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

Average Error: 7.4 → 7.4

Time: 8.0s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

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 r544645 = x;
        double r544646 = y;
        double r544647 = r544645 + r544646;
        double r544648 = 1.0;
        double r544649 = z;
        double r544650 = r544646 / r544649;
        double r544651 = r544648 - r544650;
        double r544652 = r544647 / r544651;
        return r544652;
}

↓

double f(double x, double y, double z) {
        double r544653 = x;
        double r544654 = y;
        double r544655 = r544653 + r544654;
        double r544656 = 1.0;
        double r544657 = z;
        double r544658 = r544654 / r544657;
        double r544659 = r544656 - r544658;
        double r544660 = r544655 / r544659;
        return r544660;
}

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))))