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

Average Error: 10.8 → 1.0

Time: 5.9s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a) {
        double r725844 = x;
        double r725845 = y;
        double r725846 = z;
        double r725847 = r725845 - r725846;
        double r725848 = t;
        double r725849 = r725847 * r725848;
        double r725850 = a;
        double r725851 = r725850 - r725846;
        double r725852 = r725849 / r725851;
        double r725853 = r725844 + r725852;
        return r725853;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r725854 = x;
        double r725855 = y;
        double r725856 = z;
        double r725857 = r725855 - r725856;
        double r725858 = cbrt(r725857);
        double r725859 = r725858 * r725858;
        double r725860 = a;
        double r725861 = r725860 - r725856;
        double r725862 = cbrt(r725861);
        double r725863 = r725859 / r725862;
        double r725864 = r725858 / r725862;
        double r725865 = t;
        double r725866 = r725865 / r725862;
        double r725867 = r725864 * r725866;
        double r725868 = r725863 * r725867;
        double r725869 = r725854 + r725868;
        return r725869;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	10.8
Target	0.6
Herbie	1.0

\[\begin{array}{l} \mathbf{if}\;t \lt -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

1. Initial program 10.8

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

3. Applied add-cube-cbrt 11.2

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

4. Applied times-frac 1.8

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

6. Applied add-cube-cbrt 1.7

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

7. Applied times-frac 1.7

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

8. Applied associate-*l* 1.0

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

9. Final simplification 1.0

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

Reproduce

herbie shell --seed 2020089 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :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))))