Average Error: 0.2 → 0.0
Time: 15.6s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[\log \left({\left(e^{6}\right)}^{\left(\frac{x - 1}{\sqrt{x} \cdot 4 + \left(1 + x\right)}\right)}\right)\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
\log \left({\left(e^{6}\right)}^{\left(\frac{x - 1}{\sqrt{x} \cdot 4 + \left(1 + x\right)}\right)}\right)
double f(double x) {
        double r763239 = 6.0;
        double r763240 = x;
        double r763241 = 1.0;
        double r763242 = r763240 - r763241;
        double r763243 = r763239 * r763242;
        double r763244 = r763240 + r763241;
        double r763245 = 4.0;
        double r763246 = sqrt(r763240);
        double r763247 = r763245 * r763246;
        double r763248 = r763244 + r763247;
        double r763249 = r763243 / r763248;
        return r763249;
}
↓
double f(double x) {
        double r763250 = 6.0;
        double r763251 = exp(r763250);
        double r763252 = x;
        double r763253 = 1.0;
        double r763254 = r763252 - r763253;
        double r763255 = sqrt(r763252);
        double r763256 = 4.0;
        double r763257 = r763255 * r763256;
        double r763258 = r763253 + r763252;
        double r763259 = r763257 + r763258;
        double r763260 = r763254 / r763259;
        double r763261 = pow(r763251, r763260);
        double r763262 = log(r763261);
        return r763262;
}

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 add-log-exp0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019196 
(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)))))