Average Error: 6.0 → 1.5
Time: 3.7s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -4.0406959402694649 \cdot 10^{-191}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;t \le 4.7257167554002717 \cdot 10^{33}:\\ \;\;\;\;x + \frac{1}{\frac{t}{\left(y - x\right) \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y - x}{t}}{\frac{1}{z}}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -4.0406959402694649 \cdot 10^{-191}:\\
\;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\

\mathbf{elif}\;t \le 4.7257167554002717 \cdot 10^{33}:\\
\;\;\;\;x + \frac{1}{\frac{t}{\left(y - x\right) \cdot z}}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{\frac{y - x}{t}}{\frac{1}{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 ((t <= -4.040695940269465e-191)) {
		VAR = (x + ((y - x) / (t / z)));
	} else {
		double VAR_1;
		if ((t <= 4.7257167554002717e+33)) {
			VAR_1 = (x + (1.0 / (t / ((y - x) * z))));
		} else {
			VAR_1 = (x + (((y - x) / t) / (1.0 / z)));
		}
		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

Original6.0
Target2.1
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;x \lt -9.0255111955330046 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.2750321637007147 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -4.040695940269465e-191

    1. Initial program 6.3

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

    3. Applied associate-/l*1.4

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

    if -4.040695940269465e-191 < t < 4.7257167554002717e+33

    1. Initial program 2.0

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

    3. Applied clear-num2.1

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

    if 4.7257167554002717e+33 < t

    1. Initial program 9.2

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

    3. Applied associate-/l*1.4

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

    5. Applied div-inv1.4

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

    6. Applied associate-/r*1.1

      \[\leadsto x + \color{blue}{\frac{\frac{y - x}{t}}{\frac{1}{z}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -4.0406959402694649 \cdot 10^{-191}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;t \le 4.7257167554002717 \cdot 10^{33}:\\ \;\;\;\;x + \frac{1}{\frac{t}{\left(y - x\right) \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y - x}{t}}{\frac{1}{z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020105 
(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)))