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

Average Error: 2.3 → 0.2

Time: 23.5s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a) {
        double r30475304 = x;
        double r30475305 = y;
        double r30475306 = z;
        double r30475307 = r30475305 - r30475306;
        double r30475308 = t;
        double r30475309 = r30475308 - r30475306;
        double r30475310 = 1.0;
        double r30475311 = r30475309 + r30475310;
        double r30475312 = a;
        double r30475313 = r30475311 / r30475312;
        double r30475314 = r30475307 / r30475313;
        double r30475315 = r30475304 - r30475314;
        return r30475315;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r30475316 = z;
        double r30475317 = y;
        double r30475318 = r30475316 - r30475317;
        double r30475319 = 1.0;
        double r30475320 = t;
        double r30475321 = r30475319 + r30475320;
        double r30475322 = r30475321 - r30475316;
        double r30475323 = r30475318 / r30475322;
        double r30475324 = a;
        double r30475325 = x;
        double r30475326 = fma(r30475323, r30475324, r30475325);
        return r30475326;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	2.3
Target	0.2
Herbie	0.2

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

Derivation

1. Initial program 2.3

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

2. Simplified 0.2

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

3. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019169 +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))))