = r36283871 - r36283867;
        double r36283873 = r36283870 / r36283872;
        double r36283874 = r36283865 + r36283873;
        return r36283874;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r36283875 = y;
        double r36283876 = z;
        double r36283877 = r36283875 - r36283876;
        double r36283878 = cbrt(r36283877);
        double r36283879 = a;
        double r36283880 = r36283879 - r36283876;
        double r36283881 = cbrt(r36283880);
        double r36283882 = r36283878 / r36283881;
        double r36283883 = r36283882 * r36283882;
        double r36283884 = t;
        double r36283885 = r36283881 / r36283884;
        double r36283886 = r36283878 / r36283885;
        double r36283887 = r36283883 * r36283886;
        double r36283888 = x;
        double r36283889 = r36283887 + r36283888;
        return r36283889;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	10.7
Target	0.6
Herbie	0.9

\[\begin{array}{l} \mathbf{if}\;t \lt -1.068297449017406694366747246993994850729 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.911094988758637497591020599238553861375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

1. Initial program 10.7

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

3. Applied associate-/l* 3.1

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

5. Applied *-un-lft-identity 3.1

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

6. Applied add-cube-cbrt 3.5

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

7. Applied times-frac 3.5

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

8. Applied add-cube-cbrt 3.5

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

9. Applied times-frac 0.9

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

10. Simplified 0.9

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

11. Final simplification 0.9

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

Reproduce

herbie shell --seed 2019171 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"

  :herbie-target
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

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