Average Error: 6.2 → 1.5
Time: 7.2s
Precision: binary64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -inf.0 \lor \neg \left(x + \frac{\left(y - x\right) \cdot z}{t} \le -6.0541859188204124 \cdot 10^{-204}\right):\\ \;\;\;\;x + \frac{1}{\frac{\frac{t}{z}}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -inf.0 \lor \neg \left(x + \frac{\left(y - x\right) \cdot z}{t} \le -6.0541859188204124 \cdot 10^{-204}\right):\\
\;\;\;\;x + \frac{1}{\frac{\frac{t}{z}}{y - x}}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{\left(y - x\right) \cdot z}{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 (((((double) (x + ((double) (((double) (((double) (y - x)) * z)) / t)))) <= -inf.0) || !(((double) (x + ((double) (((double) (((double) (y - x)) * z)) / t)))) <= -6.0541859188204124e-204))) {
		VAR = ((double) (x + ((double) (1.0 / ((double) (((double) (t / z)) / ((double) (y - x))))))));
	} else {
		VAR = ((double) (x + ((double) (((double) (((double) (y - x)) * z)) / 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

Original6.2
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 2 regimes

  2. if (+ x (/ (* (- y x) z) t)) < -inf.0 or -6.0541859188204124e-204 < (+ x (/ (* (- y x) z) t))

    1. Initial program 10.4

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

    3. Applied associate-/l*2.2

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

    5. Applied clear-num2.3

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

    if -inf.0 < (+ x (/ (* (- y x) z) t)) < -6.0541859188204124e-204

    1. Initial program 0.4

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -inf.0 \lor \neg \left(x + \frac{\left(y - x\right) \cdot z}{t} \le -6.0541859188204124 \cdot 10^{-204}\right):\\ \;\;\;\;x + \frac{1}{\frac{\frac{t}{z}}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020162 
(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)))