Average Error: 6.6 → 1.4
Time: 5.1s
Precision: binary64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -7.23814913016066766 \cdot 10^{-187} \lor \neg \left(t \le 4.6301998635488511 \cdot 10^{-29}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z \cdot y}{t} - \frac{x \cdot y}{t}\right)\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -7.23814913016066766 \cdot 10^{-187} \lor \neg \left(t \le 4.6301998635488511 \cdot 10^{-29}\right):\\
\;\;\;\;x + \frac{y}{t} \cdot \left(z - x\right)\\

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

\end{array}
double code(double x, double y, double z, double t) {
	return ((double) (x + ((double) (((double) (y * ((double) (z - x)))) / t))));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if (((t <= -7.238149130160668e-187) || !(t <= 4.630199863548851e-29))) {
		VAR = ((double) (x + ((double) (((double) (y / t)) * ((double) (z - x))))));
	} else {
		VAR = ((double) (x + ((double) (((double) (((double) (z * y)) / t)) - ((double) (((double) (x * y)) / 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

Original6.6
Target2.1
Herbie1.4
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 2 regimes

  2. if t < -7.23814913016066766e-187 or 4.6301998635488511e-29 < t

    1. Initial program 7.8

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

    3. Applied associate-/l*2.8

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

    5. Applied associate-/r/1.1

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

    if -7.23814913016066766e-187 < t < 4.6301998635488511e-29

    1. Initial program 2.4

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

    3. Applied associate-/l*17.6

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

    4. Taylor expanded around 0 2.4

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

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -7.23814913016066766 \cdot 10^{-187} \lor \neg \left(t \le 4.6301998635488511 \cdot 10^{-29}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z \cdot y}{t} - \frac{x \cdot y}{t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020174 
(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)) (* (neg z) (/ y t))))

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