Average Error: 6.6 → 1.9
Time: 2.7s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -8.42343126196607538 \cdot 10^{-297} \lor \neg \left(x \le 2.5740473580443801 \cdot 10^{-180}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x \le -8.42343126196607538 \cdot 10^{-297} \lor \neg \left(x \le 2.5740473580443801 \cdot 10^{-180}\right):\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\

\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 <= -8.423431261966075e-297) || !(x <= 2.57404735804438e-180))) {
		VAR = ((double) (x + ((double) (((double) (y - x)) * ((double) (z / t))))));
	} else {
		VAR = ((double) (x + ((double) (z / ((double) (t / ((double) (y - x))))))));
	}
	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

Original6.6
Target2.1
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 < -8.423431261966075e-297 or 2.57404735804438e-180 < x

    1. Initial program 6.8

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

    3. Applied *-un-lft-identity6.8

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

    4. Applied times-frac1.4

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

    5. Simplified1.4

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

    if -8.423431261966075e-297 < x < 2.57404735804438e-180

    1. Initial program 5.2

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

    3. Applied *-commutative5.2

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

    4. Applied associate-/l*5.4

      \[\leadsto x + \color{blue}{\frac{z}{\frac{t}{y - x}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -8.42343126196607538 \cdot 10^{-297} \lor \neg \left(x \le 2.5740473580443801 \cdot 10^{-180}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020113 +o rules:numerics
(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)))