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

Average Error: 1.4 → 1.4

Time: 51.4s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a) {
        double r27192927 = x;
        double r27192928 = y;
        double r27192929 = z;
        double r27192930 = t;
        double r27192931 = r27192929 - r27192930;
        double r27192932 = a;
        double r27192933 = r27192932 - r27192930;
        double r27192934 = r27192931 / r27192933;
        double r27192935 = r27192928 * r27192934;
        double r27192936 = r27192927 + r27192935;
        return r27192936;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r27192937 = x;
        double r27192938 = z;
        double r27192939 = t;
        double r27192940 = r27192938 - r27192939;
        double r27192941 = a;
        double r27192942 = r27192941 - r27192939;
        double r27192943 = r27192940 / r27192942;
        double r27192944 = y;
        double r27192945 = r27192943 * r27192944;
        double r27192946 = r27192937 + r27192945;
        return r27192946;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	1.4
Target	0.5
Herbie	1.4

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

Derivation

1. Initial program 1.4

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

2. Final simplification 1.4

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

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1.0 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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