Average Error: 7.3 → 0.5
Time: 3.8s
Precision: binary64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -6.532761053995385 \cdot 10^{+187}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq -6.728055478426512 \cdot 10^{-221} \lor \neg \left(x \cdot y - y \cdot z \leq 7.664945489828276 \cdot 10^{-195}\right) \land x \cdot y - y \cdot z \leq 2.623431135997617 \cdot 10^{+220}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - y \cdot z \leq -6.532761053995385 \cdot 10^{+187}:\\
\;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\

\mathbf{elif}\;x \cdot y - y \cdot z \leq -6.728055478426512 \cdot 10^{-221} \lor \neg \left(x \cdot y - y \cdot z \leq 7.664945489828276 \cdot 10^{-195}\right) \land x \cdot y - y \cdot z \leq 2.623431135997617 \cdot 10^{+220}:\\
\;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\

\mathbf{else}:\\
\;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\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)) -6.532761053995385e+187)
   (* (* y t) (- x z))
   (if (or (<= (- (* x y) (* y z)) -6.728055478426512e-221)
           (and (not (<= (- (* x y) (* y z)) 7.664945489828276e-195))
                (<= (- (* x y) (* y z)) 2.623431135997617e+220)))
     (* (- (* x y) (* y z)) t)
     (* y (* t (- x z))))))
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)) <= -6.532761053995385e+187) {
		tmp = (y * t) * (x - z);
	} else if ((((x * y) - (y * z)) <= -6.728055478426512e-221) || (!(((x * y) - (y * z)) <= 7.664945489828276e-195) && (((x * y) - (y * z)) <= 2.623431135997617e+220))) {
		tmp = ((x * y) - (y * z)) * t;
	} else {
		tmp = y * (t * (x - z));
	}
	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
Target3.0
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;t < -9.231879582886777 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t < 2.543067051564877 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (-.f64 (*.f64 x y) (*.f64 z y)) < -6.53276105399538514e187

    1. Initial program 24.3

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

    2. Simplified1.5

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

    4. Applied associate-*r*_binary64_75871.8

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

    if -6.53276105399538514e187 < (-.f64 (*.f64 x y) (*.f64 z y)) < -6.7280554784265118e-221 or 7.66494548982827639e-195 < (-.f64 (*.f64 x y) (*.f64 z y)) < 2.62343113599761708e220

    1. Initial program 0.2

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

    if -6.7280554784265118e-221 < (-.f64 (*.f64 x y) (*.f64 z y)) < 7.66494548982827639e-195 or 2.62343113599761708e220 < (-.f64 (*.f64 x y) (*.f64 z y))

    1. Initial program 20.3

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

    2. Simplified0.9

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -6.532761053995385 \cdot 10^{+187}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq -6.728055478426512 \cdot 10^{-221} \lor \neg \left(x \cdot y - y \cdot z \leq 7.664945489828276 \cdot 10^{-195}\right) \land x \cdot y - y \cdot z \leq 2.623431135997617 \cdot 10^{+220}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020277 
(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))