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

Average Error: 11.4 → 1.7

Time: 2.8s

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 r554390 = x;
        double r554391 = y;
        double r554392 = z;
        double r554393 = r554391 - r554392;
        double r554394 = r554390 * r554393;
        double r554395 = t;
        double r554396 = r554395 - r554392;
        double r554397 = r554394 / r554396;
        return r554397;
}

↓

double f(double x, double y, double z, double t) {
        double r554398 = x;
        double r554399 = y;
        double r554400 = z;
        double r554401 = r554399 - r554400;
        double r554402 = r554398 * r554401;
        double r554403 = t;
        double r554404 = r554403 - r554400;
        double r554405 = r554402 / r554404;
        double r554406 = 0.0;
        bool r554407 = r554405 <= r554406;
        double r554408 = 1.0;
        double r554409 = r554404 / r554401;
        double r554410 = r554408 * r554409;
        double r554411 = r554398 / r554410;
        double r554412 = 2.2859321695890317e+67;
        bool r554413 = r554405 <= r554412;
        double r554414 = r554398 / r554404;
        double r554415 = r554414 * r554401;
        double r554416 = r554413 ? r554405 : r554415;
        double r554417 = r554407 ? r554411 : r554416;
        return r554417;
}

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 +o rules:numerics
(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)))