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

Average Error: 10.8 → 0.3

Time: 13.6s

Precision: 64

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

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} = -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \le 7.2611128830759547 \cdot 10^{284}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r515741 = x;
        double r515742 = y;
        double r515743 = z;
        double r515744 = t;
        double r515745 = r515743 - r515744;
        double r515746 = r515742 * r515745;
        double r515747 = a;
        double r515748 = r515747 - r515744;
        double r515749 = r515746 / r515748;
        double r515750 = r515741 + r515749;
        return r515750;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r515751 = y;
        double r515752 = z;
        double r515753 = t;
        double r515754 = r515752 - r515753;
        double r515755 = r515751 * r515754;
        double r515756 = a;
        double r515757 = r515756 - r515753;
        double r515758 = r515755 / r515757;
        double r515759 = -inf.0;
        bool r515760 = r515758 <= r515759;
        double r515761 = 7.261112883075955e+284;
        bool r515762 = r515758 <= r515761;
        double r515763 = !r515762;
        bool r515764 = r515760 || r515763;
        double r515765 = r515751 / r515757;
        double r515766 = x;
        double r515767 = fma(r515765, r515754, r515766);
        double r515768 = r515766 + r515758;
        double r515769 = r515764 ? r515767 : r515768;
        return r515769;
}

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	1.2
Herbie	0.3

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

Derivation

1. Split input into 2 regimes

2. if (/ (* y (- z t)) (- a t)) < -inf.0 or 7.261112883075955e+284 < (/ (* y (- z t)) (- a t))

   1. Initial program 62.2

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

   2. Simplified 0.8

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

   4. Applied div-inv 0.9

      \[\leadsto \mathsf{fma}\left(\color{blue}{y \cdot \frac{1}{a - t}}, z - t, x\right)\]
   5. Using strategy rm

   6. Applied pow1 0.9

      \[\leadsto \mathsf{fma}\left(y \cdot \color{blue}{{\left(\frac{1}{a - t}\right)}^{1}}, z - t, x\right)\]

   7. Applied pow1 0.9

      \[\leadsto \mathsf{fma}\left(\color{blue}{{y}^{1}} \cdot {\left(\frac{1}{a - t}\right)}^{1}, z - t, x\right)\]

   8. Applied pow-prod-down 0.9

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(y \cdot \frac{1}{a - t}\right)}^{1}}, z - t, x\right)\]

   9. Simplified 0.8

      \[\leadsto \mathsf{fma}\left({\color{blue}{\left(\frac{y}{a - t}\right)}}^{1}, z - t, x\right)\]

   if -inf.0 < (/ (* y (- z t)) (- a t)) < 7.261112883075955e+284

   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 0.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} = -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \le 7.2611128830759547 \cdot 10^{284}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 +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))))