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

Average Error: 2.1 → 0.2

Time: 19.5s

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 r509920 = x;
        double r509921 = y;
        double r509922 = z;
        double r509923 = r509921 - r509922;
        double r509924 = t;
        double r509925 = r509924 - r509922;
        double r509926 = 1.0;
        double r509927 = r509925 + r509926;
        double r509928 = a;
        double r509929 = r509927 / r509928;
        double r509930 = r509923 / r509929;
        double r509931 = r509920 - r509930;
        return r509931;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r509932 = a;
        double r509933 = z;
        double r509934 = y;
        double r509935 = r509933 - r509934;
        double r509936 = t;
        double r509937 = r509936 - r509933;
        double r509938 = 1.0;
        double r509939 = r509937 + r509938;
        double r509940 = r509935 / r509939;
        double r509941 = x;
        double r509942 = fma(r509932, r509940, r509941);
        return r509942;
}

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))))