Average Error: 6.7 → 1.0
Time: 3.6s
Precision: binary64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq -1.8115265265078395 \cdot 10^{+291}:\\ \;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq 4.111794403446377 \cdot 10^{+305}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq -1.8115265265078395 \cdot 10^{+291}:\\
\;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\

\mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq 4.111794403446377 \cdot 10^{+305}:\\
\;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\

\mathbf{else}:\\
\;\;\;\;x + y \cdot \frac{z - x}{t}\\

\end{array}
(FPCore (x y z t) :precision binary64 (+ x (/ (* y (- z x)) t)))
↓
(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x (/ (* y (- z x)) t)) -1.8115265265078395e+291)
   (+ x (* (- z x) (/ y t)))
   (if (<= (+ x (/ (* y (- z x)) t)) 4.111794403446377e+305)
     (+ x (/ (* y (- z x)) t))
     (+ x (* y (/ (- z x) t))))))
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 tmp;
	if ((((double) (x + (((double) (y * ((double) (z - x)))) / t))) <= -1.8115265265078395e+291)) {
		tmp = ((double) (x + ((double) (((double) (z - x)) * (y / t)))));
	} else {
		double tmp_1;
		if ((((double) (x + (((double) (y * ((double) (z - x)))) / t))) <= 4.111794403446377e+305)) {
			tmp_1 = ((double) (x + (((double) (y * ((double) (z - x)))) / t)));
		} else {
			tmp_1 = ((double) (x + ((double) (y * (((double) (z - x)) / t)))));
		}
		tmp = tmp_1;
	}
	return tmp;
}

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
Target2.0
Herbie1.0
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 3 regimes

  2. if (+ x (/ (* y (- z x)) t)) < -1.8115265265078395e291

    1. Initial program Error: 47.1 bits

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

    2. SimplifiedError: 5.6 bits

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

    4. Applied clear-numError: 5.7 bits

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{t}{z - x}}}\]
    5. Using strategy rm

    6. Applied associate-/r/Error: 5.7 bits

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

    7. Applied associate-*r*Error: 2.0 bits

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

    8. SimplifiedError: 1.9 bits

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

    if -1.8115265265078395e291 < (+ x (/ (* y (- z x)) t)) < 4.11179440344637724e305

    1. Initial program Error: 1.0 bits

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

    if 4.11179440344637724e305 < (+ x (/ (* y (- z x)) t))

    1. Initial program Error: 60.4 bits

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

    2. SimplifiedError: 1.3 bits

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

  4. Final simplificationError: 1.0 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq -1.8115265265078395 \cdot 10^{+291}:\\ \;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq 4.111794403446377 \cdot 10^{+305}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020203 
(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)))