Average Error: 6.5 → 1.9
Time: 2.3s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -2.08446208910259936 \cdot 10^{-124} \lor \neg \left(x \le 1.1914003718802801 \cdot 10^{-199}\right):\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y - x\right) \cdot z\right) \cdot \frac{1}{t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x \le -2.08446208910259936 \cdot 10^{-124} \lor \neg \left(x \le 1.1914003718802801 \cdot 10^{-199}\right):\\
\;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\

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

\end{array}
double code(double x, double y, double z, double t) {
	return ((double) (x + ((double) (((double) (((double) (y - x)) * z)) / t))));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if (((x <= -2.0844620891025994e-124) || !(x <= 1.19140037188028e-199))) {
		VAR = ((double) (x + ((double) (((double) (y - x)) / ((double) (t / z))))));
	} else {
		VAR = ((double) (x + ((double) (((double) (((double) (y - x)) * z)) * ((double) (1.0 / 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

Original6.5
Target2.3
Herbie1.9
\[\begin{array}{l} \mathbf{if}\;x \lt -9.0255111955330046 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.2750321637007147 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -2.0844620891025994e-124 or 1.19140037188028e-199 < x

    1. Initial program 7.1

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

    3. Applied associate-/l*1.0

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

    if -2.0844620891025994e-124 < x < 1.19140037188028e-199

    1. Initial program 4.5

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

    3. Applied div-inv4.6

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

  4. Final simplification1.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -2.08446208910259936 \cdot 10^{-124} \lor \neg \left(x \le 1.1914003718802801 \cdot 10^{-199}\right):\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y - x\right) \cdot z\right) \cdot \frac{1}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020130 
(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)))