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

Average Error: 7.8 → 7.8

Time: 4.2s

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 r650556 = x;
        double r650557 = y;
        double r650558 = r650556 + r650557;
        double r650559 = 1.0;
        double r650560 = z;
        double r650561 = r650557 / r650560;
        double r650562 = r650559 - r650561;
        double r650563 = r650558 / r650562;
        return r650563;
}

↓

double f(double x, double y, double z) {
        double r650564 = x;
        double r650565 = y;
        double r650566 = r650564 + r650565;
        double r650567 = 1.0;
        double r650568 = z;
        double r650569 = r650565 / r650568;
        double r650570 = r650567 - r650569;
        double r650571 = r650566 / r650570;
        return r650571;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	7.8
Target	4.3
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 2020060 +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))))