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

Average Error: 1.4 → 1.4

Time: 1.2m

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 r28451454 = x;
        double r28451455 = y;
        double r28451456 = z;
        double r28451457 = t;
        double r28451458 = r28451456 - r28451457;
        double r28451459 = a;
        double r28451460 = r28451459 - r28451457;
        double r28451461 = r28451458 / r28451460;
        double r28451462 = r28451455 * r28451461;
        double r28451463 = r28451454 + r28451462;
        return r28451463;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r28451464 = x;
        double r28451465 = z;
        double r28451466 = t;
        double r28451467 = r28451465 - r28451466;
        double r28451468 = a;
        double r28451469 = r28451468 - r28451466;
        double r28451470 = r28451467 / r28451469;
        double r28451471 = y;
        double r28451472 = r28451470 * r28451471;
        double r28451473 = r28451464 + r28451472;
        return r28451473;
}

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 
(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)))))