Average Error: 6.9 → 0.7
Time: 16.6s
Precision: 64
\[\frac{x \cdot 2.0}{y \cdot z - t \cdot z}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot z - t \cdot z \le -1.229546345171507 \cdot 10^{+160}:\\ \;\;\;\;\frac{2.0 \cdot \frac{x}{z}}{y - t}\\ \mathbf{elif}\;y \cdot z - t \cdot z \le -3.2453160658630895 \cdot 10^{-117}:\\ \;\;\;\;\frac{x \cdot 2.0}{y \cdot z - t \cdot z}\\ \mathbf{elif}\;y \cdot z - t \cdot z \le 1.185757550019 \cdot 10^{-322}:\\ \;\;\;\;\frac{2.0}{y - t} \cdot \frac{x}{z}\\ \mathbf{elif}\;y \cdot z - t \cdot z \le 8.381475908009204 \cdot 10^{+226}:\\ \;\;\;\;\frac{x \cdot 2.0}{y \cdot z - t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2.0}{y - t} \cdot \frac{x}{z}\\ \end{array}\]
\frac{x \cdot 2.0}{y \cdot z - t \cdot z}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot z - t \cdot z \le -1.229546345171507 \cdot 10^{+160}:\\
\;\;\;\;\frac{2.0 \cdot \frac{x}{z}}{y - t}\\

\mathbf{elif}\;y \cdot z - t \cdot z \le -3.2453160658630895 \cdot 10^{-117}:\\
\;\;\;\;\frac{x \cdot 2.0}{y \cdot z - t \cdot z}\\

\mathbf{elif}\;y \cdot z - t \cdot z \le 1.185757550019 \cdot 10^{-322}:\\
\;\;\;\;\frac{2.0}{y - t} \cdot \frac{x}{z}\\

\mathbf{elif}\;y \cdot z - t \cdot z \le 8.381475908009204 \cdot 10^{+226}:\\
\;\;\;\;\frac{x \cdot 2.0}{y \cdot z - t \cdot z}\\

\mathbf{else}:\\
\;\;\;\;\frac{2.0}{y - t} \cdot \frac{x}{z}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r27093640 = x;
        double r27093641 = 2.0;
        double r27093642 = r27093640 * r27093641;
        double r27093643 = y;
        double r27093644 = z;
        double r27093645 = r27093643 * r27093644;
        double r27093646 = t;
        double r27093647 = r27093646 * r27093644;
        double r27093648 = r27093645 - r27093647;
        double r27093649 = r27093642 / r27093648;
        return r27093649;
}
↓
double f(double x, double y, double z, double t) {
        double r27093650 = y;
        double r27093651 = z;
        double r27093652 = r27093650 * r27093651;
        double r27093653 = t;
        double r27093654 = r27093653 * r27093651;
        double r27093655 = r27093652 - r27093654;
        double r27093656 = -1.229546345171507e+160;
        bool r27093657 = r27093655 <= r27093656;
        double r27093658 = 2.0;
        double r27093659 = x;
        double r27093660 = r27093659 / r27093651;
        double r27093661 = r27093658 * r27093660;
        double r27093662 = r27093650 - r27093653;
        double r27093663 = r27093661 / r27093662;
        double r27093664 = -3.2453160658630895e-117;
        bool r27093665 = r27093655 <= r27093664;
        double r27093666 = r27093659 * r27093658;
        double r27093667 = r27093666 / r27093655;
        double r27093668 = 1.185757550019e-322;
        bool r27093669 = r27093655 <= r27093668;
        double r27093670 = r27093658 / r27093662;
        double r27093671 = r27093670 * r27093660;
        double r27093672 = 8.381475908009204e+226;
        bool r27093673 = r27093655 <= r27093672;
        double r27093674 = r27093673 ? r27093667 : r27093671;
        double r27093675 = r27093669 ? r27093671 : r27093674;
        double r27093676 = r27093665 ? r27093667 : r27093675;
        double r27093677 = r27093657 ? r27093663 : r27093676;
        return r27093677;
}

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

Original6.9
Target2.0
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot 2.0}{y \cdot z - t \cdot z} \lt -2.559141628295061 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} \cdot 2.0\\ \mathbf{elif}\;\frac{x \cdot 2.0}{y \cdot z - t \cdot z} \lt 1.045027827330126 \cdot 10^{-269}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot 2.0}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} \cdot 2.0\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (- (* y z) (* t z)) < -1.229546345171507e+160

    1. Initial program 10.0

      \[\frac{x \cdot 2.0}{y \cdot z - t \cdot z}\]

    2. Simplified1.0

      \[\leadsto \color{blue}{\frac{2.0}{y - t} \cdot \frac{x}{z}}\]
    3. Using strategy rm

    4. Applied associate-*l/0.9

      \[\leadsto \color{blue}{\frac{2.0 \cdot \frac{x}{z}}{y - t}}\]

    if -1.229546345171507e+160 < (- (* y z) (* t z)) < -3.2453160658630895e-117 or 1.185757550019e-322 < (- (* y z) (* t z)) < 8.381475908009204e+226

    1. Initial program 0.4

      \[\frac{x \cdot 2.0}{y \cdot z - t \cdot z}\]

    if -3.2453160658630895e-117 < (- (* y z) (* t z)) < 1.185757550019e-322 or 8.381475908009204e+226 < (- (* y z) (* t z))

    1. Initial program 18.8

      \[\frac{x \cdot 2.0}{y \cdot z - t \cdot z}\]

    2. Simplified1.3

      \[\leadsto \color{blue}{\frac{2.0}{y - t} \cdot \frac{x}{z}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z - t \cdot z \le -1.229546345171507 \cdot 10^{+160}:\\ \;\;\;\;\frac{2.0 \cdot \frac{x}{z}}{y - t}\\ \mathbf{elif}\;y \cdot z - t \cdot z \le -3.2453160658630895 \cdot 10^{-117}:\\ \;\;\;\;\frac{x \cdot 2.0}{y \cdot z - t \cdot z}\\ \mathbf{elif}\;y \cdot z - t \cdot z \le 1.185757550019 \cdot 10^{-322}:\\ \;\;\;\;\frac{2.0}{y - t} \cdot \frac{x}{z}\\ \mathbf{elif}\;y \cdot z - t \cdot z \le 8.381475908009204 \cdot 10^{+226}:\\ \;\;\;\;\frac{x \cdot 2.0}{y \cdot z - t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2.0}{y - t} \cdot \frac{x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z t)
  :name "Linear.Projection:infinitePerspective from linear-1.19.1.3, A"

  :herbie-target
  (if (< (/ (* x 2.0) (- (* y z) (* t z))) -2.559141628295061e-13) (* (/ x (* (- y t) z)) 2.0) (if (< (/ (* x 2.0) (- (* y z) (* t z))) 1.045027827330126e-269) (/ (* (/ x z) 2.0) (- y t)) (* (/ x (* (- y t) z)) 2.0)))

  (/ (* x 2.0) (- (* y z) (* t z))))