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

Average Error: 2.1 → 0.2

Time: 19.6s

Precision: 64

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 r382738 = x;
        double r382739 = y;
        double r382740 = z;
        double r382741 = r382739 - r382740;
        double r382742 = t;
        double r382743 = r382742 - r382740;
        double r382744 = 1.0;
        double r382745 = r382743 + r382744;
        double r382746 = a;
        double r382747 = r382745 / r382746;
        double r382748 = r382741 / r382747;
        double r382749 = r382738 - r382748;
        return r382749;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r382750 = a;
        double r382751 = z;
        double r382752 = y;
        double r382753 = r382751 - r382752;
        double r382754 = t;
        double r382755 = r382754 - r382751;
        double r382756 = 1.0;
        double r382757 = r382755 + r382756;
        double r382758 = r382753 / r382757;
        double r382759 = x;
        double r382760 = fma(r382750, r382758, r382759);
        return r382760;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	2.1
Target	0.2
Herbie	0.2

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

Derivation

1. Initial program 2.1

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

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 2019326 +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))))