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

Average Error: 14.8 → 1.7

Time: 11.5s

Precision: 64

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

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.0989985598366828 \cdot 10^{-236}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 4.4303806781760739 \cdot 10^{-235}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 6.4284572525223976 \cdot 10^{303}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r560978 = x;
        double r560979 = y;
        double r560980 = z;
        double r560981 = r560979 / r560980;
        double r560982 = t;
        double r560983 = r560981 * r560982;
        double r560984 = r560983 / r560982;
        double r560985 = r560978 * r560984;
        return r560985;
}

↓

double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r560986 = y;
        double r560987 = z;
        double r560988 = r560986 / r560987;
        double r560989 = -2.098998559836683e-236;
        bool r560990 = r560988 <= r560989;
        double r560991 = x;
        double r560992 = r560987 / r560986;
        double r560993 = r560991 / r560992;
        double r560994 = 4.430380678176074e-235;
        bool r560995 = r560988 <= r560994;
        double r560996 = r560991 * r560986;
        double r560997 = r560996 / r560987;
        double r560998 = 6.428457252522398e+303;
        bool r560999 = r560988 <= r560998;
        double r561000 = 1.0;
        double r561001 = r561000 / r560987;
        double r561002 = r560996 * r561001;
        double r561003 = r560999 ? r560993 : r561002;
        double r561004 = r560995 ? r560997 : r561003;
        double r561005 = r560990 ? r560993 : r561004;
        return r561005;
}

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	1.7

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

Derivation

1. Split input into 3 regimes

2. if (/ y z) < -2.098998559836683e-236 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 2.3

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}}\]
   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* 2.2

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

   if -2.098998559836683e-236 < (/ y z) < 4.430380678176074e-235

   1. Initial program 18.7

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

   2. Simplified 12.1

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

   4. Applied associate-*r/ 0.4

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

   if 6.428457252522398e+303 < (/ y z)

   1. Initial program 64.0

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

   2. Simplified 61.9

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

   4. Applied div-inv 61.9

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

   5. Applied associate-*r* 0.3

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

4. Final simplification 1.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.0989985598366828 \cdot 10^{-236}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 4.4303806781760739 \cdot 10^{-235}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 6.4284572525223976 \cdot 10^{303}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \end{array}\]

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)))