Average Error: 15.0 → 10.3
Time: 6.2s
Precision: binary64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \leq -4.807158068872457 \cdot 10^{-172}:\\ \;\;\;\;x + \frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\\ \mathbf{elif}\;a \leq 1.2161147335711477 \cdot 10^{-113}:\\ \;\;\;\;t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right)\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\\ \end{array}\]
x + \left(y - z\right) \cdot \frac{t - x}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;a \leq -4.807158068872457 \cdot 10^{-172}:\\
\;\;\;\;x + \frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\\

\mathbf{elif}\;a \leq 1.2161147335711477 \cdot 10^{-113}:\\
\;\;\;\;t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\

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

\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 (<= a -4.807158068872457e-172)
   (+
    x
    (*
     (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))
     (/ (- t x) (cbrt (- a z)))))
   (if (<= a 1.2161147335711477e-113)
     (+ t (* y (- (/ x z) (/ t z))))
     (+
      x
      (*
       (*
        (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))
        (* (cbrt (- t x)) (cbrt (- t x))))
       (/ (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 ((a <= -4.807158068872457e-172)) {
		tmp = ((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 tmp_1;
		if ((a <= 1.2161147335711477e-113)) {
			tmp_1 = ((double) (t + ((double) (y * ((double) ((x / z) - (t / z)))))));
		} else {
			tmp_1 = ((double) (x + ((double) (((double) ((((double) (y - z)) / ((double) (((double) cbrt(((double) (a - z)))) * ((double) cbrt(((double) (a - z))))))) * ((double) (((double) cbrt(((double) (t - x)))) * ((double) cbrt(((double) (t - x)))))))) * (((double) cbrt(((double) (t - x)))) / ((double) cbrt(((double) (a - z)))))))));
		}
		tmp = tmp_1;
	}
	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 3 regimes

  2. if a < -4.80715806887245703e-172

    1. Initial program Error: 12.7 bits

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

    3. Applied add-cube-cbrtError: 13.2 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: 13.2 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: 13.2 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: 10.8 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: 10.8 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 -4.80715806887245703e-172 < a < 1.2161147335711477e-113

    1. Initial program Error: 24.8 bits

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

    2. Taylor expanded around inf Error: 13.1 bits

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

    3. SimplifiedError: 11.1 bits

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

    if 1.2161147335711477e-113 < a

    1. Initial program Error: 11.0 bits

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

    3. Applied add-cube-cbrtError: 11.5 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 *-un-lft-identityError: 11.5 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: 11.6 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: 9.3 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: 9.3 bits

      \[\leadsto x + \color{blue}{\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\]
    8. Using strategy rm

    9. Applied *-un-lft-identityError: 9.3 bits

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

    10. Applied add-cube-cbrtError: 9.5 bits

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

    11. Applied times-fracError: 9.5 bits

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

    12. Applied associate-*r*Error: 9.1 bits

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

    13. SimplifiedError: 9.1 bits

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

  4. Final simplificationError: 10.3 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.807158068872457 \cdot 10^{-172}:\\ \;\;\;\;x + \frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\\ \mathbf{elif}\;a \leq 1.2161147335711477 \cdot 10^{-113}:\\ \;\;\;\;t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right)\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020205 
(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)))))