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

Average Error: 1.8 → 0.2

Time: 12.7s

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 r658945 = x;
        double r658946 = y;
        double r658947 = z;
        double r658948 = r658946 - r658947;
        double r658949 = t;
        double r658950 = r658949 - r658947;
        double r658951 = 1.0;
        double r658952 = r658950 + r658951;
        double r658953 = a;
        double r658954 = r658952 / r658953;
        double r658955 = r658948 / r658954;
        double r658956 = r658945 - r658955;
        return r658956;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r658957 = a;
        double r658958 = z;
        double r658959 = y;
        double r658960 = r658958 - r658959;
        double r658961 = t;
        double r658962 = r658961 - r658958;
        double r658963 = 1.0;
        double r658964 = r658962 + r658963;
        double r658965 = r658960 / r658964;
        double r658966 = x;
        double r658967 = fma(r658957, r658965, r658966);
        return r658967;
}

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))))