Average Error: 31.6 → 18.6
Time: 1.4s
Precision: binary64
\[\sqrt{x \cdot x + y \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \leq -2.2647948816248014 \cdot 10^{+66}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 3.285560521583026 \cdot 10^{+62}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]
\sqrt{x \cdot x + y \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;x \leq -2.2647948816248014 \cdot 10^{+66}:\\
\;\;\;\;-x\\

\mathbf{elif}\;x \leq 3.285560521583026 \cdot 10^{+62}:\\
\;\;\;\;\sqrt{x \cdot x + y \cdot y}\\

\mathbf{else}:\\
\;\;\;\;x\\

\end{array}
(FPCore (x y) :precision binary64 (sqrt (+ (* x x) (* y y))))
↓
(FPCore (x y)
 :precision binary64
 (if (<= x -2.2647948816248014e+66)
   (- x)
   (if (<= x 3.285560521583026e+62) (sqrt (+ (* x x) (* y y))) x)))
double code(double x, double y) {
	return sqrt((x * x) + (y * y));
}
↓
double code(double x, double y) {
	double tmp;
	if (x <= -2.2647948816248014e+66) {
		tmp = -x;
	} else if (x <= 3.285560521583026e+62) {
		tmp = sqrt((x * x) + (y * y));
	} else {
		tmp = x;
	}
	return tmp;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original31.6
Target18.3
Herbie18.6
\[\begin{array}{l} \mathbf{if}\;x < -1.1236950826599826 \cdot 10^{+145}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x < 1.116557621183362 \cdot 10^{+93}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if x < -2.26479488162480145e66

    1. Initial program 45.5

      \[\sqrt{x \cdot x + y \cdot y}\]

    2. Taylor expanded around -inf 13.0

      \[\leadsto \color{blue}{-1 \cdot x}\]

    3. Simplified13.0

      \[\leadsto \color{blue}{-x}\]

    if -2.26479488162480145e66 < x < 3.28556052158302614e62

    1. Initial program 22.4

      \[\sqrt{x \cdot x + y \cdot y}\]

    if 3.28556052158302614e62 < x

    1. Initial program 45.9

      \[\sqrt{x \cdot x + y \cdot y}\]

    2. Taylor expanded around inf 12.5

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

  4. Final simplification18.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2647948816248014 \cdot 10^{+66}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 3.285560521583026 \cdot 10^{+62}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Reproduce

herbie shell --seed 2020219 
(FPCore (x y)
  :name "Data.Octree.Internal:octantDistance  from Octree-0.5.4.2"
  :precision binary64

  :herbie-target
  (if (< x -1.1236950826599826e+145) (- x) (if (< x 1.116557621183362e+93) (sqrt (+ (* x x) (* y y))) x))

  (sqrt (+ (* x x) (* y y))))