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

Average Error: 7.5 → 7.5

Time: 2.9s

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 r794815 = x;
        double r794816 = y;
        double r794817 = r794815 + r794816;
        double r794818 = 1.0;
        double r794819 = z;
        double r794820 = r794816 / r794819;
        double r794821 = r794818 - r794820;
        double r794822 = r794817 / r794821;
        return r794822;
}

↓

double f(double x, double y, double z) {
        double r794823 = x;
        double r794824 = y;
        double r794825 = r794823 + r794824;
        double r794826 = 1.0;
        double r794827 = z;
        double r794828 = r794824 / r794827;
        double r794829 = r794826 - r794828;
        double r794830 = r794825 / r794829;
        return r794830;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	7.5
Target	3.8
Herbie	7.5

\[\begin{array}{l} \mathbf{if}\;y \lt -3.742931076268985646434612946949172132145 \cdot 10^{171}:\\ \;\;\;\;\frac{y + x}{-y} \cdot z\\ \mathbf{elif}\;y \lt 3.553466245608673435460441960303815115662 \cdot 10^{168}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{-y} \cdot z\\ \end{array}\]

Derivation

1. Initial program 7.5

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

2. Final simplification 7.5

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

Reproduce

herbie shell --seed 2019362 
(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))))