Average Error: 7.0 → 0.3
Time: 14.8s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y \le -8.274186156879764240774351835854573918832 \cdot 10^{226}:\\ \;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;x \cdot y - z \cdot y \le -4.819622087448949409690444355976373823692 \cdot 10^{-247}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \mathbf{elif}\;x \cdot y - z \cdot y \le 1.232937047876378353025506941095613328966 \cdot 10^{-242}:\\ \;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;x \cdot y - z \cdot y \le 1.77758114352811529361559523864976797551 \cdot 10^{299}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - z \cdot y \le -8.274186156879764240774351835854573918832 \cdot 10^{226}:\\
\;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\

\mathbf{elif}\;x \cdot y - z \cdot y \le -4.819622087448949409690444355976373823692 \cdot 10^{-247}:\\
\;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\

\mathbf{elif}\;x \cdot y - z \cdot y \le 1.232937047876378353025506941095613328966 \cdot 10^{-242}:\\
\;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\

\mathbf{elif}\;x \cdot y - z \cdot y \le 1.77758114352811529361559523864976797551 \cdot 10^{299}:\\
\;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r365715 = x;
        double r365716 = y;
        double r365717 = r365715 * r365716;
        double r365718 = z;
        double r365719 = r365718 * r365716;
        double r365720 = r365717 - r365719;
        double r365721 = t;
        double r365722 = r365720 * r365721;
        return r365722;
}
↓
double f(double x, double y, double z, double t) {
        double r365723 = x;
        double r365724 = y;
        double r365725 = r365723 * r365724;
        double r365726 = z;
        double r365727 = r365726 * r365724;
        double r365728 = r365725 - r365727;
        double r365729 = -8.274186156879764e+226;
        bool r365730 = r365728 <= r365729;
        double r365731 = t;
        double r365732 = r365731 * r365724;
        double r365733 = r365723 - r365726;
        double r365734 = r365732 * r365733;
        double r365735 = -4.8196220874489494e-247;
        bool r365736 = r365728 <= r365735;
        double r365737 = r365728 * r365731;
        double r365738 = 1.2329370478763784e-242;
        bool r365739 = r365728 <= r365738;
        double r365740 = 1.7775811435281153e+299;
        bool r365741 = r365728 <= r365740;
        double r365742 = r365731 * r365733;
        double r365743 = r365724 * r365742;
        double r365744 = r365741 ? r365737 : r365743;
        double r365745 = r365739 ? r365734 : r365744;
        double r365746 = r365736 ? r365737 : r365745;
        double r365747 = r365730 ? r365734 : r365746;
        return r365747;
}

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
Target3.1
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;t \lt -9.231879582886776938073886590448747944753 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t \lt 2.543067051564877116200336808272775217995 \cdot 10^{83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (- (* x y) (* z y)) < -8.274186156879764e+226 or -4.8196220874489494e-247 < (- (* x y) (* z y)) < 1.2329370478763784e-242

    1. Initial program 21.6

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

    3. Applied distribute-rgt-out--21.6

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

    4. Applied associate-*l*0.6

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

    5. Simplified0.6

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

    7. Applied associate-*r*0.5

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

    8. Simplified0.5

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

    if -8.274186156879764e+226 < (- (* x y) (* z y)) < -4.8196220874489494e-247 or 1.2329370478763784e-242 < (- (* x y) (* z y)) < 1.7775811435281153e+299

    1. Initial program 0.2

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

    if 1.7775811435281153e+299 < (- (* x y) (* z y))

    1. Initial program 58.5

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

    3. Applied distribute-rgt-out--58.5

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

    4. Applied associate-*l*0.3

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

    5. Simplified0.3

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y \le -8.274186156879764240774351835854573918832 \cdot 10^{226}:\\ \;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;x \cdot y - z \cdot y \le -4.819622087448949409690444355976373823692 \cdot 10^{-247}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \mathbf{elif}\;x \cdot y - z \cdot y \le 1.232937047876378353025506941095613328966 \cdot 10^{-242}:\\ \;\;\;\;\left(t \cdot y\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;x \cdot y - z \cdot y \le 1.77758114352811529361559523864976797551 \cdot 10^{299}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019326 +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))