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

Average Error: 1.3 → 1.3

Time: 17.5s

Precision: 64

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 r487002 = x;
        double r487003 = y;
        double r487004 = z;
        double r487005 = t;
        double r487006 = r487004 - r487005;
        double r487007 = a;
        double r487008 = r487007 - r487005;
        double r487009 = r487006 / r487008;
        double r487010 = r487003 * r487009;
        double r487011 = r487002 + r487010;
        return r487011;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r487012 = x;
        double r487013 = y;
        double r487014 = z;
        double r487015 = t;
        double r487016 = r487014 - r487015;
        double r487017 = a;
        double r487018 = r487017 - r487015;
        double r487019 = r487016 / r487018;
        double r487020 = r487013 * r487019;
        double r487021 = r487012 + r487020;
        return r487021;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	1.3
Target	0.5
Herbie	1.3

\[\begin{array}{l} \mathbf{if}\;y \lt -8.508084860551241069024247453646278348229 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

1. Initial program 1.3

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

2. Final simplification 1.3

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

Reproduce

herbie shell --seed 2019305 
(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 -8.50808486055124107e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.8944268627920891e-49) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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