Average Error: 7.1 → 1.3
Time: 6.2s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y \le -2.00380226483629692 \cdot 10^{216} \lor \neg \left(x \cdot y - z \cdot y \le 9.74345596111120432 \cdot 10^{307}\right):\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - z \cdot y \le -2.00380226483629692 \cdot 10^{216} \lor \neg \left(x \cdot y - z \cdot y \le 9.74345596111120432 \cdot 10^{307}\right):\\
\;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r574573 = x;
        double r574574 = y;
        double r574575 = r574573 * r574574;
        double r574576 = z;
        double r574577 = r574576 * r574574;
        double r574578 = r574575 - r574577;
        double r574579 = t;
        double r574580 = r574578 * r574579;
        return r574580;
}
↓
double f(double x, double y, double z, double t) {
        double r574581 = x;
        double r574582 = y;
        double r574583 = r574581 * r574582;
        double r574584 = z;
        double r574585 = r574584 * r574582;
        double r574586 = r574583 - r574585;
        double r574587 = -2.003802264836297e+216;
        bool r574588 = r574586 <= r574587;
        double r574589 = 9.743455961111204e+307;
        bool r574590 = r574586 <= r574589;
        double r574591 = !r574590;
        bool r574592 = r574588 || r574591;
        double r574593 = r574581 - r574584;
        double r574594 = t;
        double r574595 = r574593 * r574594;
        double r574596 = r574582 * r574595;
        double r574597 = r574586 * r574594;
        double r574598 = r574592 ? r574596 : r574597;
        return r574598;
}

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

Original7.1
Target3.0
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;t \lt -9.2318795828867769 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t \lt 2.5430670515648771 \cdot 10^{83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (- (* x y) (* z y)) < -2.003802264836297e+216 or 9.743455961111204e+307 < (- (* x y) (* z y))

    1. Initial program 41.6

      \[\left(x \cdot y - z \cdot y\right) \cdot t\]
    2. Using strategy rm

    3. Applied distribute-rgt-out--41.6

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

    4. Applied associate-*l*0.4

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

    if -2.003802264836297e+216 < (- (* x y) (* z y)) < 9.743455961111204e+307

    1. Initial program 1.5

      \[\left(x \cdot y - z \cdot y\right) \cdot t\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y \le -2.00380226483629692 \cdot 10^{216} \lor \neg \left(x \cdot y - z \cdot y \le 9.74345596111120432 \cdot 10^{307}\right):\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \end{array}\]

Reproduce

herbie shell --seed 2020034 
(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))