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

Average Error: 10.8 → 0.4

Time: 22.0s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} = -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \le 4.549710930030010292882411291755713427753 \cdot 10^{254}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r474016 = x;
        double r474017 = y;
        double r474018 = z;
        double r474019 = t;
        double r474020 = r474018 - r474019;
        double r474021 = r474017 * r474020;
        double r474022 = a;
        double r474023 = r474022 - r474019;
        double r474024 = r474021 / r474023;
        double r474025 = r474016 + r474024;
        return r474025;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r474026 = y;
        double r474027 = z;
        double r474028 = t;
        double r474029 = r474027 - r474028;
        double r474030 = r474026 * r474029;
        double r474031 = a;
        double r474032 = r474031 - r474028;
        double r474033 = r474030 / r474032;
        double r474034 = -inf.0;
        bool r474035 = r474033 <= r474034;
        double r474036 = 4.5497109300300103e+254;
        bool r474037 = r474033 <= r474036;
        double r474038 = !r474037;
        bool r474039 = r474035 || r474038;
        double r474040 = r474026 / r474032;
        double r474041 = x;
        double r474042 = fma(r474040, r474029, r474041);
        double r474043 = r474041 + r474033;
        double r474044 = r474039 ? r474042 : r474043;
        return r474044;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	10.8
Target	1.4
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 4.5497109300300103e+254 < (/ (* y (- z t)) (- a t))

   1. Initial program 59.3

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

   2. Simplified 1.1

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

   if -inf.0 < (/ (* y (- z t)) (- a t)) < 4.5497109300300103e+254

   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

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} = -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \le 4.549710930030010292882411291755713427753 \cdot 10^{254}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019306 +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))))