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

Average Error: 2.1 → 0.3

Time: 16.1s

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 r28411959 = x;
        double r28411960 = y;
        double r28411961 = z;
        double r28411962 = r28411960 - r28411961;
        double r28411963 = t;
        double r28411964 = r28411963 - r28411961;
        double r28411965 = 1.0;
        double r28411966 = r28411964 + r28411965;
        double r28411967 = a;
        double r28411968 = r28411966 / r28411967;
        double r28411969 = r28411962 / r28411968;
        double r28411970 = r28411959 - r28411969;
        return r28411970;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r28411971 = a;
        double r28411972 = z;
        double r28411973 = y;
        double r28411974 = r28411972 - r28411973;
        double r28411975 = t;
        double r28411976 = r28411975 - r28411972;
        double r28411977 = 1.0;
        double r28411978 = r28411976 + r28411977;
        double r28411979 = r28411974 / r28411978;
        double r28411980 = x;
        double r28411981 = fma(r28411971, r28411979, r28411980);
        return r28411981;
}

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	0.3
Herbie	0.3

\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

1. Initial program 2.1

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

2. Simplified 0.3

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

3. Final simplification 0.3

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

Reproduce

herbie shell --seed 2019192 +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))))