Average Error: 7.0 → 2.5
Time: 8.1s
Precision: 64
\[\frac{x \cdot 2}{y \cdot z - t \cdot z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -900492426030022.75 \lor \neg \left(x \le 4.9676132502495131 \cdot 10^{-71}\right):\\ \;\;\;\;1 \cdot \frac{\frac{x}{\frac{y - t}{2}}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{y - t}{2}}\\ \end{array}\]
\frac{x \cdot 2}{y \cdot z - t \cdot z}
↓
\begin{array}{l}
\mathbf{if}\;x \le -900492426030022.75 \lor \neg \left(x \le 4.9676132502495131 \cdot 10^{-71}\right):\\
\;\;\;\;1 \cdot \frac{\frac{x}{\frac{y - t}{2}}}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{x}{z}}{\frac{y - t}{2}}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r658375 = x;
        double r658376 = 2.0;
        double r658377 = r658375 * r658376;
        double r658378 = y;
        double r658379 = z;
        double r658380 = r658378 * r658379;
        double r658381 = t;
        double r658382 = r658381 * r658379;
        double r658383 = r658380 - r658382;
        double r658384 = r658377 / r658383;
        return r658384;
}
↓
double f(double x, double y, double z, double t) {
        double r658385 = x;
        double r658386 = -900492426030022.8;
        bool r658387 = r658385 <= r658386;
        double r658388 = 4.967613250249513e-71;
        bool r658389 = r658385 <= r658388;
        double r658390 = !r658389;
        bool r658391 = r658387 || r658390;
        double r658392 = 1.0;
        double r658393 = y;
        double r658394 = t;
        double r658395 = r658393 - r658394;
        double r658396 = 2.0;
        double r658397 = r658395 / r658396;
        double r658398 = r658385 / r658397;
        double r658399 = z;
        double r658400 = r658398 / r658399;
        double r658401 = r658392 * r658400;
        double r658402 = r658385 / r658399;
        double r658403 = r658402 / r658397;
        double r658404 = r658391 ? r658401 : r658403;
        return r658404;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.0
Target2.1
Herbie2.5
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot 2}{y \cdot z - t \cdot z} \lt -2.559141628295061 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} \cdot 2\\ \mathbf{elif}\;\frac{x \cdot 2}{y \cdot z - t \cdot z} \lt 1.04502782733012586 \cdot 10^{-269}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot 2}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} \cdot 2\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -900492426030022.8 or 4.967613250249513e-71 < x

    1. Initial program 10.7

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z}\]

    2. Simplified9.8

      \[\leadsto \color{blue}{\frac{x}{\frac{z \cdot \left(y - t\right)}{2}}}\]
    3. Using strategy rm

    4. Applied *-un-lft-identity9.8

      \[\leadsto \frac{x}{\frac{z \cdot \left(y - t\right)}{\color{blue}{1 \cdot 2}}}\]

    5. Applied times-frac9.7

      \[\leadsto \frac{x}{\color{blue}{\frac{z}{1} \cdot \frac{y - t}{2}}}\]

    6. Applied *-un-lft-identity9.7

      \[\leadsto \frac{\color{blue}{1 \cdot x}}{\frac{z}{1} \cdot \frac{y - t}{2}}\]

    7. Applied times-frac3.0

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{1}} \cdot \frac{x}{\frac{y - t}{2}}}\]

    8. Simplified3.0

      \[\leadsto \color{blue}{\frac{1}{z}} \cdot \frac{x}{\frac{y - t}{2}}\]
    9. Using strategy rm

    10. Applied *-un-lft-identity3.0

      \[\leadsto \color{blue}{\left(1 \cdot \frac{1}{z}\right)} \cdot \frac{x}{\frac{y - t}{2}}\]

    11. Applied associate-*l*3.0

      \[\leadsto \color{blue}{1 \cdot \left(\frac{1}{z} \cdot \frac{x}{\frac{y - t}{2}}\right)}\]

    12. Simplified2.9

      \[\leadsto 1 \cdot \color{blue}{\frac{\frac{x}{\frac{y - t}{2}}}{z}}\]

    if -900492426030022.8 < x < 4.967613250249513e-71

    1. Initial program 3.2

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z}\]

    2. Simplified2.0

      \[\leadsto \color{blue}{\frac{x}{\frac{z \cdot \left(y - t\right)}{2}}}\]
    3. Using strategy rm

    4. Applied *-un-lft-identity2.0

      \[\leadsto \frac{x}{\frac{z \cdot \left(y - t\right)}{\color{blue}{1 \cdot 2}}}\]

    5. Applied times-frac2.0

      \[\leadsto \frac{x}{\color{blue}{\frac{z}{1} \cdot \frac{y - t}{2}}}\]

    6. Applied associate-/r*2.1

      \[\leadsto \color{blue}{\frac{\frac{x}{\frac{z}{1}}}{\frac{y - t}{2}}}\]

    7. Simplified2.1

      \[\leadsto \frac{\color{blue}{\frac{x}{z}}}{\frac{y - t}{2}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -900492426030022.75 \lor \neg \left(x \le 4.9676132502495131 \cdot 10^{-71}\right):\\ \;\;\;\;1 \cdot \frac{\frac{x}{\frac{y - t}{2}}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{y - t}{2}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020036 
(FPCore (x y z t)
  :name "Linear.Projection:infinitePerspective from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (if (< (/ (* x 2) (- (* y z) (* t z))) -2.559141628295061e-13) (* (/ x (* (- y t) z)) 2) (if (< (/ (* x 2) (- (* y z) (* t z))) 1.0450278273301259e-269) (/ (* (/ x z) 2) (- y t)) (* (/ x (* (- y t) z)) 2)))

  (/ (* x 2) (- (* y z) (* t z))))