Average Error: 14.8 → 6.7
Time: 13.3s
Precision: binary64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -6.14088739107045 \cdot 10^{-203} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 1.247406121894391 \cdot 10^{-249}\right):\\ \;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(t + \left(\frac{x \cdot y}{z} + \frac{t \cdot a}{z}\right)\right) - \left(\frac{x \cdot a}{z} + \frac{y \cdot t}{z}\right)\\ \end{array}\]
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 -6.14088739107045 \cdot 10^{-203} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 1.247406121894391 \cdot 10^{-249}\right):\\
\;\;\;\;x + \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}}\\

\mathbf{else}:\\
\;\;\;\;\left(t + \left(\frac{x \cdot y}{z} + \frac{t \cdot a}{z}\right)\right) - \left(\frac{x \cdot a}{z} + \frac{y \cdot 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)))) -6.14088739107045e-203)
         (not
          (<= (+ x (* (- y z) (/ (- t x) (- a z)))) 1.247406121894391e-249)))
   (+
    x
    (*
     (*
      (- y z)
      (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
     (/ (cbrt (- t x)) (cbrt (- a z)))))
   (- (+ t (+ (/ (* x y) z) (/ (* t a) z))) (+ (/ (* x 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)))) <= -6.14088739107045e-203) || !((x + ((y - z) * ((t - x) / (a - z)))) <= 1.247406121894391e-249)) {
		tmp = x + (((y - z) * ((cbrt(t - x) * cbrt(t - x)) / (cbrt(a - z) * cbrt(a - z)))) * (cbrt(t - x) / cbrt(a - z)));
	} else {
		tmp = (t + (((x * y) / z) + ((t * a) / z))) - (((x * 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)))) < -6.1408873910704503e-203 or 1.247406121894391e-249 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

    1. Initial program 6.5

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

    3. Applied add-cube-cbrt_binary64_31827.3

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

    4. Applied add-cube-cbrt_binary64_31827.5

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

    5. Applied times-frac_binary64_31537.5

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

    6. Applied associate-*r*_binary64_30874.6

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

    if -6.1408873910704503e-203 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.247406121894391e-249

    1. Initial program 54.9

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

    2. Taylor expanded around inf 17.0

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

  4. Final simplification6.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -6.14088739107045 \cdot 10^{-203} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 1.247406121894391 \cdot 10^{-249}\right):\\ \;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(t + \left(\frac{x \cdot y}{z} + \frac{t \cdot a}{z}\right)\right) - \left(\frac{x \cdot a}{z} + \frac{y \cdot t}{z}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2021043 
(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)))))