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

Average Error: 7.5 → 7.5

Time: 16.2s

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 r15071359 = x;
        double r15071360 = y;
        double r15071361 = r15071359 + r15071360;
        double r15071362 = 1.0;
        double r15071363 = z;
        double r15071364 = r15071360 / r15071363;
        double r15071365 = r15071362 - r15071364;
        double r15071366 = r15071361 / r15071365;
        return r15071366;
}

↓

double f(double x, double y, double z) {
        double r15071367 = y;
        double r15071368 = x;
        double r15071369 = r15071367 + r15071368;
        double r15071370 = 1.0;
        double r15071371 = z;
        double r15071372 = r15071367 / r15071371;
        double r15071373 = r15071370 - r15071372;
        double r15071374 = r15071369 / r15071373;
        return r15071374;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	7.5
Target	4.2
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

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

Reproduce

herbie shell --seed 2019171 
(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))))