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

Average Error: 10.6 → 0.5

Time: 7.5s

Precision: 64

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

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} = -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \le 6.82827154473029748 \cdot 10^{188}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r255119 = x;
        double r255120 = y;
        double r255121 = z;
        double r255122 = t;
        double r255123 = r255121 - r255122;
        double r255124 = r255120 * r255123;
        double r255125 = a;
        double r255126 = r255121 - r255125;
        double r255127 = r255124 / r255126;
        double r255128 = r255119 + r255127;
        return r255128;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r255129 = y;
        double r255130 = z;
        double r255131 = t;
        double r255132 = r255130 - r255131;
        double r255133 = r255129 * r255132;
        double r255134 = a;
        double r255135 = r255130 - r255134;
        double r255136 = r255133 / r255135;
        double r255137 = -inf.0;
        bool r255138 = r255136 <= r255137;
        double r255139 = 6.828271544730297e+188;
        bool r255140 = r255136 <= r255139;
        double r255141 = !r255140;
        bool r255142 = r255138 || r255141;
        double r255143 = x;
        double r255144 = r255135 / r255132;
        double r255145 = r255129 / r255144;
        double r255146 = r255143 + r255145;
        double r255147 = r255143 + r255136;
        double r255148 = r255142 ? r255146 : r255147;
        return r255148;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	10.6
Target	1.2
Herbie	0.5

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

Derivation

1. Split input into 2 regimes

2. if (/ (* y (- z t)) (- z a)) < -inf.0 or 6.828271544730297e+188 < (/ (* y (- z t)) (- z a))

   1. Initial program 53.0

      \[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
   2. Using strategy rm

   3. Applied associate-/l* 1.5

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

   if -inf.0 < (/ (* y (- z t)) (- z a)) < 6.828271544730297e+188

   1. Initial program 0.2

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

4. Final simplification 0.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} = -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \le 6.82827154473029748 \cdot 10^{188}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020042 
(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))))