Average Error: 15.0 → 11.9
Time: 5.9s
Precision: binary64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \leq -7.816103542221312 \cdot 10^{-99}:\\ \;\;\;\;x + \frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\\ \mathbf{elif}\;z \leq 1.291527251069965 \cdot 10^{-197}:\\ \;\;\;\;x + \left(\left(y - z\right) \cdot \left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right)\right) \cdot \frac{\sqrt[3]{t - x}}{a - z}\\ \mathbf{elif}\;z \leq 1.1037859861347199 \cdot 10^{+142}:\\ \;\;\;\;x + \frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\ \end{array}\]
x + \left(y - z\right) \cdot \frac{t - x}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;z \leq -7.816103542221312 \cdot 10^{-99}:\\
\;\;\;\;x + \frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\\

\mathbf{elif}\;z \leq 1.291527251069965 \cdot 10^{-197}:\\
\;\;\;\;x + \left(\left(y - z\right) \cdot \left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right)\right) \cdot \frac{\sqrt[3]{t - x}}{a - z}\\

\mathbf{elif}\;z \leq 1.1037859861347199 \cdot 10^{+142}:\\
\;\;\;\;x + \frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\\

\mathbf{else}:\\
\;\;\;\;t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\

\end{array}
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 VAR;
	if ((z <= -7.816103542221312e-99)) {
		VAR = ((double) (x + ((double) ((((double) (y - z)) / ((double) (((double) cbrt(((double) (a - z)))) * ((double) cbrt(((double) (a - z))))))) * (((double) (t - x)) / ((double) cbrt(((double) (a - z)))))))));
	} else {
		double VAR_1;
		if ((z <= 1.291527251069965e-197)) {
			VAR_1 = ((double) (x + ((double) (((double) (((double) (y - z)) * ((double) (((double) cbrt(((double) (t - x)))) * ((double) cbrt(((double) (t - x)))))))) * (((double) cbrt(((double) (t - x)))) / ((double) (a - z)))))));
		} else {
			double VAR_2;
			if ((z <= 1.1037859861347199e+142)) {
				VAR_2 = ((double) (x + ((double) ((((double) (y - z)) / ((double) (((double) cbrt(((double) (a - z)))) * ((double) cbrt(((double) (a - z))))))) * (((double) (t - x)) / ((double) cbrt(((double) (a - z)))))))));
			} else {
				VAR_2 = ((double) (t + ((double) (y * ((double) ((x / z) - (t / z)))))));
			}
			VAR_1 = VAR_2;
		}
		VAR = VAR_1;
	}
	return VAR;
}

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 3 regimes

  2. if z < -7.8161035422213117e-99 or 1.291527251069965e-197 < z < 1.10378598613471988e142

    1. Initial program Error: 15.3 bits

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

    3. Applied add-cube-cbrtError: 15.8 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 *-un-lft-identityError: 15.8 bits

      \[\leadsto x + \left(y - z\right) \cdot \frac{\color{blue}{1 \cdot \left(t - x\right)}}{\left(\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}\right) \cdot \sqrt[3]{a - z}}\]

    5. Applied times-fracError: 15.8 bits

      \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\left(\frac{1}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right)}\]

    6. Applied associate-*r*Error: 13.4 bits

      \[\leadsto x + \color{blue}{\left(\left(y - z\right) \cdot \frac{1}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{t - x}{\sqrt[3]{a - z}}}\]

    7. SimplifiedError: 13.4 bits

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

    if -7.8161035422213117e-99 < z < 1.291527251069965e-197

    1. Initial program Error: 6.4 bits

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

    3. Applied *-un-lft-identityError: 6.4 bits

      \[\leadsto x + \left(y - z\right) \cdot \frac{t - x}{\color{blue}{1 \cdot \left(a - z\right)}}\]

    4. Applied add-cube-cbrtError: 6.9 bits

      \[\leadsto x + \left(y - z\right) \cdot \frac{\color{blue}{\left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right) \cdot \sqrt[3]{t - x}}}{1 \cdot \left(a - z\right)}\]

    5. Applied times-fracError: 6.9 bits

      \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\left(\frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{1} \cdot \frac{\sqrt[3]{t - x}}{a - z}\right)}\]

    6. Applied associate-*r*Error: 5.4 bits

      \[\leadsto x + \color{blue}{\left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{1}\right) \cdot \frac{\sqrt[3]{t - x}}{a - z}}\]

    7. SimplifiedError: 5.4 bits

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

    if 1.10378598613471988e142 < z

    1. Initial program Error: 26.7 bits

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

    2. Taylor expanded around inf Error: 25.0 bits

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

    3. SimplifiedError: 15.9 bits

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

  4. Final simplificationError: 11.9 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.816103542221312 \cdot 10^{-99}:\\ \;\;\;\;x + \frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\\ \mathbf{elif}\;z \leq 1.291527251069965 \cdot 10^{-197}:\\ \;\;\;\;x + \left(\left(y - z\right) \cdot \left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right)\right) \cdot \frac{\sqrt[3]{t - x}}{a - z}\\ \mathbf{elif}\;z \leq 1.1037859861347199 \cdot 10^{+142}:\\ \;\;\;\;x + \frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020200 
(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)))))