Average Error: 0.2 → 0.0
Time: 14.1s
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 r44363378 = 6.0;
        double r44363379 = x;
        double r44363380 = 1.0;
        double r44363381 = r44363379 - r44363380;
        double r44363382 = r44363378 * r44363381;
        double r44363383 = r44363379 + r44363380;
        double r44363384 = 4.0;
        double r44363385 = sqrt(r44363379);
        double r44363386 = r44363384 * r44363385;
        double r44363387 = r44363383 + r44363386;
        double r44363388 = r44363382 / r44363387;
        return r44363388;
}
↓
double f(double x) {
        double r44363389 = x;
        double r44363390 = 1.0;
        double r44363391 = r44363389 - r44363390;
        double r44363392 = 4.0;
        double r44363393 = sqrt(r44363389);
        double r44363394 = r44363392 * r44363393;
        double r44363395 = r44363389 + r44363390;
        double r44363396 = r44363394 + r44363395;
        double r44363397 = r44363391 / r44363396;
        double r44363398 = 6.0;
        double r44363399 = r44363397 * r44363398;
        return r44363399;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

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 2019170 
(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)))))