Average Error: 7.2 → 1.3
Time: 11.2s
Precision: binary64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -5.7669687292582076 \cdot 10^{+253}:\\ \;\;\;\;y \cdot \left(x \cdot t - z \cdot t\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq 6.149915964063066 \cdot 10^{+227}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - y \cdot z \leq -5.7669687292582076 \cdot 10^{+253}:\\
\;\;\;\;y \cdot \left(x \cdot t - z \cdot t\right)\\

\mathbf{elif}\;x \cdot y - y \cdot z \leq 6.149915964063066 \cdot 10^{+227}:\\
\;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\

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

\end{array}
(FPCore (x y z t) :precision binary64 (* (- (* x y) (* z y)) t))
↓
(FPCore (x y z t)
 :precision binary64
 (if (<= (- (* x y) (* y z)) -5.7669687292582076e+253)
   (* y (- (* x t) (* z t)))
   (if (<= (- (* x y) (* y z)) 6.149915964063066e+227)
     (* t (* y (- x z)))
     (* (- x z) (* y t)))))
double code(double x, double y, double z, double t) {
	return ((x * y) - (z * y)) * t;
}
↓
double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * y) - (y * z)) <= -5.7669687292582076e+253) {
		tmp = y * ((x * t) - (z * t));
	} else if (((x * y) - (y * z)) <= 6.149915964063066e+227) {
		tmp = t * (y * (x - z));
	} else {
		tmp = (x - z) * (y * t);
	}
	return tmp;
}

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

Original7.2
Target2.9
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;t < -9.231879582886777 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t < 2.543067051564877 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (-.f64 (*.f64 x y) (*.f64 z y)) < -5.7669687292582076e253

    1. Initial program 41.8

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

    3. Applied distribute-rgt-out--_binary64_1162641.8

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

    4. Applied associate-*l*_binary64_116130.2

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

    5. Simplified0.2

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

    6. Taylor expanded around 0 0.2

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

    if -5.7669687292582076e253 < (-.f64 (*.f64 x y) (*.f64 z y)) < 6.1499159640630662e227

    1. Initial program 1.5

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

    3. Applied *-un-lft-identity_binary64_116721.5

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

    4. Applied associate-*l*_binary64_116131.5

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

    5. Simplified1.5

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

    if 6.1499159640630662e227 < (-.f64 (*.f64 x y) (*.f64 z y))

    1. Initial program 34.7

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

    2. Taylor expanded around 0 34.7

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

    3. Simplified34.7

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

    5. Applied associate-*r*_binary64_116120.8

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

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -5.7669687292582076 \cdot 10^{+253}:\\ \;\;\;\;y \cdot \left(x \cdot t - z \cdot t\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq 6.149915964063066 \cdot 10^{+227}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2021076 
(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))