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

Average Error: 10.5 → 0.7

Time: 17.9s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} = -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \le 6.539770865773377012647932284333126840637 \cdot 10^{177}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z - a}, z - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r401012 = x;
        double r401013 = y;
        double r401014 = z;
        double r401015 = t;
        double r401016 = r401014 - r401015;
        double r401017 = r401013 * r401016;
        double r401018 = a;
        double r401019 = r401014 - r401018;
        double r401020 = r401017 / r401019;
        double r401021 = r401012 + r401020;
        return r401021;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r401022 = y;
        double r401023 = z;
        double r401024 = t;
        double r401025 = r401023 - r401024;
        double r401026 = r401022 * r401025;
        double r401027 = a;
        double r401028 = r401023 - r401027;
        double r401029 = r401026 / r401028;
        double r401030 = -inf.0;
        bool r401031 = r401029 <= r401030;
        double r401032 = 6.539770865773377e+177;
        bool r401033 = r401029 <= r401032;
        double r401034 = !r401033;
        bool r401035 = r401031 || r401034;
        double r401036 = r401022 / r401028;
        double r401037 = x;
        double r401038 = fma(r401036, r401025, r401037);
        double r401039 = r401037 + r401029;
        double r401040 = r401035 ? r401038 : r401039;
        return r401040;
}

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	1.5
Herbie	0.7

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

Derivation

1. Split input into 2 regimes

2. if (/ (* y (- z t)) (- z a)) < -inf.0 or 6.539770865773377e+177 < (/ (* y (- z t)) (- z a))

   1. Initial program 51.1

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

   2. Simplified 2.6

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

   if -inf.0 < (/ (* y (- z t)) (- z a)) < 6.539770865773377e+177

   1. Initial program 0.3

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

4. Final simplification 0.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} = -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \le 6.539770865773377012647932284333126840637 \cdot 10^{177}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z - a}, z - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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