Average Error: 14.9 → 4.0
Time: 22.5s
Precision: binary64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -6.336278483289018 \cdot 10^{-295} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z} - \frac{z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{\frac{z}{x}} \cdot \frac{a}{z} + \left(t + \left(\frac{y}{\frac{z}{x}} + \frac{t}{\frac{z}{a}}\right)\right)\right) - \left(x \cdot \frac{a}{z} + \left(y \cdot \frac{t}{z} + \frac{a}{z} \cdot \left(y \cdot \frac{t}{z}\right)\right)\right)\\ \end{array}\]
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 -6.336278483289018 \cdot 10^{-295} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\
\;\;\;\;x + \frac{t - x}{\frac{a}{y - z} - \frac{z}{y - z}}\\

\mathbf{else}:\\
\;\;\;\;\left(\frac{y}{\frac{z}{x}} \cdot \frac{a}{z} + \left(t + \left(\frac{y}{\frac{z}{x}} + \frac{t}{\frac{z}{a}}\right)\right)\right) - \left(x \cdot \frac{a}{z} + \left(y \cdot \frac{t}{z} + \frac{a}{z} \cdot \left(y \cdot \frac{t}{z}\right)\right)\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)))) -6.336278483289018e-295)
         (not (<= (+ x (* (- y z) (/ (- t x) (- a z)))) 0.0)))
   (+ x (/ (- t x) (- (/ a (- y z)) (/ z (- y z)))))
   (-
    (+ (* (/ y (/ z x)) (/ a z)) (+ t (+ (/ y (/ z x)) (/ t (/ z a)))))
    (+ (* x (/ a z)) (+ (* y (/ t z)) (* (/ a z) (* y (/ t z))))))))
double code(double x, double y, double z, double t, double a) {
	return x + ((y - z) * ((t - x) / (a - z)));
}
↓
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x + ((y - z) * ((t - x) / (a - z)))) <= -6.336278483289018e-295) || !((x + ((y - z) * ((t - x) / (a - z)))) <= 0.0)) {
		tmp = x + ((t - x) / ((a / (y - z)) - (z / (y - z))));
	} else {
		tmp = (((y / (z / x)) * (a / z)) + (t + ((y / (z / x)) + (t / (z / a))))) - ((x * (a / z)) + ((y * (t / z)) + ((a / z) * (y * (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)))) < -6.3362784832890179e-295 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

    1. Initial program 7.7

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

    2. Simplified4.4

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

    3. Taylor expanded around 0 4.4

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

    if -6.3362784832890179e-295 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

    1. Initial program 61.4

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

    2. Simplified60.9

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

    3. Taylor expanded around 0 12.2

      \[\leadsto \color{blue}{\left(\frac{a \cdot \left(x \cdot y\right)}{{z}^{2}} + \left(\frac{a \cdot t}{z} + \left(t + \frac{x \cdot y}{z}\right)\right)\right) - \left(\frac{a \cdot x}{z} + \left(\frac{a \cdot \left(y \cdot t\right)}{{z}^{2}} + \frac{t \cdot y}{z}\right)\right)}\]

    4. Simplified1.5

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

  4. Final simplification4.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -6.336278483289018 \cdot 10^{-295} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z} - \frac{z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{\frac{z}{x}} \cdot \frac{a}{z} + \left(t + \left(\frac{y}{\frac{z}{x}} + \frac{t}{\frac{z}{a}}\right)\right)\right) - \left(x \cdot \frac{a}{z} + \left(y \cdot \frac{t}{z} + \frac{a}{z} \cdot \left(y \cdot \frac{t}{z}\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2021176 
(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)))))