Average Error: 2.4 → 2.2
Time: 3.0s
Precision: binary64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -2.0876292205169267 \cdot 10^{-89} \lor \neg \left(t \le 2.60782739113596551 \cdot 10^{-194}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot \left(z - t\right)}{y}\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;t \le -2.0876292205169267 \cdot 10^{-89} \lor \neg \left(t \le 2.60782739113596551 \cdot 10^{-194}\right):\\
\;\;\;\;t + \frac{x}{y} \cdot \left(z - t\right)\\

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

\end{array}
double code(double x, double y, double z, double t) {
	return ((double) (((double) (((double) (x / y)) * ((double) (z - t)))) + t));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if (((t <= -2.0876292205169267e-89) || !(t <= 2.6078273911359655e-194))) {
		VAR = ((double) (t + ((double) (((double) (x / y)) * ((double) (z - t))))));
	} else {
		VAR = ((double) (t + ((double) (((double) (x * ((double) (z - t)))) / y))));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original2.4
Target2.5
Herbie2.2
\[\begin{array}{l} \mathbf{if}\;z \lt 2.7594565545626922 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -2.0876292205169267e-89 or 2.60782739113596551e-194 < t

    1. Initial program 1.1

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

    if -2.0876292205169267e-89 < t < 2.60782739113596551e-194

    1. Initial program 5.4

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

    3. Applied associate-*l/4.8

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

  4. Final simplification2.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -2.0876292205169267 \cdot 10^{-89} \lor \neg \left(t \le 2.60782739113596551 \cdot 10^{-194}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot \left(z - t\right)}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020179 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (if (< z 2.759456554562692e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

  (+ (* (/ x y) (- z t)) t))