Average Error: 0.1 → 0.1
Time: 10.0s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{c}\right)\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right)\right)\right) + y \cdot i\]
\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(b - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{c}\right)\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 r90995 = x;
        double r90996 = y;
        double r90997 = log(r90996);
        double r90998 = r90995 * r90997;
        double r90999 = z;
        double r91000 = r90998 + r90999;
        double r91001 = t;
        double r91002 = r91000 + r91001;
        double r91003 = a;
        double r91004 = r91002 + r91003;
        double r91005 = b;
        double r91006 = 0.5;
        double r91007 = r91005 - r91006;
        double r91008 = c;
        double r91009 = log(r91008);
        double r91010 = r91007 * r91009;
        double r91011 = r91004 + r91010;
        double r91012 = i;
        double r91013 = r90996 * r91012;
        double r91014 = r91011 + r91013;
        return r91014;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r91015 = x;
        double r91016 = y;
        double r91017 = log(r91016);
        double r91018 = r91015 * r91017;
        double r91019 = z;
        double r91020 = r91018 + r91019;
        double r91021 = t;
        double r91022 = r91020 + r91021;
        double r91023 = a;
        double r91024 = r91022 + r91023;
        double r91025 = b;
        double r91026 = 0.5;
        double r91027 = r91025 - r91026;
        double r91028 = 2.0;
        double r91029 = c;
        double r91030 = cbrt(r91029);
        double r91031 = log(r91030);
        double r91032 = r91028 * r91031;
        double r91033 = r91027 * r91032;
        double r91034 = r91027 * r91031;
        double r91035 = r91033 + r91034;
        double r91036 = r91024 + r91035;
        double r91037 = i;
        double r91038 = r91016 * r91037;
        double r91039 = r91036 + r91038;
        return r91039;
}

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

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020057 
(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)))