Average Error: 14.6 → 10.1
Time: 6.4s
Precision: binary64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \leq -3.491633338612442 \cdot 10^{+208} \lor \neg \left(z \leq 1.9136028607171334 \cdot 10^{+132}\right):\\ \;\;\;\;t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}} \cdot \left(\left(y - z\right) \cdot \left(\frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\right)\right)\\ \end{array}\]
x + \left(y - z\right) \cdot \frac{t - x}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;z \leq -3.491633338612442 \cdot 10^{+208} \lor \neg \left(z \leq 1.9136028607171334 \cdot 10^{+132}\right):\\
\;\;\;\;t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\

\mathbf{else}:\\
\;\;\;\;x + \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}} \cdot \left(\left(y - z\right) \cdot \left(\frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\right)\right)\\

\end{array}
(FPCore (x y z t a) :precision binary64 (+ x (* (- y z) (/ (- t x) (- a z)))))
↓
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.491633338612442e+208) (not (<= z 1.9136028607171334e+132)))
   (+ t (* y (- (/ x z) (/ t z))))
   (+
    x
    (*
     (/ (cbrt (- t x)) (cbrt (- a z)))
     (*
      (- y z)
      (*
       (/ (cbrt (- t x)) (cbrt (- a z)))
       (/ (cbrt (- t x)) (cbrt (- a z)))))))))
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + ((double) (((double) (y - z)) * (((double) (t - x)) / ((double) (a - z)))))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z <= -3.491633338612442e+208) || !(z <= 1.9136028607171334e+132))) {
		tmp = ((double) (t + ((double) (y * ((double) ((x / z) - (t / z)))))));
	} else {
		tmp = ((double) (x + ((double) ((((double) cbrt(((double) (t - x)))) / ((double) cbrt(((double) (a - z))))) * ((double) (((double) (y - z)) * ((double) ((((double) cbrt(((double) (t - x)))) / ((double) cbrt(((double) (a - z))))) * (((double) cbrt(((double) (t - x)))) / ((double) cbrt(((double) (a - z)))))))))))));
	}
	return tmp;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if z < -3.49163333861244182e208 or 1.91360286071713343e132 < z

    1. Initial program Error: 28.3 bits

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]

    2. Taylor expanded around inf Error: 25.6 bits

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

    3. SimplifiedError: 16.1 bits

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

    if -3.49163333861244182e208 < z < 1.91360286071713343e132

    1. Initial program Error: 9.9 bits

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
    2. Using strategy rm

    3. Applied add-cube-cbrtError: 10.5 bits

      \[\leadsto x + \left(y - z\right) \cdot \frac{t - x}{\color{blue}{\left(\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}\right) \cdot \sqrt[3]{a - z}}}\]

    4. Applied add-cube-cbrtError: 10.6 bits

      \[\leadsto x + \left(y - z\right) \cdot \frac{\color{blue}{\left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right) \cdot \sqrt[3]{t - x}}}{\left(\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}\right) \cdot \sqrt[3]{a - z}}\]

    5. Applied times-fracError: 10.6 bits

      \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\left(\frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\right)}\]

    6. Applied associate-*r*Error: 8.0 bits

      \[\leadsto x + \color{blue}{\left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}}\]

    7. SimplifiedError: 8.0 bits

      \[\leadsto x + \color{blue}{\left(\left(y - z\right) \cdot \left(\frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\right)\right)} \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplificationError: 10.1 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.491633338612442 \cdot 10^{+208} \lor \neg \left(z \leq 1.9136028607171334 \cdot 10^{+132}\right):\\ \;\;\;\;t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}} \cdot \left(\left(y - z\right) \cdot \left(\frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020204 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))