Average Error: 62.0 → 52.1
Time: 14.4s
Precision: binary64
Cost: 64
\[lo < -1 \cdot 10^{+308} \land hi > 10^{+308}\]
\[\frac{x - lo}{hi - lo}\]
↓
\[1\]
\frac{x - lo}{hi - lo}
↓
1
(FPCore (lo hi x) :precision binary64 (/ (- x lo) (- hi lo)))
↓
(FPCore (lo hi x) :precision binary64 1.0)
double code(double lo, double hi, double x) {
	return (x - lo) / (hi - lo);
}
↓
double code(double lo, double hi, double x) {
	return 1.0;
}

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
Alternative 1
Accuracy61.8
Cost192
\[\frac{x}{hi}\]
Alternative 2
Accuracy62.0
Cost1216
\[\sqrt{\frac{x}{hi - lo}} \cdot \sqrt{\frac{x}{hi - lo}} - \frac{lo}{hi - lo}\]

Derivation

  1. Initial program 62.0

    \[\frac{x - lo}{hi - lo}\]
  2. Using strategy rm

  3. Applied div-sub_binary64_110662.0

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

  4. Taylor expanded around 0 52.1

    \[\leadsto \color{blue}{1}\]

  5. Final simplification52.1

    \[\leadsto 1\]

Reproduce

herbie shell --seed 2020322 
(FPCore (lo hi x)
  :name "(/ (- x lo) (- hi lo))"
  :precision binary64
  :pre (and (< lo -1e+308) (> hi 1e+308))
  (/ (- x lo) (- hi lo)))