Average Error: 6.8 → 1.4
Time: 3.3s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y \le -4.63836268060687826 \cdot 10^{307}:\\ \;\;\;\;{\left(\left(t \cdot y\right) \cdot \left(x - z\right)\right)}^{1}\\ \mathbf{elif}\;x \cdot y - z \cdot y \le 1.95547411306134 \cdot 10^{248}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - z \cdot y \le -4.63836268060687826 \cdot 10^{307}:\\
\;\;\;\;{\left(\left(t \cdot y\right) \cdot \left(x - z\right)\right)}^{1}\\

\mathbf{elif}\;x \cdot y - z \cdot y \le 1.95547411306134 \cdot 10^{248}:\\
\;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r539014 = x;
        double r539015 = y;
        double r539016 = r539014 * r539015;
        double r539017 = z;
        double r539018 = r539017 * r539015;
        double r539019 = r539016 - r539018;
        double r539020 = t;
        double r539021 = r539019 * r539020;
        return r539021;
}
↓
double f(double x, double y, double z, double t) {
        double r539022 = x;
        double r539023 = y;
        double r539024 = r539022 * r539023;
        double r539025 = z;
        double r539026 = r539025 * r539023;
        double r539027 = r539024 - r539026;
        double r539028 = -4.638362680606878e+307;
        bool r539029 = r539027 <= r539028;
        double r539030 = t;
        double r539031 = r539030 * r539023;
        double r539032 = r539022 - r539025;
        double r539033 = r539031 * r539032;
        double r539034 = 1.0;
        double r539035 = pow(r539033, r539034);
        double r539036 = 1.955474113061338e+248;
        bool r539037 = r539027 <= r539036;
        double r539038 = r539027 * r539030;
        double r539039 = r539032 * r539030;
        double r539040 = r539023 * r539039;
        double r539041 = r539037 ? r539038 : r539040;
        double r539042 = r539029 ? r539035 : r539041;
        return r539042;
}

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

Original6.8
Target3.1
Herbie1.4
\[\begin{array}{l} \mathbf{if}\;t \lt -9.2318795828867769 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t \lt 2.5430670515648771 \cdot 10^{83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (- (* x y) (* z y)) < -4.638362680606878e+307

    1. Initial program 63.4

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

    3. Applied pow163.4

      \[\leadsto \left(x \cdot y - z \cdot y\right) \cdot \color{blue}{{t}^{1}}\]

    4. Applied pow163.4

      \[\leadsto \color{blue}{{\left(x \cdot y - z \cdot y\right)}^{1}} \cdot {t}^{1}\]

    5. Applied pow-prod-down63.4

      \[\leadsto \color{blue}{{\left(\left(x \cdot y - z \cdot y\right) \cdot t\right)}^{1}}\]

    6. Simplified0.2

      \[\leadsto {\color{blue}{\left(\left(t \cdot y\right) \cdot \left(x - z\right)\right)}}^{1}\]

    if -4.638362680606878e+307 < (- (* x y) (* z y)) < 1.955474113061338e+248

    1. Initial program 1.6

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

    if 1.955474113061338e+248 < (- (* x y) (* z y))

    1. Initial program 39.5

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

    3. Applied distribute-rgt-out--39.5

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

    4. Applied associate-*l*0.4

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

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y \le -4.63836268060687826 \cdot 10^{307}:\\ \;\;\;\;{\left(\left(t \cdot y\right) \cdot \left(x - z\right)\right)}^{1}\\ \mathbf{elif}\;x \cdot y - z \cdot y \le 1.95547411306134 \cdot 10^{248}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020062 +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))