Average Error: 7.4 → 3.9
Time: 4.2s
Precision: binary64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -\infty \lor \neg \left(x \cdot y - y \cdot z \leq -1.3092298267031214 \cdot 10^{-92}\right) \land x \cdot y - y \cdot z \leq 3.9222565971071866 \cdot 10^{-287}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - y \cdot z \leq -\infty \lor \neg \left(x \cdot y - y \cdot z \leq -1.3092298267031214 \cdot 10^{-92}\right) \land x \cdot y - y \cdot z \leq 3.9222565971071866 \cdot 10^{-287}:\\
\;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\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 (or (<= (- (* x y) (* y z)) (- INFINITY))
         (and (not (<= (- (* x y) (* y z)) -1.3092298267031214e-92))
              (<= (- (* x y) (* y z)) 3.9222565971071866e-287)))
   (* (* y t) (- x z))
   (* (- (* 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)) <= -((double) INFINITY)) || (!(((x * y) - (y * z)) <= -1.3092298267031214e-92) && (((x * y) - (y * z)) <= 3.9222565971071866e-287))) {
		tmp = (y * t) * (x - z);
	} 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

Original7.4
Target2.9
Herbie3.9
\[\begin{array}{l} \mathbf{if}\;t < -9.231879582886777 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t < 2.543067051564877 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (-.f64 (*.f64 x y) (*.f64 z y)) < -inf.0 or -1.30922982670312139e-92 < (-.f64 (*.f64 x y) (*.f64 z y)) < 3.9222565971071866e-287

    1. Initial program 18.4

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

    2. Simplified2.1

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

    4. Applied associate-*r*_binary64_133172.1

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

    if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z y)) < -1.30922982670312139e-92 or 3.9222565971071866e-287 < (-.f64 (*.f64 x y) (*.f64 z y))

    1. Initial program 4.4

      \[\left(x \cdot y - z \cdot y\right) \cdot t\]
  3. Recombined 2 regimes into one program.

  4. Final simplification3.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -\infty \lor \neg \left(x \cdot y - y \cdot z \leq -1.3092298267031214 \cdot 10^{-92}\right) \land x \cdot y - y \cdot z \leq 3.9222565971071866 \cdot 10^{-287}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \end{array}\]

Reproduce

herbie shell --seed 2020355 
(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))