Average Error: 62.0 → 52.0
Time: 41.7s
Precision: binary64
Cost: 256
\[lo < -1 \cdot 10^{+308} \land hi > 10^{+308}\]
\[\frac{x - lo}{hi - lo}\]
↓
\[\frac{lo}{-hi}\]
\frac{x - lo}{hi - lo}
↓
\frac{lo}{-hi}
(FPCore (lo hi x) :precision binary64 (/ (- x lo) (- hi lo)))
↓
(FPCore (lo hi x) :precision binary64 (/ lo (- hi)))
double code(double lo, double hi, double x) {
	return (x - lo) / (hi - lo);
}
↓
double code(double lo, double hi, double x) {
	return lo / -hi;
}

Error

Bits error versus lo

Bits error versus hi

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error52.0
Cost64
\[1\]

Error

Time

Derivation

  1. Initial program 62.0

    \[\frac{x - lo}{hi - lo}\]

  2. Taylor expanded around inf 52.0

    \[\leadsto \color{blue}{\frac{x - lo}{hi}}\]
  3. Using strategy rm

  4. Applied frac-2neg_binary64_111252.0

    \[\leadsto \color{blue}{\frac{-\left(x - lo\right)}{-hi}}\]

  5. Simplified52.0

    \[\leadsto \frac{\color{blue}{lo - x}}{-hi}\]

  6. Taylor expanded around inf 52.0

    \[\leadsto \color{blue}{-1 \cdot \frac{lo}{hi}}\]

  7. Simplified52.0

    \[\leadsto \color{blue}{\frac{lo}{-hi}}\]

  8. Simplified52.0

    \[\leadsto \color{blue}{\frac{lo}{-hi}}\]

  9. Final simplification52.0

    \[\leadsto \frac{lo}{-hi}\]

Reproduce

herbie shell --seed 2021065 
(FPCore (lo hi x)
  :name "(/ (- x lo) (- hi lo))"
  :precision binary64
  :pre (and (< lo -1e+308) (> hi 1e+308))
  (/ (- x lo) (- hi lo)))