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

Average Error: 1.9 → 0.2

Time: 19.8s

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 r446582 = x;
        double r446583 = y;
        double r446584 = z;
        double r446585 = r446583 - r446584;
        double r446586 = t;
        double r446587 = r446586 - r446584;
        double r446588 = 1.0;
        double r446589 = r446587 + r446588;
        double r446590 = a;
        double r446591 = r446589 / r446590;
        double r446592 = r446585 / r446591;
        double r446593 = r446582 - r446592;
        return r446593;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r446594 = a;
        double r446595 = z;
        double r446596 = y;
        double r446597 = r446595 - r446596;
        double r446598 = t;
        double r446599 = r446598 - r446595;
        double r446600 = 1.0;
        double r446601 = r446599 + r446600;
        double r446602 = r446597 / r446601;
        double r446603 = x;
        double r446604 = fma(r446594, r446602, r446603);
        return r446604;
}

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))))