Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3

Average Error: 2.0 → 0.2

Time: 14.5s

Precision: 64

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

Math

\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]

↓

\[\mathsf{fma}\left(a, \frac{z - y}{\left(t - z\right) + 1}, x\right)\]

C

double f(double x, double y, double z, double t, double a) {
        double r650720 = x;
        double r650721 = y;
        double r650722 = z;
        double r650723 = r650721 - r650722;
        double r650724 = t;
        double r650725 = r650724 - r650722;
        double r650726 = 1.0;
        double r650727 = r650725 + r650726;
        double r650728 = a;
        double r650729 = r650727 / r650728;
        double r650730 = r650723 / r650729;
        double r650731 = r650720 - r650730;
        return r650731;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r650732 = a;
        double r650733 = z;
        double r650734 = y;
        double r650735 = r650733 - r650734;
        double r650736 = t;
        double r650737 = r650736 - r650733;
        double r650738 = 1.0;
        double r650739 = r650737 + r650738;
        double r650740 = r650735 / r650739;
        double r650741 = x;
        double r650742 = fma(r650732, r650740, r650741);
        return r650742;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	2.0
Target	0.2
Herbie	0.2

\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

1. Initial program 2.0

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]

2. Simplified 0.2

   \[\leadsto \color{blue}{\mathsf{fma}\left(a, \frac{z - y}{\left(t - z\right) + 1}, x\right)}\]

3. Final simplification 0.2

   \[\leadsto \mathsf{fma}\left(a, \frac{z - y}{\left(t - z\right) + 1}, x\right)\]

Reproduce

herbie shell --seed 2019350 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (- x (* (/ (- y z) (+ (- t z) 1)) a))

  (- x (/ (- y z) (/ (+ (- t z) 1) a))))