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

Average Error: 7.3 → 7.3

Time: 18.9s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z) {
        double r26146216 = x;
        double r26146217 = y;
        double r26146218 = r26146216 + r26146217;
        double r26146219 = 1.0;
        double r26146220 = z;
        double r26146221 = r26146217 / r26146220;
        double r26146222 = r26146219 - r26146221;
        double r26146223 = r26146218 / r26146222;
        return r26146223;
}

↓

double f(double x, double y, double z) {
        double r26146224 = y;
        double r26146225 = x;
        double r26146226 = r26146224 + r26146225;
        double r26146227 = 1.0;
        double r26146228 = z;
        double r26146229 = r26146224 / r26146228;
        double r26146230 = r26146227 - r26146229;
        double r26146231 = r26146226 / r26146230;
        return r26146231;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	7.3
Target	3.9
Herbie	7.3

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

Derivation

1. Initial program 7.3

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

2. Final simplification 7.3

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

Reproduce

herbie shell --seed 2019192 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"

  :herbie-target
  (if (< y -3.7429310762689856e+171) (* (/ (+ y x) (- y)) z) (if (< y 3.5534662456086734e+168) (/ (+ x y) (- 1.0 (/ y z))) (* (/ (+ y x) (- y)) z)))

  (/ (+ x y) (- 1.0 (/ y z))))