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

Average Error: 7.3 → 7.3

Time: 12.6s

Precision: 64

Math

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

↓

\[\left(y + x\right) \cdot \frac{1}{1 - \frac{y}{z}}\]

C

double f(double x, double y, double z) {
        double r27059524 = x;
        double r27059525 = y;
        double r27059526 = r27059524 + r27059525;
        double r27059527 = 1.0;
        double r27059528 = z;
        double r27059529 = r27059525 / r27059528;
        double r27059530 = r27059527 - r27059529;
        double r27059531 = r27059526 / r27059530;
        return r27059531;
}

↓

double f(double x, double y, double z) {
        double r27059532 = y;
        double r27059533 = x;
        double r27059534 = r27059532 + r27059533;
        double r27059535 = 1.0;
        double r27059536 = 1.0;
        double r27059537 = z;
        double r27059538 = r27059532 / r27059537;
        double r27059539 = r27059536 - r27059538;
        double r27059540 = r27059535 / r27059539;
        double r27059541 = r27059534 * r27059540;
        return r27059541;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	7.3
Target	4.1
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. Using strategy rm

3. Applied div-inv 7.3

   \[\leadsto \color{blue}{\left(x + y\right) \cdot \frac{1}{1 - \frac{y}{z}}}\]

4. Final simplification 7.3

   \[\leadsto \left(y + x\right) \cdot \frac{1}{1 - \frac{y}{z}}\]

Reproduce

herbie shell --seed 2019169 
(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))))