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

Average Error: 2.2 → 2.4

Time: 4.8s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;z \le 3.29194830615707638 \cdot 10^{-308} \lor \neg \left(z \le 2.88733508478686524 \cdot 10^{205}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\sqrt{z} \cdot \left(y - x\right)\right) \cdot \frac{\sqrt{z}}{t}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r664859 = x;
        double r664860 = y;
        double r664861 = r664860 - r664859;
        double r664862 = z;
        double r664863 = t;
        double r664864 = r664862 / r664863;
        double r664865 = r664861 * r664864;
        double r664866 = r664859 + r664865;
        return r664866;
}

↓

double f(double x, double y, double z, double t) {
        double r664867 = z;
        double r664868 = 3.2919483061570764e-308;
        bool r664869 = r664867 <= r664868;
        double r664870 = 2.8873350847868652e+205;
        bool r664871 = r664867 <= r664870;
        double r664872 = !r664871;
        bool r664873 = r664869 || r664872;
        double r664874 = x;
        double r664875 = y;
        double r664876 = r664875 - r664874;
        double r664877 = t;
        double r664878 = r664867 / r664877;
        double r664879 = r664876 * r664878;
        double r664880 = r664874 + r664879;
        double r664881 = sqrt(r664867);
        double r664882 = r664881 * r664876;
        double r664883 = r664881 / r664877;
        double r664884 = r664882 * r664883;
        double r664885 = r664874 + r664884;
        double r664886 = r664873 ? r664880 : r664885;
        return r664886;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	2.2
Target	2.5
Herbie	2.4

\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.887:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

1. Split input into 2 regimes

2. if z < 3.2919483061570764e-308 or 2.8873350847868652e+205 < z

   1. Initial program 2.6

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

   if 3.2919483061570764e-308 < z < 2.8873350847868652e+205

   1. Initial program 1.8

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

   3. Applied *-un-lft-identity 1.8

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

   4. Applied add-sqr-sqrt 2.0

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

   5. Applied times-frac 2.0

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

   6. Applied associate-*r* 2.3

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

   7. Simplified 2.3

      \[\leadsto x + \color{blue}{\left(\sqrt{z} \cdot \left(y - x\right)\right)} \cdot \frac{\sqrt{z}}{t}\]
3. Recombined 2 regimes into one program.

4. Final simplification 2.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \le 3.29194830615707638 \cdot 10^{-308} \lor \neg \left(z \le 2.88733508478686524 \cdot 10^{205}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\sqrt{z} \cdot \left(y - x\right)\right) \cdot \frac{\sqrt{z}}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 
(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))))