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

Average Error: 10.0 → 1.0

Time: 23.4s

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 r31398626 = x;
        double r31398627 = y;
        double r31398628 = z;
        double r31398629 = r31398627 - r31398628;
        double r31398630 = t;
        double r31398631 = r31398629 * r31398630;
        double r31398632 = a;
        double r31398633 = r31398632 - r31398628;
        double r31398634 = r31398631 / r31398633;
        double r31398635 = r31398626 + r31398634;
        return r31398635;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r31398636 = y;
        double r31398637 = z;
        double r31398638 = r31398636 - r31398637;
        double r31398639 = cbrt(r31398638);
        double r31398640 = a;
        double r31398641 = r31398640 - r31398637;
        double r31398642 = cbrt(r31398641);
        double r31398643 = r31398639 / r31398642;
        double r31398644 = r31398643 * r31398643;
        double r31398645 = t;
        double r31398646 = r31398642 / r31398645;
        double r31398647 = r31398639 / r31398646;
        double r31398648 = r31398644 * r31398647;
        double r31398649 = x;
        double r31398650 = r31398648 + r31398649;
        return r31398650;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	10.0
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 10.0

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

3. Applied associate-/l* 2.9

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

5. Applied *-un-lft-identity 2.9

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

6. Applied add-cube-cbrt 3.3

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

7. Applied times-frac 3.4

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

8. Applied add-cube-cbrt 3.3

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

9. Applied times-frac 1.0

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

10. Simplified 1.0

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

11. Final simplification 1.0

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

Reproduce

herbie shell --seed 2019162 
(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))))