Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1

Average Error: 14.7 → 1.1

Time: 14.6s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.588366971627017444543194392656819407323 \cdot 10^{79}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -7.584778841906227496781487885537839730751 \cdot 10^{-279}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 0.0:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 1.406079879178553538420301463833789327206 \cdot 10^{177}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r106452 = x;
        double r106453 = y;
        double r106454 = z;
        double r106455 = r106453 / r106454;
        double r106456 = t;
        double r106457 = r106455 * r106456;
        double r106458 = r106457 / r106456;
        double r106459 = r106452 * r106458;
        return r106459;
}

↓

double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r106460 = y;
        double r106461 = z;
        double r106462 = r106460 / r106461;
        double r106463 = -2.5883669716270174e+79;
        bool r106464 = r106462 <= r106463;
        double r106465 = x;
        double r106466 = r106465 / r106461;
        double r106467 = r106460 * r106466;
        double r106468 = -7.584778841906227e-279;
        bool r106469 = r106462 <= r106468;
        double r106470 = r106462 * r106465;
        double r106471 = 0.0;
        bool r106472 = r106462 <= r106471;
        double r106473 = r106465 * r106460;
        double r106474 = r106473 / r106461;
        double r106475 = 1.4060798791785535e+177;
        bool r106476 = r106462 <= r106475;
        double r106477 = r106461 / r106460;
        double r106478 = r106465 / r106477;
        double r106479 = r106476 ? r106478 : r106467;
        double r106480 = r106472 ? r106474 : r106479;
        double r106481 = r106469 ? r106470 : r106480;
        double r106482 = r106464 ? r106467 : r106481;
        return r106482;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Derivation

1. Split input into 4 regimes

2. if (/ y z) < -2.5883669716270174e+79 or 1.4060798791785535e+177 < (/ y z)

   1. Initial program 31.5

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

   2. Simplified 16.2

      \[\leadsto \color{blue}{\frac{y}{z} \cdot x}\]
   3. Using strategy rm

   4. Applied div-inv 16.2

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

   5. Applied associate-*l* 4.1

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

   6. Simplified 4.0

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

   if -2.5883669716270174e+79 < (/ y z) < -7.584778841906227e-279

   1. Initial program 8.4

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

   2. Simplified 0.2

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

   if -7.584778841906227e-279 < (/ y z) < 0.0

   1. Initial program 18.3

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

   2. Simplified 15.3

      \[\leadsto \color{blue}{\frac{y}{z} \cdot x}\]
   3. Using strategy rm

   4. Applied pow1 15.3

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

   5. Applied pow1 15.3

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

   6. Applied pow-prod-down 15.3

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

   7. Simplified 0.1

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

   if 0.0 < (/ y z) < 1.4060798791785535e+177

   1. Initial program 10.0

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

   2. Simplified 3.4

      \[\leadsto \color{blue}{\frac{y}{z} \cdot x}\]
   3. Using strategy rm

   4. Applied pow1 3.4

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

   5. Applied pow1 3.4

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

   6. Applied pow-prod-down 3.4

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

   7. Simplified 7.3

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

   9. Applied associate-/l* 3.6

      \[\leadsto {\color{blue}{\left(\frac{x}{\frac{z}{y}}\right)}}^{1}\]
3. Recombined 4 regimes into one program.

4. Final simplification 1.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.588366971627017444543194392656819407323 \cdot 10^{79}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -7.584778841906227496781487885537839730751 \cdot 10^{-279}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 0.0:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 1.406079879178553538420301463833789327206 \cdot 10^{177}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019351 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  :precision binary64
  (* x (/ (* (/ y z) t) t)))