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

Average Error: 1.4 → 1.4

Time: 14.7s

Precision: 64

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

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a) {
        double r483738 = x;
        double r483739 = y;
        double r483740 = z;
        double r483741 = t;
        double r483742 = r483740 - r483741;
        double r483743 = a;
        double r483744 = r483743 - r483741;
        double r483745 = r483742 / r483744;
        double r483746 = r483739 * r483745;
        double r483747 = r483738 + r483746;
        return r483747;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r483748 = z;
        double r483749 = t;
        double r483750 = r483748 - r483749;
        double r483751 = a;
        double r483752 = r483751 - r483749;
        double r483753 = r483750 / r483752;
        double r483754 = y;
        double r483755 = x;
        double r483756 = fma(r483753, r483754, r483755);
        return r483756;
}

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	0.4
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. Simplified 1.4

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

3. Final simplification 1.4

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

Reproduce

herbie shell --seed 2019351 +o rules:numerics
(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)))))