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

Average Error: 14.0 → 6.3

Time: 15.3s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t) {
        double r87082 = x;
        double r87083 = y;
        double r87084 = z;
        double r87085 = r87083 / r87084;
        double r87086 = t;
        double r87087 = r87085 * r87086;
        double r87088 = r87087 / r87086;
        double r87089 = r87082 * r87088;
        return r87089;
}

↓

double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r87090 = x;
        double r87091 = y;
        double r87092 = z;
        double r87093 = r87091 / r87092;
        double r87094 = r87090 * r87093;
        return r87094;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Derivation

1. Split input into 2 regimes

2. if (/ y z) < -inf.0 or -1.9001417427877727e-270 < (/ y z) < 1.9873965595470336e-307 or 1.0511610758752524e+156 < (/ y z)

   1. Initial program 27.6

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

   2. Simplified 21.5

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

   4. Applied associate-*r/ 0.8

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

   if -inf.0 < (/ y z) < -1.9001417427877727e-270 or 1.9873965595470336e-307 < (/ y z) < 1.0511610758752524e+156

   1. Initial program 8.6

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

   2. Simplified 0.2

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

4. Final simplification 6.3

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

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  :precision binary64
  (* x (/ (* (/ y z) t) t)))