Average Error: 6.8 → 0.9
Time: 3.1s
Precision: binary64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} \leq -\infty:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \leq 1.6545753478282346 \cdot 10^{+281}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} \leq -\infty:\\
\;\;\;\;x + z \cdot \frac{y - x}{t}\\

\mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \leq 1.6545753478282346 \cdot 10^{+281}:\\
\;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\

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

\end{array}
double code(double x, double y, double z, double t) {
	return ((double) (x + (((double) (((double) (y - x)) * z)) / t)));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if ((((double) (x + (((double) (((double) (y - x)) * z)) / t))) <= ((double) -(((double) INFINITY))))) {
		VAR = ((double) (x + ((double) (z * (((double) (y - x)) / t)))));
	} else {
		double VAR_1;
		if ((((double) (x + (((double) (((double) (y - x)) * z)) / t))) <= 1.6545753478282346e+281)) {
			VAR_1 = ((double) (x + (((double) (((double) (y - x)) * z)) / t)));
		} else {
			VAR_1 = ((double) (x + ((double) (((double) (y - x)) * (z / 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

Original6.8
Target2.1
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;x < -9.025511195533005 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x < 4.275032163700715 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (+ x (/ (* (- y x) z) t)) < -inf.0

    1. Initial program 64.0

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

    3. Applied associate-/l*0.2

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

    5. Applied associate-/r/0.2

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

    if -inf.0 < (+ x (/ (* (- y x) z) t)) < 1.6545753478282346e281

    1. Initial program 0.9

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

    if 1.6545753478282346e281 < (+ x (/ (* (- y x) z) t))

    1. Initial program 42.3

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

    2. Simplified1.7

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} \leq -\infty:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \leq 1.6545753478282346 \cdot 10^{+281}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020196 
(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)))