Average Error: 6.3 → 1.6
Time: 2.3s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \le -1.26141673842760905 \cdot 10^{-149} \lor \neg \left(x + \frac{y \cdot \left(z - x\right)}{t} \le 1.2752422669114295 \cdot 10^{297}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \le -1.26141673842760905 \cdot 10^{-149} \lor \neg \left(x + \frac{y \cdot \left(z - x\right)}{t} \le 1.2752422669114295 \cdot 10^{297}\right):\\
\;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)\\

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

\end{array}
double code(double x, double y, double z, double t) {
	return (x + ((y * (z - x)) / t));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if ((((x + ((y * (z - x)) / t)) <= -1.261416738427609e-149) || !((x + ((y * (z - x)) / t)) <= 1.2752422669114295e+297))) {
		VAR = fma((y / t), (z - x), x);
	} else {
		VAR = (x + ((y * (z - x)) / 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

Original6.3
Target2.1
Herbie1.6
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 2 regimes

  2. if (+ x (/ (* y (- z x)) t)) < -1.261416738427609e-149 or 1.2752422669114295e+297 < (+ x (/ (* y (- z x)) t))

    1. Initial program 11.6

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

    2. Simplified1.9

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

    if -1.261416738427609e-149 < (+ x (/ (* y (- z x)) t)) < 1.2752422669114295e+297

    1. Initial program 1.2

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

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \le -1.26141673842760905 \cdot 10^{-149} \lor \neg \left(x + \frac{y \cdot \left(z - x\right)}{t} \le 1.2752422669114295 \cdot 10^{297}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020079 +o rules:numerics
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

  :herbie-target
  (- x (+ (* x (/ y t)) (* (- z) (/ y t))))

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