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

Average Error: 7.4 → 7.4

Time: 24.0s

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 r24816214 = x;
        double r24816215 = y;
        double r24816216 = r24816214 + r24816215;
        double r24816217 = 1.0;
        double r24816218 = z;
        double r24816219 = r24816215 / r24816218;
        double r24816220 = r24816217 - r24816219;
        double r24816221 = r24816216 / r24816220;
        return r24816221;
}

↓

double f(double x, double y, double z) {
        double r24816222 = y;
        double r24816223 = x;
        double r24816224 = r24816222 + r24816223;
        double r24816225 = 1.0;
        double r24816226 = z;
        double r24816227 = r24816222 / r24816226;
        double r24816228 = r24816225 - r24816227;
        double r24816229 = r24816224 / r24816228;
        return r24816229;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	7.4
Target	4.0
Herbie	7.4

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

Derivation

1. Initial program 7.4

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

2. Final simplification 7.4

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

Reproduce

herbie shell --seed 2019179 +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))))