Average Error: 7.3 → 1.0
Time: 9.1s
Precision: binary64
\[[y, t]=\mathsf{sort}([y, t])\]
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -1.5582939101302764 \cdot 10^{+275}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq -3.958165785224774 \cdot 10^{-133}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq 1.1155150438433126 \cdot 10^{-191} \lor \neg \left(x \cdot y - y \cdot z \leq 6.8524311405980945 \cdot 10^{+96}\right):\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - y \cdot z \leq -1.5582939101302764 \cdot 10^{+275}:\\
\;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\

\mathbf{elif}\;x \cdot y - y \cdot z \leq -3.958165785224774 \cdot 10^{-133}:\\
\;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\

\mathbf{elif}\;x \cdot y - y \cdot z \leq 1.1155150438433126 \cdot 10^{-191} \lor \neg \left(x \cdot y - y \cdot z \leq 6.8524311405980945 \cdot 10^{+96}\right):\\
\;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\

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

\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)) -1.5582939101302764e+275)
   (* y (* t (- x z)))
   (if (<= (- (* x y) (* y z)) -3.958165785224774e-133)
     (* t (* y (- x z)))
     (if (or (<= (- (* x y) (* y z)) 1.1155150438433126e-191)
             (not (<= (- (* x y) (* y z)) 6.8524311405980945e+96)))
       (* (- x z) (* y t))
       (* (- (* x y) (* y z)) 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)) <= -1.5582939101302764e+275) {
		tmp = y * (t * (x - z));
	} else if (((x * y) - (y * z)) <= -3.958165785224774e-133) {
		tmp = t * (y * (x - z));
	} else if ((((x * y) - (y * z)) <= 1.1155150438433126e-191) || !(((x * y) - (y * z)) <= 6.8524311405980945e+96)) {
		tmp = (x - z) * (y * t);
	} else {
		tmp = ((x * y) - (y * z)) * 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

Original7.3
Target3.2
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;t < -9.231879582886777 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t < 2.543067051564877 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if (-.f64 (*.f64 x y) (*.f64 z y)) < -1.55829391013027639e275

    1. Initial program 48.4

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

    2. Simplified0.2

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

    if -1.55829391013027639e275 < (-.f64 (*.f64 x y) (*.f64 z y)) < -3.95816578522477369e-133

    1. Initial program 0.3

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

    2. Taylor expanded around 0 0.3

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

    3. Simplified0.3

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

    if -3.95816578522477369e-133 < (-.f64 (*.f64 x y) (*.f64 z y)) < 1.1155150438433126e-191 or 6.8524311405980945e96 < (-.f64 (*.f64 x y) (*.f64 z y))

    1. Initial program 11.7

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

    2. Taylor expanded around 0 11.7

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

    3. Simplified11.7

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

    5. Applied associate-*r*_binary64_163862.3

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

    if 1.1155150438433126e-191 < (-.f64 (*.f64 x y) (*.f64 z y)) < 6.8524311405980945e96

    1. Initial program 0.2

      \[\left(x \cdot y - z \cdot y\right) \cdot t\]
  3. Recombined 4 regimes into one program.

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -1.5582939101302764 \cdot 10^{+275}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq -3.958165785224774 \cdot 10^{-133}:\\ \;\;\;\;t \cdot \left(y \cdot \left(x - z\right)\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq 1.1155150438433126 \cdot 10^{-191} \lor \neg \left(x \cdot y - y \cdot z \leq 6.8524311405980945 \cdot 10^{+96}\right):\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \end{array}\]

Reproduce

herbie shell --seed 2021098 
(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))