Average Error: 12.8 → 1.6
Time: 2.4s
Precision: binary64
\[\frac{x \cdot \left(y + z\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y + z\right)}{z} \leq 9.178964882172369 \cdot 10^{-26} \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \leq 2.6136428524201943 \cdot 10^{+301}\right):\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ \end{array}\]
\frac{x \cdot \left(y + z\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(y + z\right)}{z} \leq 9.178964882172369 \cdot 10^{-26} \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \leq 2.6136428524201943 \cdot 10^{+301}\right):\\
\;\;\;\;\frac{x}{\frac{z}{y + z}}\\

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

\end{array}
(FPCore (x y z) :precision binary64 (/ (* x (+ y z)) z))
↓
(FPCore (x y z)
 :precision binary64
 (if (or (<= (/ (* x (+ y z)) z) 9.178964882172369e-26)
         (not (<= (/ (* x (+ y z)) z) 2.6136428524201943e+301)))
   (/ x (/ z (+ y z)))
   (/ (* x (+ y z)) z)))
double code(double x, double y, double z) {
	return (x * (y + z)) / z;
}
↓
double code(double x, double y, double z) {
	double tmp;
	if ((((x * (y + z)) / z) <= 9.178964882172369e-26) || !(((x * (y + z)) / z) <= 2.6136428524201943e+301)) {
		tmp = x / (z / (y + z));
	} else {
		tmp = (x * (y + z)) / z;
	}
	return tmp;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original12.8
Target3.1
Herbie1.6
\[\frac{x}{\frac{z}{y + z}}\]

Derivation

  1. Split input into 2 regimes

  2. if (/.f64 (*.f64 x (+.f64 y z)) z) < 9.1789648821723689e-26 or 2.6136428524201943e301 < (/.f64 (*.f64 x (+.f64 y z)) z)

    1. Initial program 16.5

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

    3. Applied associate-/l*_binary642.1

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

    if 9.1789648821723689e-26 < (/.f64 (*.f64 x (+.f64 y z)) z) < 2.6136428524201943e301

    1. Initial program 0.2

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

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y + z\right)}{z} \leq 9.178964882172369 \cdot 10^{-26} \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \leq 2.6136428524201943 \cdot 10^{+301}\right):\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020233 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:choose from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (/ x (/ z (+ y z)))

  (/ (* x (+ y z)) z))