Average Error: 2.0 → 1.9
Time: 4.4s
Precision: binary64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -7.6537366595487337 \cdot 10^{-284} \lor \neg \left(t \le 5.63678529066163735 \cdot 10^{-158}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(x \cdot \frac{z}{y} - x \cdot \frac{t}{y}\right)\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;t \le -7.6537366595487337 \cdot 10^{-284} \lor \neg \left(t \le 5.63678529066163735 \cdot 10^{-158}\right):\\
\;\;\;\;t + \frac{x}{y} \cdot \left(z - t\right)\\

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

\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 <= -7.653736659548734e-284) || !(t <= 5.636785290661637e-158))) {
		VAR = ((double) (t + ((double) (((double) (x / y)) * ((double) (z - t))))));
	} else {
		VAR = ((double) (t + ((double) (((double) (x * ((double) (z / y)))) - ((double) (x * ((double) (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

Original2.0
Target2.1
Herbie1.9
\[\begin{array}{l} \mathbf{if}\;z \lt 2.7594565545626922 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -7.6537366595487337e-284 or 5.63678529066163735e-158 < t

    1. Initial program 1.3

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

    if -7.6537366595487337e-284 < t < 5.63678529066163735e-158

    1. Initial program 5.2

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

    3. Applied sub-neg5.2

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

    4. Applied distribute-lft-in5.2

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

    5. Simplified7.6

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

    6. Simplified5.1

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

  4. Final simplification1.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -7.6537366595487337 \cdot 10^{-284} \lor \neg \left(t \le 5.63678529066163735 \cdot 10^{-158}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(x \cdot \frac{z}{y} - x \cdot \frac{t}{y}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020184 
(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))