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

Average Error: 1.6 → 1.6

Time: 9.6s

Precision: 64

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

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a) {
        double r509727 = x;
        double r509728 = y;
        double r509729 = z;
        double r509730 = t;
        double r509731 = r509729 - r509730;
        double r509732 = a;
        double r509733 = r509732 - r509730;
        double r509734 = r509731 / r509733;
        double r509735 = r509728 * r509734;
        double r509736 = r509727 + r509735;
        return r509736;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r509737 = x;
        double r509738 = y;
        double r509739 = z;
        double r509740 = t;
        double r509741 = r509739 - r509740;
        double r509742 = a;
        double r509743 = r509742 - r509740;
        double r509744 = r509741 / r509743;
        double r509745 = r509738 * r509744;
        double r509746 = r509737 + r509745;
        return r509746;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	1.6
Target	0.5
Herbie	1.6

\[\begin{array}{l} \mathbf{if}\;y \lt -8.50808486055124107 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

1. Initial program 1.6

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

2. Final simplification 1.6

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

Reproduce

herbie shell --seed 2020045 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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