Average Error: 7.0 → 0.3
Time: 5.8s
Precision: binary64
\[[y, t]=\mathsf{sort}([y, t])\]
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -6.018090186336724 \cdot 10^{+285}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq -4.0019207553879035 \cdot 10^{-294}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq 0:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq 5.74572278966329 \cdot 10^{+234}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - y \cdot z \leq -6.018090186336724 \cdot 10^{+285}:\\
\;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\

\mathbf{elif}\;x \cdot y - y \cdot z \leq -4.0019207553879035 \cdot 10^{-294}:\\
\;\;\;\;\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 5.74572278966329 \cdot 10^{+234}:\\
\;\;\;\;\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)) -6.018090186336724e+285)
   (* y (* t (- x z)))
   (if (<= (- (* x y) (* y z)) -4.0019207553879035e-294)
     (* (- (* x y) (* y z)) t)
     (if (<= (- (* x y) (* y z)) 0.0)
       (* (- x z) (* y t))
       (if (<= (- (* x y) (* y z)) 5.74572278966329e+234)
         (* (- (* 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)) <= -6.018090186336724e+285) {
		tmp = y * (t * (x - z));
	} else if (((x * y) - (y * z)) <= -4.0019207553879035e-294) {
		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)) <= 5.74572278966329e+234) {
		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

Original7.0
Target3.4
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;t < -9.231879582886777 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t < 2.543067051564877 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (-.f64 (*.f64 x y) (*.f64 z y)) < -6.01809018633672386e285 or 5.74572278966329e234 < (-.f64 (*.f64 x y) (*.f64 z y))

    1. Initial program 41.6

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

    2. Simplified0.4

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

    if -6.01809018633672386e285 < (-.f64 (*.f64 x y) (*.f64 z y)) < -4.0019207553879035e-294 or 0.0 < (-.f64 (*.f64 x y) (*.f64 z y)) < 5.74572278966329e234

    1. Initial program 0.3

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

    if -4.0019207553879035e-294 < (-.f64 (*.f64 x y) (*.f64 z y)) < 0.0

    1. Initial program 20.0

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

    2. Simplified0.1

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

    4. Applied associate-*r*_binary64_133170.1

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -6.018090186336724 \cdot 10^{+285}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq -4.0019207553879035 \cdot 10^{-294}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq 0:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq 5.74572278966329 \cdot 10^{+234}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2021043 
(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))