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

Average Error: 2.1 → 0.3

Time: 34.2s

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 r446152 = x;
        double r446153 = y;
        double r446154 = z;
        double r446155 = r446153 - r446154;
        double r446156 = t;
        double r446157 = r446156 - r446154;
        double r446158 = 1.0;
        double r446159 = r446157 + r446158;
        double r446160 = a;
        double r446161 = r446159 / r446160;
        double r446162 = r446155 / r446161;
        double r446163 = r446152 - r446162;
        return r446163;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r446164 = a;
        double r446165 = z;
        double r446166 = y;
        double r446167 = r446165 - r446166;
        double r446168 = t;
        double r446169 = r446168 - r446165;
        double r446170 = 1.0;
        double r446171 = r446169 + r446170;
        double r446172 = r446167 / r446171;
        double r446173 = x;
        double r446174 = fma(r446164, r446172, r446173);
        return r446174;
}

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

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

3. Final simplification 0.3

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

Reproduce

herbie shell --seed 2019198 +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))))