Average Error: 7.6 → 3.5
Time: 2.4s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.43405946159005389 \cdot 10^{-73}:\\ \;\;\;\;\left(\left(x - z\right) \cdot t\right) \cdot y\\ \mathbf{elif}\;y \le 8.82218830134679759 \cdot 10^{-152}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(t \cdot y\right)\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.43405946159005389 \cdot 10^{-73}:\\
\;\;\;\;\left(\left(x - z\right) \cdot t\right) \cdot y\\

\mathbf{elif}\;y \le 8.82218830134679759 \cdot 10^{-152}:\\
\;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r633523 = x;
        double r633524 = y;
        double r633525 = r633523 * r633524;
        double r633526 = z;
        double r633527 = r633526 * r633524;
        double r633528 = r633525 - r633527;
        double r633529 = t;
        double r633530 = r633528 * r633529;
        return r633530;
}
↓
double f(double x, double y, double z, double t) {
        double r633531 = y;
        double r633532 = -1.434059461590054e-73;
        bool r633533 = r633531 <= r633532;
        double r633534 = x;
        double r633535 = z;
        double r633536 = r633534 - r633535;
        double r633537 = t;
        double r633538 = r633536 * r633537;
        double r633539 = r633538 * r633531;
        double r633540 = 8.822188301346798e-152;
        bool r633541 = r633531 <= r633540;
        double r633542 = r633531 * r633536;
        double r633543 = r633537 * r633542;
        double r633544 = r633537 * r633531;
        double r633545 = r633536 * r633544;
        double r633546 = r633541 ? r633543 : r633545;
        double r633547 = r633533 ? r633539 : r633546;
        return r633547;
}

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

Original7.6
Target3.1
Herbie3.5
\[\begin{array}{l} \mathbf{if}\;t \lt -9.2318795828867769 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t \lt 2.5430670515648771 \cdot 10^{83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -1.434059461590054e-73

    1. Initial program 12.4

      \[\left(x \cdot y - z \cdot y\right) \cdot t\]

    2. Simplified12.4

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

    4. Applied associate-*r*3.6

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

    6. Applied *-commutative3.6

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

    8. Applied associate-*r*3.5

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

    if -1.434059461590054e-73 < y < 8.822188301346798e-152

    1. Initial program 2.9

      \[\left(x \cdot y - z \cdot y\right) \cdot t\]

    2. Simplified2.9

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

    if 8.822188301346798e-152 < y

    1. Initial program 9.7

      \[\left(x \cdot y - z \cdot y\right) \cdot t\]

    2. Simplified9.7

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

    4. Applied associate-*r*4.3

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

    6. Applied *-commutative4.3

      \[\leadsto \color{blue}{\left(x - z\right) \cdot \left(t \cdot y\right)}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification3.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.43405946159005389 \cdot 10^{-73}:\\ \;\;\;\;\left(\left(x - z\right) \cdot t\right) \cdot y\\ \mathbf{elif}\;y \le 8.82218830134679759 \cdot 10^{-152}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(t \cdot y\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 
(FPCore (x y z t)
  :name "Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -9.231879582886777e-80) (* (* y t) (- x z)) (if (< t 2.543067051564877e+83) (* y (* t (- x z))) (* (* y (- x z)) t)))

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