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

Average Error: 1.9 → 0.2

Time: 22.2s

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 r24766312 = x;
        double r24766313 = y;
        double r24766314 = z;
        double r24766315 = r24766313 - r24766314;
        double r24766316 = t;
        double r24766317 = r24766316 - r24766314;
        double r24766318 = 1.0;
        double r24766319 = r24766317 + r24766318;
        double r24766320 = a;
        double r24766321 = r24766319 / r24766320;
        double r24766322 = r24766315 / r24766321;
        double r24766323 = r24766312 - r24766322;
        return r24766323;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r24766324 = a;
        double r24766325 = z;
        double r24766326 = y;
        double r24766327 = r24766325 - r24766326;
        double r24766328 = t;
        double r24766329 = r24766328 - r24766325;
        double r24766330 = 1.0;
        double r24766331 = r24766329 + r24766330;
        double r24766332 = r24766327 / r24766331;
        double r24766333 = x;
        double r24766334 = fma(r24766324, r24766332, r24766333);
        return r24766334;
}

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

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

3. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019174 +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))))