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

Average Error: 1.8 → 0.2

Time: 10.5s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

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 r729853 = x;
        double r729854 = y;
        double r729855 = z;
        double r729856 = r729854 - r729855;
        double r729857 = t;
        double r729858 = r729857 - r729855;
        double r729859 = 1.0;
        double r729860 = r729858 + r729859;
        double r729861 = a;
        double r729862 = r729860 / r729861;
        double r729863 = r729856 / r729862;
        double r729864 = r729853 - r729863;
        return r729864;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r729865 = a;
        double r729866 = z;
        double r729867 = y;
        double r729868 = r729866 - r729867;
        double r729869 = t;
        double r729870 = r729869 - r729866;
        double r729871 = 1.0;
        double r729872 = r729870 + r729871;
        double r729873 = r729868 / r729872;
        double r729874 = x;
        double r729875 = fma(r729865, r729873, r729874);
        return r729875;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	1.8
Target	0.2
Herbie	0.2

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

Derivation

1. Initial program 1.8

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

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 2020047 +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))))