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

Average Error: 2.1 → 0.2

Time: 22.2s

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 r838903 = x;
        double r838904 = y;
        double r838905 = z;
        double r838906 = r838904 - r838905;
        double r838907 = t;
        double r838908 = r838907 - r838905;
        double r838909 = 1.0;
        double r838910 = r838908 + r838909;
        double r838911 = a;
        double r838912 = r838910 / r838911;
        double r838913 = r838906 / r838912;
        double r838914 = r838903 - r838913;
        return r838914;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r838915 = a;
        double r838916 = z;
        double r838917 = y;
        double r838918 = r838916 - r838917;
        double r838919 = t;
        double r838920 = r838919 - r838916;
        double r838921 = 1.0;
        double r838922 = r838920 + r838921;
        double r838923 = r838918 / r838922;
        double r838924 = x;
        double r838925 = fma(r838915, r838923, r838924);
        return r838925;
}

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 2019305 +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))))