Average Error: 0.1 → 0.1
Time: 17.0s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(2 \cdot \log \left(\sqrt[3]{{c}^{\frac{2}{3}}} \cdot \sqrt[3]{\sqrt[3]{c}}\right)\right) \cdot \left(b - 0.5\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right)\right)\right) + y \cdot i\]
\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(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(2 \cdot \log \left(\sqrt[3]{{c}^{\frac{2}{3}}} \cdot \sqrt[3]{\sqrt[3]{c}}\right)\right) \cdot \left(b - 0.5\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right)\right)\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r95992 = x;
        double r95993 = y;
        double r95994 = log(r95993);
        double r95995 = r95992 * r95994;
        double r95996 = z;
        double r95997 = r95995 + r95996;
        double r95998 = t;
        double r95999 = r95997 + r95998;
        double r96000 = a;
        double r96001 = r95999 + r96000;
        double r96002 = b;
        double r96003 = 0.5;
        double r96004 = r96002 - r96003;
        double r96005 = c;
        double r96006 = log(r96005);
        double r96007 = r96004 * r96006;
        double r96008 = r96001 + r96007;
        double r96009 = i;
        double r96010 = r95993 * r96009;
        double r96011 = r96008 + r96010;
        return r96011;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r96012 = x;
        double r96013 = y;
        double r96014 = log(r96013);
        double r96015 = r96012 * r96014;
        double r96016 = z;
        double r96017 = r96015 + r96016;
        double r96018 = t;
        double r96019 = r96017 + r96018;
        double r96020 = a;
        double r96021 = r96019 + r96020;
        double r96022 = 2.0;
        double r96023 = c;
        double r96024 = 0.6666666666666666;
        double r96025 = pow(r96023, r96024);
        double r96026 = cbrt(r96025);
        double r96027 = cbrt(r96023);
        double r96028 = cbrt(r96027);
        double r96029 = r96026 * r96028;
        double r96030 = log(r96029);
        double r96031 = r96022 * r96030;
        double r96032 = b;
        double r96033 = 0.5;
        double r96034 = r96032 - r96033;
        double r96035 = r96031 * r96034;
        double r96036 = log(r96027);
        double r96037 = r96034 * r96036;
        double r96038 = r96035 + r96037;
        double r96039 = r96021 + r96038;
        double r96040 = i;
        double r96041 = r96013 * r96040;
        double r96042 = r96039 + r96041;
        return r96042;
}

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

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Simplified0.1

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

  8. Applied add-cube-cbrt0.1

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

  9. Applied cbrt-prod0.1

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

  10. Simplified0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2020047 
(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)))