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

Average Error: 2.0 → 2.0

Time: 12.3s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x \le -3.867509036970048745891178036710973818173 \cdot 10^{-290} \lor \neg \left(x \le 9.954863872437945886830732175117733893802 \cdot 10^{-260}\right):\\ \;\;\;\;x - \left(x - y\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{t} \cdot z\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r376063 = x;
        double r376064 = y;
        double r376065 = r376064 - r376063;
        double r376066 = z;
        double r376067 = t;
        double r376068 = r376066 / r376067;
        double r376069 = r376065 * r376068;
        double r376070 = r376063 + r376069;
        return r376070;
}

↓

double f(double x, double y, double z, double t) {
        double r376071 = x;
        double r376072 = -3.867509036970049e-290;
        bool r376073 = r376071 <= r376072;
        double r376074 = 9.954863872437946e-260;
        bool r376075 = r376071 <= r376074;
        double r376076 = !r376075;
        bool r376077 = r376073 || r376076;
        double r376078 = y;
        double r376079 = r376071 - r376078;
        double r376080 = z;
        double r376081 = t;
        double r376082 = r376080 / r376081;
        double r376083 = r376079 * r376082;
        double r376084 = r376071 - r376083;
        double r376085 = r376079 / r376081;
        double r376086 = r376085 * r376080;
        double r376087 = r376071 - r376086;
        double r376088 = r376077 ? r376084 : r376087;
        return r376088;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	2.0
Target	2.2
Herbie	2.0

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

Derivation

1. Split input into 2 regimes

2. if x < -3.867509036970049e-290 or 9.954863872437946e-260 < x

   1. Initial program 1.7

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

   2. Simplified 1.7

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

   if -3.867509036970049e-290 < x < 9.954863872437946e-260

   1. Initial program 7.1

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

   2. Simplified 7.1

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

   4. Applied pow1 7.1

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

   5. Applied pow1 7.1

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

   6. Applied pow-prod-down 7.1

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

   7. Simplified 7.2

      \[\leadsto x - {\color{blue}{\left(\frac{x - y}{\frac{t}{z}}\right)}}^{1}\]
   8. Using strategy rm

   9. Applied associate-/r/ 6.6

      \[\leadsto x - {\color{blue}{\left(\frac{x - y}{t} \cdot z\right)}}^{1}\]
3. Recombined 2 regimes into one program.

4. Final simplification 2.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -3.867509036970048745891178036710973818173 \cdot 10^{-290} \lor \neg \left(x \le 9.954863872437945886830732175117733893802 \cdot 10^{-260}\right):\\ \;\;\;\;x - \left(x - y\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{t} \cdot z\\ \end{array}\]

Reproduce

herbie shell --seed 2019196 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.8867) (+ 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))))