Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A

Average Error: 1.4 → 1.3

Time: 11.1s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[x + y \cdot \frac{z - t}{z - a}\]

↓

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

C

double f(double x, double y, double z, double t, double a) {
        double r461146 = x;
        double r461147 = y;
        double r461148 = z;
        double r461149 = t;
        double r461150 = r461148 - r461149;
        double r461151 = a;
        double r461152 = r461148 - r461151;
        double r461153 = r461150 / r461152;
        double r461154 = r461147 * r461153;
        double r461155 = r461146 + r461154;
        return r461155;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r461156 = z;
        double r461157 = a;
        double r461158 = r461156 - r461157;
        double r461159 = r461156 / r461158;
        double r461160 = t;
        double r461161 = r461160 / r461158;
        double r461162 = r461159 - r461161;
        double r461163 = y;
        double r461164 = x;
        double r461165 = fma(r461162, r461163, r461164);
        return r461165;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	1.4
Target	1.2
Herbie	1.3

\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

1. Initial program 1.4

   \[x + y \cdot \frac{z - t}{z - a}\]

2. Simplified 1.3

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{z - a}, y, x\right)}\]
3. Using strategy rm

4. Applied div-sub 1.3

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

5. Final simplification 1.3

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

Reproduce

herbie shell --seed 2019350 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

  (+ x (* y (/ (- z t) (- z a)))))