Main:bigenough3 from C

Average Error: 29.5 → 0.2

Time: 6.8s

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 r657747 = x;
        double r657748 = 1.0;
        double r657749 = r657747 + r657748;
        double r657750 = sqrt(r657749);
        double r657751 = sqrt(r657747);
        double r657752 = r657750 - r657751;
        return r657752;
}

↓

double f(double x) {
        double r657753 = 1.0;
        double r657754 = x;
        double r657755 = r657754 + r657753;
        double r657756 = sqrt(r657755);
        double r657757 = sqrt(r657754);
        double r657758 = r657756 + r657757;
        double r657759 = r657753 / r657758;
        return r657759;
}

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

   \[\leadsto \frac{\color{blue}{0 + 1}}{\sqrt{x + 1} + \sqrt{x}}\]

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)))