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

Average Error: 7.8 → 7.8

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 r588739 = x;
        double r588740 = y;
        double r588741 = r588739 + r588740;
        double r588742 = 1.0;
        double r588743 = z;
        double r588744 = r588740 / r588743;
        double r588745 = r588742 - r588744;
        double r588746 = r588741 / r588745;
        return r588746;
}

↓

double f(double x, double y, double z) {
        double r588747 = x;
        double r588748 = y;
        double r588749 = r588747 + r588748;
        double r588750 = 1.0;
        double r588751 = z;
        double r588752 = r588748 / r588751;
        double r588753 = r588750 - r588752;
        double r588754 = r588749 / r588753;
        return r588754;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	7.8
Target	4.1
Herbie	7.8

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

Derivation

1. Initial program 7.8

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

2. Final simplification 7.8

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

Reproduce

herbie shell --seed 2020062 +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))))