Average Error: 2.1 → 1.2
Time: 3.9s
Precision: binary64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.752278609399082 \cdot 10^{+207} \lor \neg \left(\frac{x}{y} \leq -2.507387929897188 \cdot 10^{-152}\right) \land \frac{x}{y} \leq 0:\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot \left(z - t\right)\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;\frac{x}{y} \leq -2.752278609399082 \cdot 10^{+207} \lor \neg \left(\frac{x}{y} \leq -2.507387929897188 \cdot 10^{-152}\right) \land \frac{x}{y} \leq 0:\\
\;\;\;\;t + x \cdot \frac{z - t}{y}\\

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

\end{array}
double code(double x, double y, double z, double t) {
	return ((double) (((double) ((x / y) * ((double) (z - t)))) + t));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if ((((x / y) <= -2.752278609399082e+207) || (!((x / y) <= -2.507387929897188e-152) && ((x / y) <= 0.0)))) {
		VAR = ((double) (t + ((double) (x * (((double) (z - t)) / y)))));
	} else {
		VAR = ((double) (t + ((double) ((x / y) * ((double) (z - t))))));
	}
	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

Original2.1
Target2.4
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;z < 2.759456554562692 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z < 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ x y) < -2.7522786093990821e207 or -2.5073879298971879e-152 < (/ x y) < 0.0

    1. Initial program Error: 3.8 bits

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

    2. SimplifiedError: 0.8 bits

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

    if -2.7522786093990821e207 < (/ x y) < -2.5073879298971879e-152 or 0.0 < (/ x y)

    1. Initial program Error: 1.3 bits

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

  4. Final simplificationError: 1.2 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.752278609399082 \cdot 10^{+207} \lor \neg \left(\frac{x}{y} \leq -2.507387929897188 \cdot 10^{-152}\right) \land \frac{x}{y} \leq 0:\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot \left(z - t\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020200 
(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))