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

Average Error: 14.8 → 0.3

Time: 2.5s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} = -\infty:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{elif}\;\frac{y}{z} \le -2.032946575227289082299442188903898755778 \cdot 10^{-265}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 1.707355746264835359667361500171699768251 \cdot 10^{-300}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{elif}\;\frac{y}{z} \le 7.166584424187464259231246965323639075754 \cdot 10^{225}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r721380 = x;
        double r721381 = y;
        double r721382 = z;
        double r721383 = r721381 / r721382;
        double r721384 = t;
        double r721385 = r721383 * r721384;
        double r721386 = r721385 / r721384;
        double r721387 = r721380 * r721386;
        return r721387;
}

↓

double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r721388 = y;
        double r721389 = z;
        double r721390 = r721388 / r721389;
        double r721391 = -inf.0;
        bool r721392 = r721390 <= r721391;
        double r721393 = 1.0;
        double r721394 = x;
        double r721395 = r721394 * r721388;
        double r721396 = r721389 / r721395;
        double r721397 = r721393 / r721396;
        double r721398 = -2.032946575227289e-265;
        bool r721399 = r721390 <= r721398;
        double r721400 = r721389 / r721388;
        double r721401 = r721394 / r721400;
        double r721402 = 1.7073557462648354e-300;
        bool r721403 = r721390 <= r721402;
        double r721404 = 7.166584424187464e+225;
        bool r721405 = r721390 <= r721404;
        double r721406 = r721394 * r721390;
        double r721407 = r721405 ? r721406 : r721397;
        double r721408 = r721403 ? r721397 : r721407;
        double r721409 = r721399 ? r721401 : r721408;
        double r721410 = r721392 ? r721397 : r721409;
        return r721410;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	14.8
Target	1.6
Herbie	0.3

\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \lt -1.206722051230450047215521150762600712224 \cdot 10^{245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt -5.90752223693390632993316700759382836344 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 5.658954423153415216825328199697215652986 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 2.008718050240713347941382056648619307142 \cdot 10^{217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Derivation

1. Split input into 3 regimes

2. if (/ y z) < -inf.0 or -2.032946575227289e-265 < (/ y z) < 1.7073557462648354e-300 or 7.166584424187464e+225 < (/ y z)

   1. Initial program 29.1

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

   2. Simplified 24.1

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

   4. Applied associate-*r/ 0.3

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

   6. Applied clear-num 0.7

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

   if -inf.0 < (/ y z) < -2.032946575227289e-265

   1. Initial program 10.6

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

   2. Simplified 0.2

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

   4. Applied associate-*r/ 8.2

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

   6. Applied associate-/l* 0.2

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

   if 1.7073557462648354e-300 < (/ y z) < 7.166584424187464e+225

   1. Initial program 9.1

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

   2. Simplified 0.2

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

4. Final simplification 0.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} = -\infty:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{elif}\;\frac{y}{z} \le -2.032946575227289082299442188903898755778 \cdot 10^{-265}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 1.707355746264835359667361500171699768251 \cdot 10^{-300}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{elif}\;\frac{y}{z} \le 7.166584424187464259231246965323639075754 \cdot 10^{225}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019353 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, B"
  :precision binary64

  :herbie-target
  (if (< (/ (* (/ y z) t) t) -1.20672205123045e+245) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) -5.907522236933906e-275) (* x (/ y z)) (if (< (/ (* (/ y z) t) t) 5.658954423153415e-65) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) 2.0087180502407133e+217) (* x (/ y z)) (/ (* y x) z)))))

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