Average Error: 7.1 → 0.5
Time: 10.8s
Precision: 64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y \le -2.112605073419438906656738477879925446144 \cdot 10^{293}:\\ \;\;\;\;\left(t \cdot \left(x - z\right)\right) \cdot y\\ \mathbf{elif}\;x \cdot y - z \cdot y \le -4.915495002659053232957672250858607769431 \cdot 10^{-133}:\\ \;\;\;\;t \cdot \left(x \cdot y - z \cdot y\right)\\ \mathbf{elif}\;x \cdot y - z \cdot y \le 1.719546404882711300932688246576743977043 \cdot 10^{-292}:\\ \;\;\;\;\left(t \cdot \left(x - z\right)\right) \cdot y\\ \mathbf{elif}\;x \cdot y - z \cdot y \le 9.281447287153549320457976819327732070409 \cdot 10^{192}:\\ \;\;\;\;t \cdot \left(x \cdot y - z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - z \cdot y \le -2.112605073419438906656738477879925446144 \cdot 10^{293}:\\
\;\;\;\;\left(t \cdot \left(x - z\right)\right) \cdot y\\

\mathbf{elif}\;x \cdot y - z \cdot y \le -4.915495002659053232957672250858607769431 \cdot 10^{-133}:\\
\;\;\;\;t \cdot \left(x \cdot y - z \cdot y\right)\\

\mathbf{elif}\;x \cdot y - z \cdot y \le 1.719546404882711300932688246576743977043 \cdot 10^{-292}:\\
\;\;\;\;\left(t \cdot \left(x - z\right)\right) \cdot y\\

\mathbf{elif}\;x \cdot y - z \cdot y \le 9.281447287153549320457976819327732070409 \cdot 10^{192}:\\
\;\;\;\;t \cdot \left(x \cdot y - z \cdot y\right)\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r23078955 = x;
        double r23078956 = y;
        double r23078957 = r23078955 * r23078956;
        double r23078958 = z;
        double r23078959 = r23078958 * r23078956;
        double r23078960 = r23078957 - r23078959;
        double r23078961 = t;
        double r23078962 = r23078960 * r23078961;
        return r23078962;
}
↓
double f(double x, double y, double z, double t) {
        double r23078963 = x;
        double r23078964 = y;
        double r23078965 = r23078963 * r23078964;
        double r23078966 = z;
        double r23078967 = r23078966 * r23078964;
        double r23078968 = r23078965 - r23078967;
        double r23078969 = -2.112605073419439e+293;
        bool r23078970 = r23078968 <= r23078969;
        double r23078971 = t;
        double r23078972 = r23078963 - r23078966;
        double r23078973 = r23078971 * r23078972;
        double r23078974 = r23078973 * r23078964;
        double r23078975 = -4.915495002659053e-133;
        bool r23078976 = r23078968 <= r23078975;
        double r23078977 = r23078971 * r23078968;
        double r23078978 = 1.7195464048827113e-292;
        bool r23078979 = r23078968 <= r23078978;
        double r23078980 = 9.28144728715355e+192;
        bool r23078981 = r23078968 <= r23078980;
        double r23078982 = r23078964 * r23078971;
        double r23078983 = r23078972 * r23078982;
        double r23078984 = r23078981 ? r23078977 : r23078983;
        double r23078985 = r23078979 ? r23078974 : r23078984;
        double r23078986 = r23078976 ? r23078977 : r23078985;
        double r23078987 = r23078970 ? r23078974 : r23078986;
        return r23078987;
}

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
Target2.9
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;t \lt -9.231879582886776938073886590448747944753 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t \lt 2.543067051564877116200336808272775217995 \cdot 10^{83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (- (* x y) (* z y)) < -2.112605073419439e+293 or -4.915495002659053e-133 < (- (* x y) (* z y)) < 1.7195464048827113e-292

    1. Initial program 19.2

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

    2. Simplified1.3

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

    4. Applied associate-*r*1.5

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

    if -2.112605073419439e+293 < (- (* x y) (* z y)) < -4.915495002659053e-133 or 1.7195464048827113e-292 < (- (* x y) (* z y)) < 9.28144728715355e+192

    1. Initial program 0.2

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

    if 9.28144728715355e+192 < (- (* x y) (* z y))

    1. Initial program 29.1

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

    2. Simplified0.9

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y \le -2.112605073419438906656738477879925446144 \cdot 10^{293}:\\ \;\;\;\;\left(t \cdot \left(x - z\right)\right) \cdot y\\ \mathbf{elif}\;x \cdot y - z \cdot y \le -4.915495002659053232957672250858607769431 \cdot 10^{-133}:\\ \;\;\;\;t \cdot \left(x \cdot y - z \cdot y\right)\\ \mathbf{elif}\;x \cdot y - z \cdot y \le 1.719546404882711300932688246576743977043 \cdot 10^{-292}:\\ \;\;\;\;\left(t \cdot \left(x - z\right)\right) \cdot y\\ \mathbf{elif}\;x \cdot y - z \cdot y \le 9.281447287153549320457976819327732070409 \cdot 10^{192}:\\ \;\;\;\;t \cdot \left(x \cdot y - z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019192 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3"

  :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))