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

Average Error: 10.6 → 0.5

Time: 7.6s

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 r689465 = x;
        double r689466 = y;
        double r689467 = z;
        double r689468 = t;
        double r689469 = r689467 - r689468;
        double r689470 = r689466 * r689469;
        double r689471 = a;
        double r689472 = r689467 - r689471;
        double r689473 = r689470 / r689472;
        double r689474 = r689465 + r689473;
        return r689474;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r689475 = y;
        double r689476 = z;
        double r689477 = t;
        double r689478 = r689476 - r689477;
        double r689479 = r689475 * r689478;
        double r689480 = a;
        double r689481 = r689476 - r689480;
        double r689482 = r689479 / r689481;
        double r689483 = -inf.0;
        bool r689484 = r689482 <= r689483;
        double r689485 = 6.828271544730297e+188;
        bool r689486 = r689482 <= r689485;
        double r689487 = !r689486;
        bool r689488 = r689484 || r689487;
        double r689489 = x;
        double r689490 = r689481 / r689478;
        double r689491 = r689475 / r689490;
        double r689492 = r689489 + r689491;
        double r689493 = r689489 + r689482;
        double r689494 = r689488 ? r689492 : r689493;
        return r689494;
}

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))))