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

Average Error: 11.4 → 1.7

Time: 2.6s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \le 0.0:\\ \;\;\;\;\frac{x}{1 \cdot \frac{t - z}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \le 2.28593216958903165 \cdot 10^{67}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r663786 = x;
        double r663787 = y;
        double r663788 = z;
        double r663789 = r663787 - r663788;
        double r663790 = r663786 * r663789;
        double r663791 = t;
        double r663792 = r663791 - r663788;
        double r663793 = r663790 / r663792;
        return r663793;
}

↓

double f(double x, double y, double z, double t) {
        double r663794 = x;
        double r663795 = y;
        double r663796 = z;
        double r663797 = r663795 - r663796;
        double r663798 = r663794 * r663797;
        double r663799 = t;
        double r663800 = r663799 - r663796;
        double r663801 = r663798 / r663800;
        double r663802 = 0.0;
        bool r663803 = r663801 <= r663802;
        double r663804 = 1.0;
        double r663805 = r663800 / r663797;
        double r663806 = r663804 * r663805;
        double r663807 = r663794 / r663806;
        double r663808 = 2.2859321695890317e+67;
        bool r663809 = r663801 <= r663808;
        double r663810 = r663794 / r663800;
        double r663811 = r663810 * r663797;
        double r663812 = r663809 ? r663801 : r663811;
        double r663813 = r663803 ? r663807 : r663812;
        return r663813;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	11.4
Target	2.1
Herbie	1.7

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

Derivation

1. Split input into 3 regimes

2. if (/ (* x (- y z)) (- t z)) < 0.0

   1. Initial program 11.1

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

   3. Applied associate-/l* 2.0

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

   5. Applied *-un-lft-identity 2.0

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

   6. Applied *-un-lft-identity 2.0

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

   7. Applied times-frac 2.0

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

   8. Simplified 2.0

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

   if 0.0 < (/ (* x (- y z)) (- t z)) < 2.2859321695890317e+67

   1. Initial program 0.3

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

   if 2.2859321695890317e+67 < (/ (* x (- y z)) (- t z))

   1. Initial program 29.5

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

   3. Applied associate-/l* 2.6

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

   5. Applied associate-/r/ 3.1

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

4. Final simplification 1.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \le 0.0:\\ \;\;\;\;\frac{x}{1 \cdot \frac{t - z}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \le 2.28593216958903165 \cdot 10^{67}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020062 
(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)))