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

Average Error: 15.4 → 0.6

Time: 21.3s

Precision: 64

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

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -8.7469245905233031 \cdot 10^{265} \lor \neg \left(\frac{y}{z} \le -1.0665637347194774 \cdot 10^{-221} \lor \neg \left(\frac{y}{z} \le 1.5828563463705101 \cdot 10^{-127}\right) \land \frac{y}{z} \le 2.5905951762285947 \cdot 10^{176}\right):\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r656409 = x;
        double r656410 = y;
        double r656411 = z;
        double r656412 = r656410 / r656411;
        double r656413 = t;
        double r656414 = r656412 * r656413;
        double r656415 = r656414 / r656413;
        double r656416 = r656409 * r656415;
        return r656416;
}

↓

double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r656417 = y;
        double r656418 = z;
        double r656419 = r656417 / r656418;
        double r656420 = -8.746924590523303e+265;
        bool r656421 = r656419 <= r656420;
        double r656422 = -1.0665637347194774e-221;
        bool r656423 = r656419 <= r656422;
        double r656424 = 1.5828563463705101e-127;
        bool r656425 = r656419 <= r656424;
        double r656426 = !r656425;
        double r656427 = 2.5905951762285947e+176;
        bool r656428 = r656419 <= r656427;
        bool r656429 = r656426 && r656428;
        bool r656430 = r656423 || r656429;
        double r656431 = !r656430;
        bool r656432 = r656421 || r656431;
        double r656433 = x;
        double r656434 = r656433 * r656417;
        double r656435 = r656434 / r656418;
        double r656436 = r656418 / r656417;
        double r656437 = r656433 / r656436;
        double r656438 = r656432 ? r656435 : r656437;
        return r656438;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	15.4
Target	1.5
Herbie	0.6

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

Derivation

1. Split input into 2 regimes

2. if (/ y z) < -8.746924590523303e+265 or -1.0665637347194774e-221 < (/ y z) < 1.5828563463705101e-127 or 2.5905951762285947e+176 < (/ y z)

   1. Initial program 24.7

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

   2. Simplified 14.8

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

   4. Applied associate-*r/ 1.2

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

   if -8.746924590523303e+265 < (/ y z) < -1.0665637347194774e-221 or 1.5828563463705101e-127 < (/ y z) < 2.5905951762285947e+176

   1. Initial program 8.4

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

   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 0.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -8.7469245905233031 \cdot 10^{265} \lor \neg \left(\frac{y}{z} \le -1.0665637347194774 \cdot 10^{-221} \lor \neg \left(\frac{y}{z} \le 1.5828563463705101 \cdot 10^{-127}\right) \land \frac{y}{z} \le 2.5905951762285947 \cdot 10^{176}\right):\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020042 +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)))