Average Error: 0.2 → 0.0
Time: 11.7s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[\frac{x - 1}{4 \cdot \sqrt{x} + \left(x + 1\right)} \cdot 6\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
\frac{x - 1}{4 \cdot \sqrt{x} + \left(x + 1\right)} \cdot 6
double f(double x) {
        double r43522373 = 6.0;
        double r43522374 = x;
        double r43522375 = 1.0;
        double r43522376 = r43522374 - r43522375;
        double r43522377 = r43522373 * r43522376;
        double r43522378 = r43522374 + r43522375;
        double r43522379 = 4.0;
        double r43522380 = sqrt(r43522374);
        double r43522381 = r43522379 * r43522380;
        double r43522382 = r43522378 + r43522381;
        double r43522383 = r43522377 / r43522382;
        return r43522383;
}
↓
double f(double x) {
        double r43522384 = x;
        double r43522385 = 1.0;
        double r43522386 = r43522384 - r43522385;
        double r43522387 = 4.0;
        double r43522388 = sqrt(r43522384);
        double r43522389 = r43522387 * r43522388;
        double r43522390 = r43522384 + r43522385;
        double r43522391 = r43522389 + r43522390;
        double r43522392 = r43522386 / r43522391;
        double r43522393 = 6.0;
        double r43522394 = r43522392 * r43522393;
        return r43522394;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Target

Original0.2
Target0.1
Herbie0.0
\[\frac{6}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}\]

Derivation

  1. Initial program 0.2

    \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.2

    \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{1 \cdot \left(\left(x + 1\right) + 4 \cdot \sqrt{x}\right)}}\]

  4. Applied times-frac0.0

    \[\leadsto \color{blue}{\frac{6}{1} \cdot \frac{x - 1}{\left(x + 1\right) + 4 \cdot \sqrt{x}}}\]

  5. Simplified0.0

    \[\leadsto \color{blue}{6} \cdot \frac{x - 1}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]

  6. Final simplification0.0

    \[\leadsto \frac{x - 1}{4 \cdot \sqrt{x} + \left(x + 1\right)} \cdot 6\]

Reproduce

herbie shell --seed 2019172 
(FPCore (x)
  :name "Data.Approximate.Numerics:blog from approximate-0.2.2.1"

  :herbie-target
  (/ 6.0 (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0)))

  (/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x)))))