Average Error: 14.5 → 5.1
Time: 23.5s
Precision: binary64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -\infty:\\ \;\;\;\;x + \left(\left(\frac{y \cdot t}{a - z} + \frac{x \cdot z}{a - z}\right) - \left(\frac{x \cdot y}{a - z} + \frac{z \cdot t}{a - z}\right)\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2.107537073467051 \cdot 10^{-159}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5.564850423439244 \cdot 10^{-293}:\\ \;\;\;\;\left(\frac{y \cdot t}{a - z} + \left(x + \frac{x \cdot z}{a - z}\right)\right) - \left(\frac{x \cdot y}{a - z} + \frac{z \cdot t}{a - z}\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;\left(t + \left(\frac{x \cdot y}{z} + \frac{t \cdot a}{z}\right)\right) - \left(\frac{x \cdot a}{z} + \frac{y \cdot t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y - z}{a - z}}{\frac{1}{t - x}}\\ \end{array}\]
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 -\infty:\\
\;\;\;\;x + \left(\left(\frac{y \cdot t}{a - z} + \frac{x \cdot z}{a - z}\right) - \left(\frac{x \cdot y}{a - z} + \frac{z \cdot t}{a - z}\right)\right)\\

\mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2.107537073467051 \cdot 10^{-159}:\\
\;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\

\mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5.564850423439244 \cdot 10^{-293}:\\
\;\;\;\;\left(\frac{y \cdot t}{a - z} + \left(x + \frac{x \cdot z}{a - z}\right)\right) - \left(\frac{x \cdot y}{a - z} + \frac{z \cdot t}{a - z}\right)\\

\mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\
\;\;\;\;\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)\\

\mathbf{else}:\\
\;\;\;\;x + \frac{\frac{y - z}{a - z}}{\frac{1}{t - x}}\\

\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 (<= (+ x (* (- y z) (/ (- t x) (- a z)))) (- INFINITY))
   (+
    x
    (-
     (+ (/ (* y t) (- a z)) (/ (* x z) (- a z)))
     (+ (/ (* x y) (- a z)) (/ (* z t) (- a z)))))
   (if (<= (+ x (* (- y z) (/ (- t x) (- a z)))) -2.107537073467051e-159)
     (+ x (* (- y z) (/ (- t x) (- a z))))
     (if (<= (+ x (* (- y z) (/ (- t x) (- a z)))) -5.564850423439244e-293)
       (-
        (+ (/ (* y t) (- a z)) (+ x (/ (* x z) (- a z))))
        (+ (/ (* x y) (- a z)) (/ (* z t) (- a z))))
       (if (<= (+ x (* (- y z) (/ (- t x) (- a z)))) 0.0)
         (-
          (+ t (+ (/ (* x y) z) (/ (* t a) z)))
          (+ (/ (* x a) z) (/ (* y t) z)))
         (+ x (/ (/ (- y z) (- a z)) (/ 1.0 (- t x)))))))))
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)))) <= -((double) INFINITY)) {
		tmp = x + ((((y * t) / (a - z)) + ((x * z) / (a - z))) - (((x * y) / (a - z)) + ((z * t) / (a - z))));
	} else if ((x + ((y - z) * ((t - x) / (a - z)))) <= -2.107537073467051e-159) {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	} else if ((x + ((y - z) * ((t - x) / (a - z)))) <= -5.564850423439244e-293) {
		tmp = (((y * t) / (a - z)) + (x + ((x * z) / (a - z)))) - (((x * y) / (a - z)) + ((z * t) / (a - z)));
	} else if ((x + ((y - z) * ((t - x) / (a - z)))) <= 0.0) {
		tmp = (t + (((x * y) / z) + ((t * a) / z))) - (((x * a) / z) + ((y * t) / z));
	} else {
		tmp = x + (((y - z) / (a - z)) / (1.0 / (t - x)));
	}
	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 5 regimes

  2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -inf.0

    1. Initial program 64.0

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

    2. Taylor expanded around 0 11.4

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

    if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2.1075370734670509e-159

    1. Initial program 3.4

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

    if -2.1075370734670509e-159 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.5648504234392436e-293

    1. Initial program 23.3

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

    2. Taylor expanded around 0 1.7

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

    if -5.5648504234392436e-293 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

    1. Initial program 61.0

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

    2. Taylor expanded around inf 12.3

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

    3. Simplified12.3

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

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

    1. Initial program 7.6

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

    3. Applied clear-num_binary64_17827.9

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

    5. Applied div-inv_binary64_17808.0

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

    6. Applied *-un-lft-identity_binary64_17838.0

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

    7. Applied times-frac_binary64_17897.7

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

    8. Applied associate-*r*_binary64_17234.5

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

    9. Simplified4.4

      \[\leadsto x + \color{blue}{\frac{y - z}{a - z}} \cdot \frac{1}{\frac{1}{t - x}}\]
    10. Using strategy rm

    11. Applied un-div-inv_binary64_17814.4

      \[\leadsto x + \color{blue}{\frac{\frac{y - z}{a - z}}{\frac{1}{t - x}}}\]
  3. Recombined 5 regimes into one program.

  4. Final simplification5.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -\infty:\\ \;\;\;\;x + \left(\left(\frac{y \cdot t}{a - z} + \frac{x \cdot z}{a - z}\right) - \left(\frac{x \cdot y}{a - z} + \frac{z \cdot t}{a - z}\right)\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2.107537073467051 \cdot 10^{-159}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5.564850423439244 \cdot 10^{-293}:\\ \;\;\;\;\left(\frac{y \cdot t}{a - z} + \left(x + \frac{x \cdot z}{a - z}\right)\right) - \left(\frac{x \cdot y}{a - z} + \frac{z \cdot t}{a - z}\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;\left(t + \left(\frac{x \cdot y}{z} + \frac{t \cdot a}{z}\right)\right) - \left(\frac{x \cdot a}{z} + \frac{y \cdot t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y - z}{a - z}}{\frac{1}{t - x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2021044 
(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)))))