Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4

Average Error: 2.2 → 2.2

Time: 27.3s

Precision: 64

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

Math

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

↓

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

C

double f(double x, double y, double z, double t) {
        double r536923 = x;
        double r536924 = y;
        double r536925 = r536924 - r536923;
        double r536926 = z;
        double r536927 = t;
        double r536928 = r536926 / r536927;
        double r536929 = r536925 * r536928;
        double r536930 = r536923 + r536929;
        return r536930;
}

↓

double f(double x, double y, double z, double t) {
        double r536931 = y;
        double r536932 = x;
        double r536933 = r536931 - r536932;
        double r536934 = z;
        double r536935 = t;
        double r536936 = r536934 / r536935;
        double r536937 = fma(r536933, r536936, r536932);
        return r536937;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	2.2
Target	2.3
Herbie	2.2

\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.887:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

1. Initial program 2.2

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

2. Simplified 2.2

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

4. Applied *-un-lft-identity 2.2

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

5. Final simplification 2.2

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.887) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) -0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))

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