Average Error: 1.9 → 1.5
Time: 3.1s
Precision: binary64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \le -1.8030915408536723 \cdot 10^{-221} \lor \neg \left(\frac{x}{y} \le 0.0\right):\\ \;\;\;\;t + \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \left(\frac{z}{y} - \frac{t}{y}\right)\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;\frac{x}{y} \le -1.8030915408536723 \cdot 10^{-221} \lor \neg \left(\frac{x}{y} \le 0.0\right):\\
\;\;\;\;t + \frac{x}{y} \cdot \left(z - t\right)\\

\mathbf{else}:\\
\;\;\;\;t + x \cdot \left(\frac{z}{y} - \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 (((((double) (x / y)) <= -1.8030915408536723e-221) || !(((double) (x / y)) <= 0.0))) {
		VAR = ((double) (t + ((double) (((double) (x / y)) * ((double) (z - t))))));
	} else {
		VAR = ((double) (t + ((double) (x * ((double) (((double) (z / y)) - ((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

Original1.9
Target2.3
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;z \lt 2.7594565545626922 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ x y) < -1.8030915408536723e-221 or 0.0 < (/ x y)

    1. Initial program 1.8

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

    if -1.8030915408536723e-221 < (/ x y) < 0.0

    1. Initial program 2.4

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

    2. Simplified0.2

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

    4. Applied div-sub0.2

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \le -1.8030915408536723 \cdot 10^{-221} \lor \neg \left(\frac{x}{y} \le 0.0\right):\\ \;\;\;\;t + \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \left(\frac{z}{y} - \frac{t}{y}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020185 
(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))