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

Average Error: 7.6 → 7.6

Time: 4.5s

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 r581191 = x;
        double r581192 = y;
        double r581193 = r581191 + r581192;
        double r581194 = 1.0;
        double r581195 = z;
        double r581196 = r581192 / r581195;
        double r581197 = r581194 - r581196;
        double r581198 = r581193 / r581197;
        return r581198;
}

↓

double f(double x, double y, double z) {
        double r581199 = x;
        double r581200 = y;
        double r581201 = r581199 + r581200;
        double r581202 = 1.0;
        double r581203 = z;
        double r581204 = r581200 / r581203;
        double r581205 = r581202 - r581204;
        double r581206 = r581201 / r581205;
        return r581206;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	7.6
Target	3.8
Herbie	7.6

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

Derivation

1. Initial program 7.6

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

2. Final simplification 7.6

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

Reproduce

herbie shell --seed 2020002 
(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))))