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

Average Error: 14.8 → 1.9

Time: 10.2s

Precision: 64

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

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -6.77638088471923947 \cdot 10^{-181} \lor \neg \left(\frac{y}{z} \le 4.4303806781760739 \cdot 10^{-235}\right) \land \frac{y}{z} \le 6.4284572525223976 \cdot 10^{303}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r606239 = x;
        double r606240 = y;
        double r606241 = z;
        double r606242 = r606240 / r606241;
        double r606243 = t;
        double r606244 = r606242 * r606243;
        double r606245 = r606244 / r606243;
        double r606246 = r606239 * r606245;
        return r606246;
}

↓

double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r606247 = y;
        double r606248 = z;
        double r606249 = r606247 / r606248;
        double r606250 = -6.77638088471924e-181;
        bool r606251 = r606249 <= r606250;
        double r606252 = 4.430380678176074e-235;
        bool r606253 = r606249 <= r606252;
        double r606254 = !r606253;
        double r606255 = 6.428457252522398e+303;
        bool r606256 = r606249 <= r606255;
        bool r606257 = r606254 && r606256;
        bool r606258 = r606251 || r606257;
        double r606259 = x;
        double r606260 = r606248 / r606247;
        double r606261 = r606259 / r606260;
        double r606262 = 1.0;
        double r606263 = r606248 / r606259;
        double r606264 = r606263 / r606247;
        double r606265 = r606262 / r606264;
        double r606266 = r606258 ? r606261 : r606265;
        return r606266;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	14.8
Target	1.5
Herbie	1.9

\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \lt -1.20672205123045005 \cdot 10^{245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt -5.90752223693390633 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 5.65895442315341522 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 2.0087180502407133 \cdot 10^{217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Derivation

1. Split input into 2 regimes

2. if (/ y z) < -6.77638088471924e-181 or 4.430380678176074e-235 < (/ y z) < 6.428457252522398e+303

   1. Initial program 11.8

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

   2. Simplified 2.5

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

   4. Applied associate-*r/ 8.4

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

   6. Applied associate-/l* 2.3

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

   if -6.77638088471924e-181 < (/ y z) < 4.430380678176074e-235 or 6.428457252522398e+303 < (/ y z)

   1. Initial program 22.0

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

   2. Simplified 15.0

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

   4. Applied associate-*r/ 0.9

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

   6. Applied clear-num 1.5

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

   7. Simplified 1.1

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{z}{x}}{y}}}\]
3. Recombined 2 regimes into one program.

4. Final simplification 1.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -6.77638088471923947 \cdot 10^{-181} \lor \neg \left(\frac{y}{z} \le 4.4303806781760739 \cdot 10^{-235}\right) \land \frac{y}{z} \le 6.4284572525223976 \cdot 10^{303}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(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)))