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

Average Error: 1.6 → 1.6

Time: 13.1s

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 r579111 = x;
        double r579112 = y;
        double r579113 = z;
        double r579114 = t;
        double r579115 = r579113 - r579114;
        double r579116 = a;
        double r579117 = r579116 - r579114;
        double r579118 = r579115 / r579117;
        double r579119 = r579112 * r579118;
        double r579120 = r579111 + r579119;
        return r579120;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r579121 = z;
        double r579122 = t;
        double r579123 = r579121 - r579122;
        double r579124 = a;
        double r579125 = r579124 - r579122;
        double r579126 = r579123 / r579125;
        double r579127 = y;
        double r579128 = x;
        double r579129 = fma(r579126, r579127, r579128);
        return r579129;
}

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. Simplified 1.6

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

3. Final simplification 1.6

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

Reproduce

herbie shell --seed 2020045 +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)))))