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

Average Error: 10.4 → 0.2

Time: 20.8s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} = -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \le 5.105950757333242047287578696854372670873 \cdot 10^{306}\right):\\ \;\;\;\;\frac{z}{\frac{a - t}{y}} - \left(\frac{t}{\frac{a - t}{y}} - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r363515 = x;
        double r363516 = y;
        double r363517 = z;
        double r363518 = t;
        double r363519 = r363517 - r363518;
        double r363520 = r363516 * r363519;
        double r363521 = a;
        double r363522 = r363521 - r363518;
        double r363523 = r363520 / r363522;
        double r363524 = r363515 + r363523;
        return r363524;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r363525 = y;
        double r363526 = z;
        double r363527 = t;
        double r363528 = r363526 - r363527;
        double r363529 = r363525 * r363528;
        double r363530 = a;
        double r363531 = r363530 - r363527;
        double r363532 = r363529 / r363531;
        double r363533 = -inf.0;
        bool r363534 = r363532 <= r363533;
        double r363535 = 5.105950757333242e+306;
        bool r363536 = r363532 <= r363535;
        double r363537 = !r363536;
        bool r363538 = r363534 || r363537;
        double r363539 = r363531 / r363525;
        double r363540 = r363526 / r363539;
        double r363541 = r363527 / r363539;
        double r363542 = x;
        double r363543 = r363541 - r363542;
        double r363544 = r363540 - r363543;
        double r363545 = r363542 + r363532;
        double r363546 = r363538 ? r363544 : r363545;
        return r363546;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	10.4
Target	1.5
Herbie	0.2

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

Derivation

1. Split input into 2 regimes

2. if (/ (* y (- z t)) (- a t)) < -inf.0 or 5.105950757333242e+306 < (/ (* y (- z t)) (- a t))

   1. Initial program 63.8

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

   2. Simplified 0.3

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

   4. Applied clear-num 0.4

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

   6. Applied fma-udef 0.4

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

   7. Simplified 0.3

      \[\leadsto \color{blue}{\frac{z - t}{\frac{a - t}{y}}} + x\]
   8. Using strategy rm

   9. Applied div-sub 0.3

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

   10. Applied associate-+l- 0.3

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

   if -inf.0 < (/ (* y (- z t)) (- a t)) < 5.105950757333242e+306

   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 0.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} = -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \le 5.105950757333242047287578696854372670873 \cdot 10^{306}\right):\\ \;\;\;\;\frac{z}{\frac{a - t}{y}} - \left(\frac{t}{\frac{a - t}{y}} - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019325 +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))))