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

Average Error: 7.4 → 7.4

Time: 3.5s

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 r621659 = x;
        double r621660 = y;
        double r621661 = r621659 + r621660;
        double r621662 = 1.0;
        double r621663 = z;
        double r621664 = r621660 / r621663;
        double r621665 = r621662 - r621664;
        double r621666 = r621661 / r621665;
        return r621666;
}

↓

double f(double x, double y, double z) {
        double r621667 = x;
        double r621668 = y;
        double r621669 = r621667 + r621668;
        double r621670 = 1.0;
        double r621671 = z;
        double r621672 = r621668 / r621671;
        double r621673 = r621670 - r621672;
        double r621674 = r621669 / r621673;
        return r621674;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	7.4
Target	3.8
Herbie	7.4

\[\begin{array}{l} \mathbf{if}\;y \lt -3.74293107626898565 \cdot 10^{171}:\\ \;\;\;\;\frac{y + x}{-y} \cdot z\\ \mathbf{elif}\;y \lt 3.55346624560867344 \cdot 10^{168}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{-y} \cdot z\\ \end{array}\]

Derivation

1. Initial program 7.4

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

2. Final simplification 7.4

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

Reproduce

herbie shell --seed 2020047 +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))))