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

Average Error: 10.5 → 1.5

Time: 13.5s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{t - z} = -\infty:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{t - z} \le 3.4474718287681383 \cdot 10^{+211}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r42045029 = x;
        double r42045030 = y;
        double r42045031 = z;
        double r42045032 = r42045030 - r42045031;
        double r42045033 = r42045029 * r42045032;
        double r42045034 = t;
        double r42045035 = r42045034 - r42045031;
        double r42045036 = r42045033 / r42045035;
        return r42045036;
}

↓

double f(double x, double y, double z, double t) {
        double r42045037 = y;
        double r42045038 = z;
        double r42045039 = r42045037 - r42045038;
        double r42045040 = x;
        double r42045041 = r42045039 * r42045040;
        double r42045042 = t;
        double r42045043 = r42045042 - r42045038;
        double r42045044 = r42045041 / r42045043;
        double r42045045 = -inf.0;
        bool r42045046 = r42045044 <= r42045045;
        double r42045047 = r42045040 / r42045043;
        double r42045048 = r42045047 * r42045039;
        double r42045049 = 3.4474718287681383e+211;
        bool r42045050 = r42045044 <= r42045049;
        double r42045051 = r42045039 / r42045043;
        double r42045052 = r42045040 * r42045051;
        double r42045053 = r42045050 ? r42045044 : r42045052;
        double r42045054 = r42045046 ? r42045048 : r42045053;
        return r42045054;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	10.5
Target	2.2
Herbie	1.5

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

Derivation

1. Split input into 3 regimes

2. if (/ (* x (- y z)) (- t z)) < -inf.0

   1. Initial program 60.1

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

   3. Applied *-un-lft-identity 60.1

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

   4. Applied *-commutative 60.1

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

   5. Applied times-frac 0.2

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

   6. Simplified 0.2

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

   if -inf.0 < (/ (* x (- y z)) (- t z)) < 3.4474718287681383e+211

   1. Initial program 1.4

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

   if 3.4474718287681383e+211 < (/ (* x (- y z)) (- t z))

   1. Initial program 46.3

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

   3. Applied *-un-lft-identity 46.3

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

   4. Applied times-frac 2.9

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

   5. Simplified 2.9

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

4. Final simplification 1.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{t - z} = -\infty:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{t - z} \le 3.4474718287681383 \cdot 10^{+211}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"

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

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