Average Error: 0.5 → 0.5
Time: 2.0s
Precision: binary64
\[\sqrt{x - 1} \cdot \sqrt{x}\]
↓
\[\sqrt{\sqrt{x - 1} \cdot \sqrt{x}} \cdot \sqrt{\sqrt{x - 1} \cdot \sqrt{x}}\]
\sqrt{x - 1} \cdot \sqrt{x}
↓
\sqrt{\sqrt{x - 1} \cdot \sqrt{x}} \cdot \sqrt{\sqrt{x - 1} \cdot \sqrt{x}}
double code(double x) {
	return ((double) (((double) sqrt(((double) (x - 1.0)))) * ((double) sqrt(x))));
}
↓
double code(double x) {
	return ((double) (((double) sqrt(((double) (((double) sqrt(((double) (x - 1.0)))) * ((double) sqrt(x)))))) * ((double) sqrt(((double) (((double) sqrt(((double) (x - 1.0)))) * ((double) sqrt(x))))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.5

    \[\sqrt{x - 1} \cdot \sqrt{x}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.5

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

  4. Final simplification0.5

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

Reproduce

herbie shell --seed 2020181 
(FPCore (x)
  :name "sqrt times"
  :precision binary64
  (* (sqrt (- x 1.0)) (sqrt x)))