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

Average Error: 14.4 → 0.7

Time: 3.6s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.31647839900996075 \cdot 10^{201} \lor \neg \left(\frac{y}{z} \le -1.08230262257267508 \cdot 10^{-225} \lor \neg \left(\frac{y}{z} \le 7.8156456972782032 \cdot 10^{-118} \lor \neg \left(\frac{y}{z} \le 2.4596581156209282 \cdot 10^{208}\right)\right)\right):\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r608551 = x;
        double r608552 = y;
        double r608553 = z;
        double r608554 = r608552 / r608553;
        double r608555 = t;
        double r608556 = r608554 * r608555;
        double r608557 = r608556 / r608555;
        double r608558 = r608551 * r608557;
        return r608558;
}

↓

double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r608559 = y;
        double r608560 = z;
        double r608561 = r608559 / r608560;
        double r608562 = -2.3164783990099608e+201;
        bool r608563 = r608561 <= r608562;
        double r608564 = -1.0823026225726751e-225;
        bool r608565 = r608561 <= r608564;
        double r608566 = 7.815645697278203e-118;
        bool r608567 = r608561 <= r608566;
        double r608568 = 2.459658115620928e+208;
        bool r608569 = r608561 <= r608568;
        double r608570 = !r608569;
        bool r608571 = r608567 || r608570;
        double r608572 = !r608571;
        bool r608573 = r608565 || r608572;
        double r608574 = !r608573;
        bool r608575 = r608563 || r608574;
        double r608576 = x;
        double r608577 = r608576 * r608559;
        double r608578 = r608577 / r608560;
        double r608579 = r608560 / r608559;
        double r608580 = r608576 / r608579;
        double r608581 = r608575 ? r608578 : r608580;
        return r608581;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	14.4
Target	1.6
Herbie	0.7

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

Derivation

1. Split input into 2 regimes

2. if (/ y z) < -2.3164783990099608e+201 or -1.0823026225726751e-225 < (/ y z) < 7.815645697278203e-118 or 2.459658115620928e+208 < (/ y z)

   1. Initial program 23.0

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

   2. Simplified 13.9

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

   4. Applied associate-*r/ 1.3

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

   if -2.3164783990099608e+201 < (/ y z) < -1.0823026225726751e-225 or 7.815645697278203e-118 < (/ y z) < 2.459658115620928e+208

   1. Initial program 7.6

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

   2. Simplified 0.2

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

   4. Applied associate-*r/ 9.9

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

   6. Applied associate-/l* 0.2

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

4. Final simplification 0.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.31647839900996075 \cdot 10^{201} \lor \neg \left(\frac{y}{z} \le -1.08230262257267508 \cdot 10^{-225} \lor \neg \left(\frac{y}{z} \le 7.8156456972782032 \cdot 10^{-118} \lor \neg \left(\frac{y}{z} \le 2.4596581156209282 \cdot 10^{208}\right)\right)\right):\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020089 +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)))