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

Average Error: 1.9 → 0.2

Time: 15.1s

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 r674327 = x;
        double r674328 = y;
        double r674329 = z;
        double r674330 = r674328 - r674329;
        double r674331 = t;
        double r674332 = r674331 - r674329;
        double r674333 = 1.0;
        double r674334 = r674332 + r674333;
        double r674335 = a;
        double r674336 = r674334 / r674335;
        double r674337 = r674330 / r674336;
        double r674338 = r674327 - r674337;
        return r674338;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r674339 = a;
        double r674340 = z;
        double r674341 = y;
        double r674342 = r674340 - r674341;
        double r674343 = t;
        double r674344 = r674343 - r674340;
        double r674345 = 1.0;
        double r674346 = r674344 + r674345;
        double r674347 = r674342 / r674346;
        double r674348 = x;
        double r674349 = fma(r674339, r674347, r674348);
        return r674349;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	1.9
Target	0.2
Herbie	0.2

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

Derivation

1. Initial program 1.9

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

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 2020043 +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))))