Average Error: 14.6 → 10.7
Time: 5.1s
Precision: binary64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \leq -3.0798685194927104 \cdot 10^{-74} \lor \neg \left(a \leq 2.710508130171763 \cdot 10^{-285}\right):\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t + \frac{x \cdot y}{z}\right) - \frac{y \cdot t}{z}\\ \end{array}\]
x + \left(y - z\right) \cdot \frac{t - x}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;a \leq -3.0798685194927104 \cdot 10^{-74} \lor \neg \left(a \leq 2.710508130171763 \cdot 10^{-285}\right):\\
\;\;\;\;x + \frac{y - z}{a - z} \cdot \left(t - x\right)\\

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

\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 (<= a -3.0798685194927104e-74) (not (<= a 2.710508130171763e-285)))
   (+ x (* (/ (- y z) (- a z)) (- t x)))
   (- (+ t (/ (* x y) 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 ((a <= -3.0798685194927104e-74) || !(a <= 2.710508130171763e-285)) {
		tmp = x + (((y - z) / (a - z)) * (t - x));
	} else {
		tmp = (t + ((x * y) / 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 a < -3.0798685194927104e-74 or 2.71050813017176306e-285 < a

    1. Initial program 12.4

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

    3. Applied clear-num_binary6412.7

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

    5. Applied associate-/r/_binary6412.5

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

    6. Applied associate-*r*_binary649.6

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

    7. Simplified9.5

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

    if -3.0798685194927104e-74 < a < 2.71050813017176306e-285

    1. Initial program 23.9

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

    3. Applied add-cube-cbrt_binary6424.6

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

    4. Applied add-cube-cbrt_binary6424.8

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

    5. Applied times-frac_binary6424.8

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

    6. Applied associate-*r*_binary6420.0

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

    7. Taylor expanded around inf 15.7

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

    8. Simplified15.7

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

  4. Final simplification10.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.0798685194927104 \cdot 10^{-74} \lor \neg \left(a \leq 2.710508130171763 \cdot 10^{-285}\right):\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t + \frac{x \cdot y}{z}\right) - \frac{y \cdot t}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020220 
(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)))))