Average Error: 0.1 → 0.1
Time: 40.8s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \log \left(\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{y}\right)\right)\right) \cdot x\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i
↓
\left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \log \left(\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{y}\right)\right)\right) \cdot x\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r82800 = x;
        double r82801 = y;
        double r82802 = log(r82801);
        double r82803 = r82800 * r82802;
        double r82804 = z;
        double r82805 = r82803 + r82804;
        double r82806 = t;
        double r82807 = r82805 + r82806;
        double r82808 = a;
        double r82809 = r82807 + r82808;
        double r82810 = b;
        double r82811 = 0.5;
        double r82812 = r82810 - r82811;
        double r82813 = c;
        double r82814 = log(r82813);
        double r82815 = r82812 * r82814;
        double r82816 = r82809 + r82815;
        double r82817 = i;
        double r82818 = r82801 * r82817;
        double r82819 = r82816 + r82818;
        return r82819;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r82820 = x;
        double r82821 = 2.0;
        double r82822 = y;
        double r82823 = cbrt(r82822);
        double r82824 = log(r82823);
        double r82825 = r82821 * r82824;
        double r82826 = r82820 * r82825;
        double r82827 = log1p(r82823);
        double r82828 = expm1(r82827);
        double r82829 = log(r82828);
        double r82830 = r82829 * r82820;
        double r82831 = r82826 + r82830;
        double r82832 = z;
        double r82833 = r82831 + r82832;
        double r82834 = t;
        double r82835 = r82833 + r82834;
        double r82836 = a;
        double r82837 = r82835 + r82836;
        double r82838 = b;
        double r82839 = 0.5;
        double r82840 = r82838 - r82839;
        double r82841 = c;
        double r82842 = log(r82841);
        double r82843 = r82840 * r82842;
        double r82844 = r82837 + r82843;
        double r82845 = i;
        double r82846 = r82822 * r82845;
        double r82847 = r82844 + r82846;
        return r82847;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.1

    \[\leadsto \left(\left(\left(\left(x \cdot \log \color{blue}{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right)} + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  4. Applied log-prod0.1

    \[\leadsto \left(\left(\left(\left(x \cdot \color{blue}{\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right)} + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  5. Applied distribute-lft-in0.1

    \[\leadsto \left(\left(\left(\left(\color{blue}{\left(x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right)} + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  6. Simplified0.1

    \[\leadsto \left(\left(\left(\left(\left(\color{blue}{x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right)} + x \cdot \log \left(\sqrt[3]{y}\right)\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  7. Simplified0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \color{blue}{\log \left(\sqrt[3]{y}\right) \cdot x}\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
  8. Using strategy rm

  9. Applied expm1-log1p-u0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \log \color{blue}{\left(\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{y}\right)\right)\right)} \cdot x\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  10. Final simplification0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \log \left(\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{y}\right)\right)\right) \cdot x\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B"
  :precision binary64
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))