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

Average Error: 7.5 → 7.5

Time: 3.8s

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 r784812 = x;
        double r784813 = y;
        double r784814 = r784812 + r784813;
        double r784815 = 1.0;
        double r784816 = z;
        double r784817 = r784813 / r784816;
        double r784818 = r784815 - r784817;
        double r784819 = r784814 / r784818;
        return r784819;
}

↓

double f(double x, double y, double z) {
        double r784820 = x;
        double r784821 = y;
        double r784822 = r784820 + r784821;
        double r784823 = 1.0;
        double r784824 = z;
        double r784825 = r784821 / r784824;
        double r784826 = r784823 - r784825;
        double r784827 = r784822 / r784826;
        return r784827;
}

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 +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))))