Average Error: 6.7 → 2.0
Time: 6.2s
Precision: binary64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.37836980272270247 \cdot 10^{107}:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \mathbf{elif}\;t \le 1.02575467142016984 \cdot 10^{74}:\\ \;\;\;\;x + \left(y \cdot \left(z - x\right)\right) \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -1.37836980272270247 \cdot 10^{107}:\\
\;\;\;\;x + y \cdot \frac{z - x}{t}\\

\mathbf{elif}\;t \le 1.02575467142016984 \cdot 10^{74}:\\
\;\;\;\;x + \left(y \cdot \left(z - x\right)\right) \cdot \frac{1}{t}\\

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

\end{array}
double code(double x, double y, double z, double t) {
	return ((double) (x + (((double) (y * ((double) (z - x)))) / t)));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if ((t <= -1.3783698027227025e+107)) {
		VAR = ((double) (x + ((double) (y * (((double) (z - x)) / t)))));
	} else {
		double VAR_1;
		if ((t <= 1.0257546714201698e+74)) {
			VAR_1 = ((double) (x + ((double) (((double) (y * ((double) (z - x)))) * (1.0 / t)))));
		} else {
			VAR_1 = ((double) (x + ((double) (((double) (z - x)) * (y / t)))));
		}
		VAR = VAR_1;
	}
	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

Original6.7
Target2.1
Herbie2.0
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 3 regimes

  2. if t < -1.37836980272270247e107

    1. Initial program 12.5

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

    3. Applied *-un-lft-identity12.5

      \[\leadsto x + \frac{y \cdot \left(z - x\right)}{\color{blue}{1 \cdot t}}\]

    4. Applied times-frac1.3

      \[\leadsto x + \color{blue}{\frac{y}{1} \cdot \frac{z - x}{t}}\]

    5. Simplified1.3

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

    if -1.37836980272270247e107 < t < 1.02575467142016984e74

    1. Initial program 2.5

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

    3. Applied div-inv2.5

      \[\leadsto x + \color{blue}{\left(y \cdot \left(z - x\right)\right) \cdot \frac{1}{t}}\]

    if 1.02575467142016984e74 < t

    1. Initial program 10.7

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

    2. Taylor expanded around 0 10.7

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

    3. Simplified1.5

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

  4. Final simplification2.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.37836980272270247 \cdot 10^{107}:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \mathbf{elif}\;t \le 1.02575467142016984 \cdot 10^{74}:\\ \;\;\;\;x + \left(y \cdot \left(z - x\right)\right) \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020182 
(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)))