Average Error: 15.1 → 11.7
Time: 5.0s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -8.7908458686707122 \cdot 10^{144}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{x}{z} - \frac{t}{z}, t\right)\\ \mathbf{elif}\;z \le -4.0528384344896528 \cdot 10^{-143}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \left(t - x\right) \cdot \frac{1}{a - z}, x\right)\\ \mathbf{elif}\;z \le -2.42842816428938809 \cdot 10^{-304}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \le 3.64013298540895573 \cdot 10^{143}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{1}{\frac{a - z}{t - x}}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{x}{z} - \frac{t}{z}, t\right)\\ \end{array}\]
x + \left(y - z\right) \cdot \frac{t - x}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -8.7908458686707122 \cdot 10^{144}:\\
\;\;\;\;\mathsf{fma}\left(y, \frac{x}{z} - \frac{t}{z}, t\right)\\

\mathbf{elif}\;z \le -4.0528384344896528 \cdot 10^{-143}:\\
\;\;\;\;\mathsf{fma}\left(y - z, \left(t - x\right) \cdot \frac{1}{a - z}, x\right)\\

\mathbf{elif}\;z \le -2.42842816428938809 \cdot 10^{-304}:\\
\;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\

\mathbf{elif}\;z \le 3.64013298540895573 \cdot 10^{143}:\\
\;\;\;\;\mathsf{fma}\left(y - z, \frac{1}{\frac{a - z}{t - x}}, x\right)\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(y, \frac{x}{z} - \frac{t}{z}, t\right)\\

\end{array}
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 VAR;
	if ((z <= -8.790845868670712e+144)) {
		VAR = fma(y, ((x / z) - (t / z)), t);
	} else {
		double VAR_1;
		if ((z <= -4.052838434489653e-143)) {
			VAR_1 = fma((y - z), ((t - x) * (1.0 / (a - z))), x);
		} else {
			double VAR_2;
			if ((z <= -2.428428164289388e-304)) {
				VAR_2 = (x + (((y - z) * (t - x)) / (a - z)));
			} else {
				double VAR_3;
				if ((z <= 3.6401329854089557e+143)) {
					VAR_3 = fma((y - z), (1.0 / ((a - z) / (t - x))), x);
				} else {
					VAR_3 = fma(y, ((x / z) - (t / z)), t);
				}
				VAR_2 = VAR_3;
			}
			VAR_1 = VAR_2;
		}
		VAR = VAR_1;
	}
	return VAR;
}

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 4 regimes

  2. if z < -8.790845868670712e+144 or 3.6401329854089557e+143 < z

    1. Initial program 28.0

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

    2. Simplified27.9

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)}\]

    3. Taylor expanded around inf 25.7

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

    4. Simplified16.9

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{x}{z} - \frac{t}{z}, t\right)}\]

    if -8.790845868670712e+144 < z < -4.052838434489653e-143

    1. Initial program 10.9

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

    2. Simplified10.9

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)}\]
    3. Using strategy rm

    4. Applied div-inv10.9

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

    if -4.052838434489653e-143 < z < -2.428428164289388e-304

    1. Initial program 7.2

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

    3. Applied associate-*r/6.5

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

    if -2.428428164289388e-304 < z < 3.6401329854089557e+143

    1. Initial program 9.1

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

    2. Simplified9.1

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)}\]
    3. Using strategy rm

    4. Applied clear-num9.2

      \[\leadsto \mathsf{fma}\left(y - z, \color{blue}{\frac{1}{\frac{a - z}{t - x}}}, x\right)\]
  3. Recombined 4 regimes into one program.

  4. Final simplification11.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -8.7908458686707122 \cdot 10^{144}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{x}{z} - \frac{t}{z}, t\right)\\ \mathbf{elif}\;z \le -4.0528384344896528 \cdot 10^{-143}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \left(t - x\right) \cdot \frac{1}{a - z}, x\right)\\ \mathbf{elif}\;z \le -2.42842816428938809 \cdot 10^{-304}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \le 3.64013298540895573 \cdot 10^{143}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{1}{\frac{a - z}{t - x}}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{x}{z} - \frac{t}{z}, t\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020105 +o rules:numerics
(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)))))