Average Error: 10.8 → 0.3
Time: 3.4s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} = -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \le 7.2611128830759547 \cdot 10^{284}\right):\\ \;\;\;\;\frac{z - t}{\frac{a - t}{y}} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]
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):\\
\;\;\;\;\frac{z - t}{\frac{a - t}{y}} + x\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r562433 = x;
        double r562434 = y;
        double r562435 = z;
        double r562436 = t;
        double r562437 = r562435 - r562436;
        double r562438 = r562434 * r562437;
        double r562439 = a;
        double r562440 = r562439 - r562436;
        double r562441 = r562438 / r562440;
        double r562442 = r562433 + r562441;
        return r562442;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r562443 = y;
        double r562444 = z;
        double r562445 = t;
        double r562446 = r562444 - r562445;
        double r562447 = r562443 * r562446;
        double r562448 = a;
        double r562449 = r562448 - r562445;
        double r562450 = r562447 / r562449;
        double r562451 = -inf.0;
        bool r562452 = r562450 <= r562451;
        double r562453 = 7.261112883075955e+284;
        bool r562454 = r562450 <= r562453;
        double r562455 = !r562454;
        bool r562456 = r562452 || r562455;
        double r562457 = r562449 / r562443;
        double r562458 = r562446 / r562457;
        double r562459 = x;
        double r562460 = r562458 + r562459;
        double r562461 = r562459 + r562450;
        double r562462 = r562456 ? r562460 : r562461;
        return r562462;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.8
Target1.2
Herbie0.3
\[x + \frac{y}{\frac{a - t}{z - t}}\]

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. Simplified0.8

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

    4. Applied clear-num0.9

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

    6. Applied fma-udef0.9

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

    7. Simplified0.7

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

    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 simplification0.3

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

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))))