Average Error: 6.9 → 0.7
Time: 4.1s
Precision: binary64
\[[y, t]=\mathsf{sort}([y, t])\]
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -4.2777475910843955 \cdot 10^{+149}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq -1.0073855893875482 \cdot 10^{-189}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq 0:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq 9.693889291176866 \cdot 10^{+159}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - y \cdot z \leq -4.2777475910843955 \cdot 10^{+149}:\\
\;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\

\mathbf{elif}\;x \cdot y - y \cdot z \leq -1.0073855893875482 \cdot 10^{-189}:\\
\;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\

\mathbf{elif}\;x \cdot y - y \cdot z \leq 0:\\
\;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\

\mathbf{elif}\;x \cdot y - y \cdot z \leq 9.693889291176866 \cdot 10^{+159}:\\
\;\;\;\;\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)) -4.2777475910843955e+149)
   (* y (* t (- x z)))
   (if (<= (- (* x y) (* y z)) -1.0073855893875482e-189)
     (* (- (* x y) (* y z)) t)
     (if (<= (- (* x y) (* y z)) 0.0)
       (* (- x z) (* y t))
       (if (<= (- (* x y) (* y z)) 9.693889291176866e+159)
         (* (- (* 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)) <= -4.2777475910843955e+149) {
		tmp = y * (t * (x - z));
	} else if (((x * y) - (y * z)) <= -1.0073855893875482e-189) {
		tmp = ((x * y) - (y * z)) * t;
	} else if (((x * y) - (y * z)) <= 0.0) {
		tmp = (x - z) * (y * t);
	} else if (((x * y) - (y * z)) <= 9.693889291176866e+159) {
		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

Original6.9
Target3.3
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;t < -9.231879582886777 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t < 2.543067051564877 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (-.f64 (*.f64 x y) (*.f64 z y)) < -4.27774759108439546e149 or 9.69388929117686636e159 < (-.f64 (*.f64 x y) (*.f64 z y))

    1. Initial program 21.3

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

    2. Simplified1.6

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

    if -4.27774759108439546e149 < (-.f64 (*.f64 x y) (*.f64 z y)) < -1.00738558938754816e-189 or 0.0 < (-.f64 (*.f64 x y) (*.f64 z y)) < 9.69388929117686636e159

    1. Initial program 0.3

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

    if -1.00738558938754816e-189 < (-.f64 (*.f64 x y) (*.f64 z y)) < 0.0

    1. Initial program 11.8

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

    2. Simplified1.0

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

    4. Applied associate-*r*_binary641.5

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

    5. Simplified1.5

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -4.2777475910843955 \cdot 10^{+149}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq -1.0073855893875482 \cdot 10^{-189}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq 0:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq 9.693889291176866 \cdot 10^{+159}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2021147 
(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))