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

Average Error: 2.3 → 2.3

Time: 18.6s

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 r454844 = x;
        double r454845 = y;
        double r454846 = r454845 - r454844;
        double r454847 = z;
        double r454848 = t;
        double r454849 = r454847 / r454848;
        double r454850 = r454846 * r454849;
        double r454851 = r454844 + r454850;
        return r454851;
}

↓

double f(double x, double y, double z, double t) {
        double r454852 = y;
        double r454853 = x;
        double r454854 = r454852 - r454853;
        double r454855 = z;
        double r454856 = t;
        double r454857 = r454855 / r454856;
        double r454858 = fma(r454854, r454857, r454853);
        return r454858;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	2.3
Target	2.4
Herbie	2.3

\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.88671875:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

1. Initial program 2.3

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

2. Simplified 2.3

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

3. Final simplification 2.3

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

Reproduce

herbie shell --seed 2019351 +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))))