Average Error: 6.3 → 2.0
Time: 2.0s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -5.97785691526746104 \cdot 10^{41} \lor \neg \left(z \le 2.93242027125134076 \cdot 10^{-143}\right):\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{t}{\left(y - x\right) \cdot z}}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\begin{array}{l}
\mathbf{if}\;z \le -5.97785691526746104 \cdot 10^{41} \lor \neg \left(z \le 2.93242027125134076 \cdot 10^{-143}\right):\\
\;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{1}{\frac{t}{\left(y - x\right) \cdot z}}\\

\end{array}
double code(double x, double y, double z, double t) {
	return (x + (((y - x) * z) / t));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if (((z <= -5.977856915267461e+41) || !(z <= 2.9324202712513408e-143))) {
		VAR = (x + (z / (t / (y - x))));
	} else {
		VAR = (x + (1.0 / (t / ((y - x) * z))));
	}
	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
Target2.0
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;x \lt -9.0255111955330046 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.2750321637007147 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -5.977856915267461e+41 or 2.9324202712513408e-143 < z

    1. Initial program 12.0

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

    3. Applied *-commutative12.0

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

    4. Applied associate-/l*3.0

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

    if -5.977856915267461e+41 < z < 2.9324202712513408e-143

    1. Initial program 1.2

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

    3. Applied clear-num1.2

      \[\leadsto x + \color{blue}{\frac{1}{\frac{t}{\left(y - x\right) \cdot z}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -5.97785691526746104 \cdot 10^{41} \lor \neg \left(z \le 2.93242027125134076 \cdot 10^{-143}\right):\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{t}{\left(y - x\right) \cdot z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020078 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< x -9.025511195533005e-135) (- x (* (/ z t) (- x y))) (if (< x 4.275032163700715e-250) (+ x (* (/ (- y x) t) z)) (+ x (/ (- y x) (/ t z)))))

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