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

Average Error: 1.9 → 1.9

Time: 12.6s

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 r636446 = x;
        double r636447 = y;
        double r636448 = r636447 - r636446;
        double r636449 = z;
        double r636450 = t;
        double r636451 = r636449 / r636450;
        double r636452 = r636448 * r636451;
        double r636453 = r636446 + r636452;
        return r636453;
}

↓

double f(double x, double y, double z, double t) {
        double r636454 = y;
        double r636455 = x;
        double r636456 = r636454 - r636455;
        double r636457 = z;
        double r636458 = t;
        double r636459 = r636457 / r636458;
        double r636460 = fma(r636456, r636459, r636455);
        return r636460;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	1.9
Target	2.1
Herbie	1.9

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

Derivation

1. Initial program 1.9

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

2. Simplified 1.9

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

3. Final simplification 1.9

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

Reproduce

herbie shell --seed 2020042 +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))))