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

Average Error: 2.1 → 0.2

Time: 15.7s

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 r25662891 = x;
        double r25662892 = y;
        double r25662893 = z;
        double r25662894 = r25662892 - r25662893;
        double r25662895 = t;
        double r25662896 = r25662895 - r25662893;
        double r25662897 = 1.0;
        double r25662898 = r25662896 + r25662897;
        double r25662899 = a;
        double r25662900 = r25662898 / r25662899;
        double r25662901 = r25662894 / r25662900;
        double r25662902 = r25662891 - r25662901;
        return r25662902;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r25662903 = a;
        double r25662904 = z;
        double r25662905 = y;
        double r25662906 = r25662904 - r25662905;
        double r25662907 = t;
        double r25662908 = r25662907 - r25662904;
        double r25662909 = 1.0;
        double r25662910 = r25662908 + r25662909;
        double r25662911 = r25662906 / r25662910;
        double r25662912 = x;
        double r25662913 = fma(r25662903, r25662911, r25662912);
        return r25662913;
}

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

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

3. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"

  :herbie-target
  (- x (* (/ (- y z) (+ (- t z) 1.0)) a))

  (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))