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

Average Error: 2.1 → 0.2

Time: 14.8s

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 r388303 = x;
        double r388304 = y;
        double r388305 = z;
        double r388306 = r388304 - r388305;
        double r388307 = t;
        double r388308 = r388307 - r388305;
        double r388309 = 1.0;
        double r388310 = r388308 + r388309;
        double r388311 = a;
        double r388312 = r388310 / r388311;
        double r388313 = r388306 / r388312;
        double r388314 = r388303 - r388313;
        return r388314;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r388315 = a;
        double r388316 = z;
        double r388317 = y;
        double r388318 = r388316 - r388317;
        double r388319 = t;
        double r388320 = r388319 - r388316;
        double r388321 = 1.0;
        double r388322 = r388320 + r388321;
        double r388323 = r388318 / r388322;
        double r388324 = x;
        double r388325 = fma(r388315, r388323, r388324);
        return r388325;
}

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

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

3. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019179 +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))))