Average Error: 14.8 → 12.1
Time: 7.3s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -1.128219015475836 \cdot 10^{-90} \lor \neg \left(a \le 6.27623202358413759 \cdot 10^{-6}\right):\\ \;\;\;\;x + \frac{y - z}{-\left(a - z\right)} \cdot \left(-\left(t - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \end{array}\]
x + \left(y - z\right) \cdot \frac{t - x}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;a \le -1.128219015475836 \cdot 10^{-90} \lor \neg \left(a \le 6.27623202358413759 \cdot 10^{-6}\right):\\
\;\;\;\;x + \frac{y - z}{-\left(a - z\right)} \cdot \left(-\left(t - x\right)\right)\\

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

\end{array}
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + ((double) (((double) (y - z)) * ((double) (((double) (t - x)) / ((double) (a - z))))))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if (((a <= -1.128219015475836e-90) || !(a <= 6.276232023584138e-06))) {
		VAR = ((double) (x + ((double) (((double) (((double) (y - z)) / ((double) -(((double) (a - z)))))) * ((double) -(((double) (t - x))))))));
	} else {
		VAR = ((double) (((double) (((double) (((double) (x * y)) / z)) + t)) - ((double) (((double) (t * y)) / z))));
	}
	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 2 regimes

  2. if a < -1.128219015475836e-90 or 6.276232023584138e-06 < a

    1. Initial program 9.6

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

    3. Applied clear-num9.8

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

    4. Applied un-div-inv9.7

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

    6. Applied frac-2neg9.7

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

    7. Applied associate-/r/7.5

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

    if -1.128219015475836e-90 < a < 6.276232023584138e-06

    1. Initial program 23.7

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

    2. Taylor expanded around inf 19.9

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

  4. Final simplification12.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -1.128219015475836 \cdot 10^{-90} \lor \neg \left(a \le 6.27623202358413759 \cdot 10^{-6}\right):\\ \;\;\;\;x + \frac{y - z}{-\left(a - z\right)} \cdot \left(-\left(t - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020114 
(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)))))