Average Error: 7.6 → 3.5
Time: 3.3s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -2.86465313134083604 \cdot 10^{34} \lor \neg \left(y \le 4.2234916393641059 \cdot 10^{-153}\right):\\ \;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;y \le -2.86465313134083604 \cdot 10^{34} \lor \neg \left(y \le 4.2234916393641059 \cdot 10^{-153}\right):\\
\;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r615932 = x;
        double r615933 = y;
        double r615934 = r615932 * r615933;
        double r615935 = z;
        double r615936 = r615935 * r615933;
        double r615937 = r615934 - r615936;
        double r615938 = t;
        double r615939 = r615937 * r615938;
        return r615939;
}
↓
double f(double x, double y, double z, double t) {
        double r615940 = y;
        double r615941 = -2.864653131340836e+34;
        bool r615942 = r615940 <= r615941;
        double r615943 = 4.223491639364106e-153;
        bool r615944 = r615940 <= r615943;
        double r615945 = !r615944;
        bool r615946 = r615942 || r615945;
        double r615947 = t;
        double r615948 = r615947 * r615940;
        double r615949 = x;
        double r615950 = z;
        double r615951 = r615949 - r615950;
        double r615952 = r615948 * r615951;
        double r615953 = r615940 * r615951;
        double r615954 = r615947 * r615953;
        double r615955 = r615946 ? r615952 : r615954;
        return r615955;
}

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 2 regimes

  2. if y < -2.864653131340836e+34 or 4.223491639364106e-153 < y

    1. Initial program 12.6

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

    2. Simplified12.6

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

    4. Applied associate-*r*4.3

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

    if -2.864653131340836e+34 < y < 4.223491639364106e-153

    1. Initial program 2.6

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

    2. Simplified2.6

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

  4. Final simplification3.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -2.86465313134083604 \cdot 10^{34} \lor \neg \left(y \le 4.2234916393641059 \cdot 10^{-153}\right):\\ \;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(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))