Average Error: 14.5 → 6.8
Time: 5.3s
Precision: binary64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1.943304021665259 \cdot 10^{-308}:\\ \;\;\;\;x + \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}} \cdot \left(\left(y - z\right) \cdot \left(\frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\right)\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\\ \end{array}\]
x + \left(y - z\right) \cdot \frac{t - x}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1.943304021665259 \cdot 10^{-308}:\\
\;\;\;\;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)\\

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

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

\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 ((((double) (x + ((double) (((double) (y - z)) * (((double) (t - x)) / ((double) (a - z))))))) <= -1.943304021665259e-308)) {
		VAR = ((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)))))))))))));
	} else {
		double VAR_1;
		if ((((double) (x + ((double) (((double) (y - z)) * (((double) (t - x)) / ((double) (a - z))))))) <= 0.0)) {
			VAR_1 = ((double) (t + ((double) (y * ((double) ((x / z) - (t / z)))))));
		} else {
			VAR_1 = ((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)))))))));
		}
		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 (+ x (* (- y z) (/ (- t x) (- a z)))) < -1.943304021665259e-308

    1. Initial program 7.5

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

    3. Applied add-cube-cbrt8.2

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

    4. Applied add-cube-cbrt8.4

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

    5. Applied times-frac8.4

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

    6. Applied associate-*r*4.8

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

    7. Simplified4.8

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

    if -1.943304021665259e-308 < (+ x (* (- y z) (/ (- t x) (- a z)))) < 0.0

    1. Initial program 61.8

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

    2. Taylor expanded around inf 25.2

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

    3. Simplified18.7

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

    if 0.0 < (+ x (* (- y z) (/ (- t x) (- a z))))

    1. Initial program 7.3

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

    3. Applied add-cube-cbrt8.0

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

    4. Applied *-un-lft-identity8.0

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

    5. Applied times-frac8.0

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

    6. Applied associate-*r*5.2

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

    7. Simplified5.2

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

  4. Final simplification6.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1.943304021665259 \cdot 10^{-308}:\\ \;\;\;\;x + \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}} \cdot \left(\left(y - z\right) \cdot \left(\frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\right)\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020196 
(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)))))