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

Average Error: 1.8 → 0.2

Time: 14.0s

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 r539381 = x;
        double r539382 = y;
        double r539383 = z;
        double r539384 = r539382 - r539383;
        double r539385 = t;
        double r539386 = r539385 - r539383;
        double r539387 = 1.0;
        double r539388 = r539386 + r539387;
        double r539389 = a;
        double r539390 = r539388 / r539389;
        double r539391 = r539384 / r539390;
        double r539392 = r539381 - r539391;
        return r539392;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r539393 = a;
        double r539394 = z;
        double r539395 = y;
        double r539396 = r539394 - r539395;
        double r539397 = t;
        double r539398 = r539397 - r539394;
        double r539399 = 1.0;
        double r539400 = r539398 + r539399;
        double r539401 = r539396 / r539400;
        double r539402 = x;
        double r539403 = fma(r539393, r539401, r539402);
        return r539403;
}

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))))