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

Average Error: 7.4 → 7.4

Time: 4.8s

Precision: 64

Math

\[\frac{x + y}{1 - \frac{y}{z}}\]

↓

\[\frac{x + y}{1 - \frac{y}{z}}\]

C

double f(double x, double y, double z) {
        double r636856 = x;
        double r636857 = y;
        double r636858 = r636856 + r636857;
        double r636859 = 1.0;
        double r636860 = z;
        double r636861 = r636857 / r636860;
        double r636862 = r636859 - r636861;
        double r636863 = r636858 / r636862;
        return r636863;
}

↓

double f(double x, double y, double z) {
        double r636864 = x;
        double r636865 = y;
        double r636866 = r636864 + r636865;
        double r636867 = 1.0;
        double r636868 = z;
        double r636869 = r636865 / r636868;
        double r636870 = r636867 - r636869;
        double r636871 = r636866 / r636870;
        return r636871;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	7.4
Target	4.0
Herbie	7.4

\[\begin{array}{l} \mathbf{if}\;y \lt -3.74293107626898565 \cdot 10^{171}:\\ \;\;\;\;\frac{y + x}{-y} \cdot z\\ \mathbf{elif}\;y \lt 3.55346624560867344 \cdot 10^{168}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{-y} \cdot z\\ \end{array}\]

Derivation

1. Initial program 7.4

   \[\frac{x + y}{1 - \frac{y}{z}}\]

2. Final simplification 7.4

   \[\leadsto \frac{x + y}{1 - \frac{y}{z}}\]

Reproduce

herbie shell --seed 2020024 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

  :herbie-target
  (if (< y -3.7429310762689856e+171) (* (/ (+ y x) (- y)) z) (if (< y 3.5534662456086734e+168) (/ (+ x y) (- 1 (/ y z))) (* (/ (+ y x) (- y)) z)))

  (/ (+ x y) (- 1 (/ y z))))