Main:bigenough3 from C

Average Error: 29.5 → 0.2

Time: 8.4s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[\sqrt{x + 1} - \sqrt{x}\]

↓

\[\frac{1}{\sqrt{x + 1} + \sqrt{x}}\]

C

double f(double x) {
        double r382433 = x;
        double r382434 = 1.0;
        double r382435 = r382433 + r382434;
        double r382436 = sqrt(r382435);
        double r382437 = sqrt(r382433);
        double r382438 = r382436 - r382437;
        return r382438;
}

↓

double f(double x) {
        double r382439 = 1.0;
        double r382440 = x;
        double r382441 = r382440 + r382439;
        double r382442 = sqrt(r382441);
        double r382443 = sqrt(r382440);
        double r382444 = r382442 + r382443;
        double r382445 = r382439 / r382444;
        return r382445;
}

Error

Bits error versus x

Target

Original	29.5
Target	0.2
Herbie	0.2

\[\frac{1}{\sqrt{x + 1} + \sqrt{x}}\]

Derivation

1. Initial program 29.5

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

3. Applied flip-- 29.4

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

4. Simplified 0.2

   \[\leadsto \frac{\color{blue}{1}}{\sqrt{x + 1} + \sqrt{x}}\]

5. Final simplification 0.2

   \[\leadsto \frac{1}{\sqrt{x + 1} + \sqrt{x}}\]

Reproduce

herbie shell --seed 2020046 
(FPCore (x)
  :name "Main:bigenough3 from C"
  :precision binary64

  :herbie-target
  (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

  (- (sqrt (+ x 1)) (sqrt x)))