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

Average Error: 2.0 → 0.2

Time: 59.4s

Precision: 64

Math

\[x - \frac{y - z}{\frac{\left(t - z\right) + 1.0}{a}}\]

↓

\[\mathsf{fma}\left(a, \frac{z - y}{\left(1.0 - z\right) + t}, x\right)\]

C

double f(double x, double y, double z, double t, double a) {
        double r12426514 = x;
        double r12426515 = y;
        double r12426516 = z;
        double r12426517 = r12426515 - r12426516;
        double r12426518 = t;
        double r12426519 = r12426518 - r12426516;
        double r12426520 = 1.0;
        double r12426521 = r12426519 + r12426520;
        double r12426522 = a;
        double r12426523 = r12426521 / r12426522;
        double r12426524 = r12426517 / r12426523;
        double r12426525 = r12426514 - r12426524;
        return r12426525;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r12426526 = a;
        double r12426527 = z;
        double r12426528 = y;
        double r12426529 = r12426527 - r12426528;
        double r12426530 = 1.0;
        double r12426531 = r12426530 - r12426527;
        double r12426532 = t;
        double r12426533 = r12426531 + r12426532;
        double r12426534 = r12426529 / r12426533;
        double r12426535 = x;
        double r12426536 = fma(r12426526, r12426534, r12426535);
        return r12426536;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	2.0
Target	0.2
Herbie	0.2

\[x - \frac{y - z}{\left(t - z\right) + 1.0} \cdot a\]

Derivation

1. Initial program 2.0

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1.0}{a}}\]

2. Simplified 0.2

   \[\leadsto \color{blue}{\mathsf{fma}\left(a, \frac{z - y}{t + \left(1.0 - z\right)}, x\right)}\]

3. Final simplification 0.2

   \[\leadsto \mathsf{fma}\left(a, \frac{z - y}{\left(1.0 - z\right) + t}, x\right)\]

Reproduce

herbie shell --seed 2019156 +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))))