Average Error: 32.1 → 0
Time: 2.6s
Precision: binary64
\[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x} \]
↓
\[\begin{array}{l} \mathbf{if}\;x \leq 1.30521497135303 \cdot 10^{-310}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]
\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}
↓
\begin{array}{l}
\mathbf{if}\;x \leq 1.30521497135303 \cdot 10^{-310}:\\
\;\;\;\;2\\

\mathbf{else}:\\
\;\;\;\;0\\


\end{array}

(FPCore (x) :precision binary64 (- (/ x x) (* (/ 1.0 x) (sqrt (* x x)))))
↓
(FPCore (x) :precision binary64 (if (<= x 1.30521497135303e-310) 2.0 0.0))
double code(double x) {
	return (x / x) - ((1.0 / x) * sqrt((x * x)));
}
↓
double code(double x) {
	double tmp;
	if (x <= 1.30521497135303e-310) {
		tmp = 2.0;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.1
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x < 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

Derivation

  1. Split input into 2 regimes

  2. if x < 1.305214971353029e-310

    1. Initial program 27.9

      \[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x} \]

    2. Taylor expanded in x around -inf 0

      \[\leadsto \color{blue}{2} \]

    if 1.305214971353029e-310 < x

    1. Initial program 36.5

      \[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x} \]

    2. Taylor expanded in x around 0 0

      \[\leadsto \color{blue}{0} \]
  3. Recombined 2 regimes into one program.

  4. Final simplification0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.30521497135303 \cdot 10^{-310}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

Reproduce

herbie shell --seed 2022129 
(FPCore (x)
  :name "sqrt sqr"
  :precision binary64

  :herbie-target
  (if (< x 0.0) 2.0 0.0)

  (- (/ x x) (* (/ 1.0 x) (sqrt (* x x)))))