Average Error: 0.2 → 0.0
Time: 13.1s
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 r609756 = 6.0;
        double r609757 = x;
        double r609758 = 1.0;
        double r609759 = r609757 - r609758;
        double r609760 = r609756 * r609759;
        double r609761 = r609757 + r609758;
        double r609762 = 4.0;
        double r609763 = sqrt(r609757);
        double r609764 = r609762 * r609763;
        double r609765 = r609761 + r609764;
        double r609766 = r609760 / r609765;
        return r609766;
}
↓
double f(double x) {
        double r609767 = 6.0;
        double r609768 = exp(r609767);
        double r609769 = x;
        double r609770 = 1.0;
        double r609771 = r609769 - r609770;
        double r609772 = sqrt(r609769);
        double r609773 = 4.0;
        double r609774 = r609772 * r609773;
        double r609775 = r609770 + r609769;
        double r609776 = r609774 + r609775;
        double r609777 = r609771 / r609776;
        double r609778 = pow(r609768, r609777);
        double r609779 = log(r609778);
        return r609779;
}

Error

Bits error versus x

Try it out

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 2019194 
(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)))))