Average Error: 7.4 → 0.7
Time: 5.5s
Precision: binary64
\[\left(x \cdot y - z \cdot y\right) \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -1.2029529979154415 \cdot 10^{+248} \lor \neg \left(x \cdot y - y \cdot z \leq -5.4082231212758156 \cdot 10^{-151} \lor \neg \left(x \cdot y - y \cdot z \leq 1.3383246875081994 \cdot 10^{-117}\right) \land x \cdot y - y \cdot z \leq 3.9727995986019546 \cdot 10^{+207}\right):\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \end{array}\]
\left(x \cdot y - z \cdot y\right) \cdot t
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - y \cdot z \leq -1.2029529979154415 \cdot 10^{+248} \lor \neg \left(x \cdot y - y \cdot z \leq -5.4082231212758156 \cdot 10^{-151} \lor \neg \left(x \cdot y - y \cdot z \leq 1.3383246875081994 \cdot 10^{-117}\right) \land x \cdot y - y \cdot z \leq 3.9727995986019546 \cdot 10^{+207}\right):\\
\;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\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)) -1.2029529979154415e+248)
         (not
          (or (<= (- (* x y) (* y z)) -5.4082231212758156e-151)
              (and (not (<= (- (* x y) (* y z)) 1.3383246875081994e-117))
                   (<= (- (* x y) (* y z)) 3.9727995986019546e+207)))))
   (* y (* t (- x z)))
   (* (- (* x y) (* y z)) t)))
double code(double x, double y, double z, double t) {
	return ((double) (((double) (((double) (x * y)) - ((double) (z * y)))) * t));
}
↓
double code(double x, double y, double z, double t) {
	double tmp;
	if (((((double) (((double) (x * y)) - ((double) (y * z)))) <= -1.2029529979154415e+248) || !((((double) (((double) (x * y)) - ((double) (y * z)))) <= -5.4082231212758156e-151) || (!(((double) (((double) (x * y)) - ((double) (y * z)))) <= 1.3383246875081994e-117) && (((double) (((double) (x * y)) - ((double) (y * z)))) <= 3.9727995986019546e+207))))) {
		tmp = ((double) (y * ((double) (t * ((double) (x - z))))));
	} else {
		tmp = ((double) (((double) (((double) (x * y)) - ((double) (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
Target3.0
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 2 regimes

  2. if (- (* x y) (* z y)) < -1.20295299791544149e248 or -5.40822312127581559e-151 < (- (* x y) (* z y)) < 1.3383246875081994e-117 or 3.9727995986019546e207 < (- (* x y) (* z y))

    1. Initial program Error: 18.5 bits

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

    2. SimplifiedError: 1.5 bits

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

    if -1.20295299791544149e248 < (- (* x y) (* z y)) < -5.40822312127581559e-151 or 1.3383246875081994e-117 < (- (* x y) (* z y)) < 3.9727995986019546e207

    1. Initial program Error: 0.3 bits

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

  4. Final simplificationError: 0.7 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -1.2029529979154415 \cdot 10^{+248} \lor \neg \left(x \cdot y - y \cdot z \leq -5.4082231212758156 \cdot 10^{-151} \lor \neg \left(x \cdot y - y \cdot z \leq 1.3383246875081994 \cdot 10^{-117}\right) \land x \cdot y - y \cdot z \leq 3.9727995986019546 \cdot 10^{+207}\right):\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \end{array}\]

Reproduce

herbie shell --seed 2020204 
(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))