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

Average Error: 10.5 → 0.4

Time: 4.4s

Precision: 64

Math

\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} = -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \le 1.4504653135111757 \cdot 10^{264}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r559193 = x;
        double r559194 = y;
        double r559195 = z;
        double r559196 = t;
        double r559197 = r559195 - r559196;
        double r559198 = r559194 * r559197;
        double r559199 = a;
        double r559200 = r559199 - r559196;
        double r559201 = r559198 / r559200;
        double r559202 = r559193 + r559201;
        return r559202;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r559203 = y;
        double r559204 = z;
        double r559205 = t;
        double r559206 = r559204 - r559205;
        double r559207 = r559203 * r559206;
        double r559208 = a;
        double r559209 = r559208 - r559205;
        double r559210 = r559207 / r559209;
        double r559211 = -inf.0;
        bool r559212 = r559210 <= r559211;
        double r559213 = 1.4504653135111757e+264;
        bool r559214 = r559210 <= r559213;
        double r559215 = !r559214;
        bool r559216 = r559212 || r559215;
        double r559217 = r559203 / r559209;
        double r559218 = x;
        double r559219 = fma(r559217, r559206, r559218);
        double r559220 = r559218 + r559210;
        double r559221 = r559216 ? r559219 : r559220;
        return r559221;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	10.5
Target	1.3
Herbie	0.4

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

Derivation

1. Split input into 2 regimes

2. if (/ (* y (- z t)) (- a t)) < -inf.0 or 1.4504653135111757e+264 < (/ (* y (- z t)) (- a t))

   1. Initial program 60.6

      \[x + \frac{y \cdot \left(z - t\right)}{a - t}\]

   2. Simplified 1.2

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

   if -inf.0 < (/ (* y (- z t)) (- a t)) < 1.4504653135111757e+264

   1. Initial program 0.2

      \[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
3. Recombined 2 regimes into one program.

4. Final simplification 0.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} = -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \le 1.4504653135111757 \cdot 10^{264}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020024 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- a t) (- z t))))

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