Average Error: 0.2 → 0.0
Time: 11.7s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[\frac{x - 1}{\left(x + 1\right) + \sqrt{x} \cdot 4} \cdot 6\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
\frac{x - 1}{\left(x + 1\right) + \sqrt{x} \cdot 4} \cdot 6
double f(double x) {
        double r962306 = 6.0;
        double r962307 = x;
        double r962308 = 1.0;
        double r962309 = r962307 - r962308;
        double r962310 = r962306 * r962309;
        double r962311 = r962307 + r962308;
        double r962312 = 4.0;
        double r962313 = sqrt(r962307);
        double r962314 = r962312 * r962313;
        double r962315 = r962311 + r962314;
        double r962316 = r962310 / r962315;
        return r962316;
}
↓
double f(double x) {
        double r962317 = x;
        double r962318 = 1.0;
        double r962319 = r962317 - r962318;
        double r962320 = r962317 + r962318;
        double r962321 = sqrt(r962317);
        double r962322 = 4.0;
        double r962323 = r962321 * r962322;
        double r962324 = r962320 + r962323;
        double r962325 = r962319 / r962324;
        double r962326 = 6.0;
        double r962327 = r962325 * r962326;
        return r962327;
}

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. Simplified0.0

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

  4. Applied +-commutative0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 
(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)))))