Average Error: 6.3 → 1.8
Time: 2.9s
Precision: binary64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -8.7772396722328355 \cdot 10^{103}:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - x\right)\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;y \le -8.7772396722328355 \cdot 10^{103}:\\
\;\;\;\;x + y \cdot \frac{z - x}{t}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y}{t} \cdot \left(z - x\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 ((y <= -8.777239672232835e+103)) {
		VAR = ((double) (x + ((double) (y * ((double) (((double) (z - x)) / t))))));
	} else {
		VAR = ((double) (x + ((double) (((double) (y / t)) * ((double) (z - x))))));
	}
	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
Target2.2
Herbie1.8
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 2 regimes

  2. if y < -8.7772396722328355e103

    1. Initial program 21.9

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

    3. Applied *-un-lft-identity21.9

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

    4. Applied times-frac2.5

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

    5. Simplified2.5

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

    if -8.7772396722328355e103 < y

    1. Initial program 4.5

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

    3. Applied associate-/l*6.1

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

    5. Applied associate-/r/1.8

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

  4. Final simplification1.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -8.7772396722328355 \cdot 10^{103}:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(z - x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020155 
(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)))