Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3

Average Error: 11.6 → 2.1

Time: 10.7s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x \le -5.089780698062090774608904448505777443405 \cdot 10^{-199} \lor \neg \left(x \le 118151073605098128543842304\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{t - z} \cdot \left(x \cdot \left(y - z\right)\right)\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r386013 = x;
        double r386014 = y;
        double r386015 = z;
        double r386016 = r386014 - r386015;
        double r386017 = r386013 * r386016;
        double r386018 = t;
        double r386019 = r386018 - r386015;
        double r386020 = r386017 / r386019;
        return r386020;
}

↓

double f(double x, double y, double z, double t) {
        double r386021 = x;
        double r386022 = -5.089780698062091e-199;
        bool r386023 = r386021 <= r386022;
        double r386024 = 1.1815107360509813e+26;
        bool r386025 = r386021 <= r386024;
        double r386026 = !r386025;
        bool r386027 = r386023 || r386026;
        double r386028 = t;
        double r386029 = z;
        double r386030 = r386028 - r386029;
        double r386031 = y;
        double r386032 = r386031 - r386029;
        double r386033 = r386030 / r386032;
        double r386034 = r386021 / r386033;
        double r386035 = 1.0;
        double r386036 = r386035 / r386030;
        double r386037 = r386021 * r386032;
        double r386038 = r386036 * r386037;
        double r386039 = r386027 ? r386034 : r386038;
        return r386039;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	11.6
Target	2.2
Herbie	2.1

\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

1. Split input into 2 regimes

2. if x < -5.089780698062091e-199 or 1.1815107360509813e+26 < x

   1. Initial program 17.7

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

   3. Applied associate-/l* 2.1

      \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}}\]

   if -5.089780698062091e-199 < x < 1.1815107360509813e+26

   1. Initial program 2.0

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

   3. Applied clear-num 2.4

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

   5. Applied div-inv 2.8

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

   6. Applied add-cube-cbrt 2.8

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

   7. Applied times-frac 2.5

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

   8. Simplified 2.5

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

   9. Simplified 2.1

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

4. Final simplification 2.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -5.089780698062090774608904448505777443405 \cdot 10^{-199} \lor \neg \left(x \le 118151073605098128543842304\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{t - z} \cdot \left(x \cdot \left(y - z\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (/ x (/ (- t z) (- y z)))

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