Average Error: 14.6 → 9.1
Time: 7.0s
Precision: binary64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2.8377217397670284 \cdot 10^{-276} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\ \end{array}\]
x + \left(y - z\right) \cdot \frac{t - x}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2.8377217397670284 \cdot 10^{-276} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\
\;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\

\mathbf{else}:\\
\;\;\;\;t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\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 (<= (+ x (* (- y z) (/ (- t x) (- a z)))) -2.8377217397670284e-276)
         (not (<= (+ x (* (- y z) (/ (- t x) (- a z)))) 0.0)))
   (+ x (* (- y z) (/ (- t x) (- a z))))
   (+ t (* y (- (/ x z) (/ t 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 (((((double) (x + ((double) (((double) (y - z)) * (((double) (t - x)) / ((double) (a - z))))))) <= -2.8377217397670284e-276) || !(((double) (x + ((double) (((double) (y - z)) * (((double) (t - x)) / ((double) (a - z))))))) <= 0.0))) {
		tmp = ((double) (x + ((double) (((double) (y - z)) * (((double) (t - x)) / ((double) (a - z)))))));
	} else {
		tmp = ((double) (t + ((double) (y * ((double) ((x / z) - (t / 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 (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2.83772173976702841e-276 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

    1. Initial program 7.5

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

    if -2.83772173976702841e-276 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

    1. Initial program 60.3

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

    2. Taylor expanded around inf 25.9

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

    3. Simplified19.9

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

  4. Final simplification9.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2.8377217397670284 \cdot 10^{-276} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020210 
(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)))))