Average Error: 7.6 → 3.5
Time: 2.7s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -2.86465313134083604 \cdot 10^{34} \lor \neg \left(y \le 4.2234916393641059 \cdot 10^{-153}\right):\\ \;\;\;\;\left(t \cdot y\right) \cdot x + \left(t \cdot y\right) \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \end{array}\]
\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 x + \left(t \cdot y\right) \cdot \left(-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 r598462 = x;
        double r598463 = y;
        double r598464 = r598462 * r598463;
        double r598465 = z;
        double r598466 = r598465 * r598463;
        double r598467 = r598464 - r598466;
        double r598468 = t;
        double r598469 = r598467 * r598468;
        return r598469;
}
↓
double f(double x, double y, double z, double t) {
        double r598470 = y;
        double r598471 = -2.864653131340836e+34;
        bool r598472 = r598470 <= r598471;
        double r598473 = 4.223491639364106e-153;
        bool r598474 = r598470 <= r598473;
        double r598475 = !r598474;
        bool r598476 = r598472 || r598475;
        double r598477 = t;
        double r598478 = r598477 * r598470;
        double r598479 = x;
        double r598480 = r598478 * r598479;
        double r598481 = z;
        double r598482 = -r598481;
        double r598483 = r598478 * r598482;
        double r598484 = r598480 + r598483;
        double r598485 = r598479 - r598481;
        double r598486 = r598470 * r598485;
        double r598487 = r598477 * r598486;
        double r598488 = r598476 ? r598484 : r598487;
        return r598488;
}

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

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

    6. Applied sub-neg4.3

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

    7. Applied distribute-lft-in4.3

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

    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

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

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))