Average Error: 0.1 → 0.1
Time: 10.0s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(x \cdot \log \left(\sqrt[3]{y} \cdot {y}^{\frac{1}{3}}\right) + \left(\log \left(\sqrt[3]{y}\right) \cdot x + z\right)\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
\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(x \cdot \log \left(\sqrt[3]{y} \cdot {y}^{\frac{1}{3}}\right) + \left(\log \left(\sqrt[3]{y}\right) \cdot x + z\right)\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 r72064 = x;
        double r72065 = y;
        double r72066 = log(r72065);
        double r72067 = r72064 * r72066;
        double r72068 = z;
        double r72069 = r72067 + r72068;
        double r72070 = t;
        double r72071 = r72069 + r72070;
        double r72072 = a;
        double r72073 = r72071 + r72072;
        double r72074 = b;
        double r72075 = 0.5;
        double r72076 = r72074 - r72075;
        double r72077 = c;
        double r72078 = log(r72077);
        double r72079 = r72076 * r72078;
        double r72080 = r72073 + r72079;
        double r72081 = i;
        double r72082 = r72065 * r72081;
        double r72083 = r72080 + r72082;
        return r72083;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r72084 = x;
        double r72085 = y;
        double r72086 = cbrt(r72085);
        double r72087 = 0.3333333333333333;
        double r72088 = pow(r72085, r72087);
        double r72089 = r72086 * r72088;
        double r72090 = log(r72089);
        double r72091 = r72084 * r72090;
        double r72092 = log(r72086);
        double r72093 = r72092 * r72084;
        double r72094 = z;
        double r72095 = r72093 + r72094;
        double r72096 = r72091 + r72095;
        double r72097 = t;
        double r72098 = r72096 + r72097;
        double r72099 = a;
        double r72100 = r72098 + r72099;
        double r72101 = b;
        double r72102 = 0.5;
        double r72103 = r72101 - r72102;
        double r72104 = c;
        double r72105 = log(r72104);
        double r72106 = r72103 * r72105;
        double r72107 = r72100 + r72106;
        double r72108 = i;
        double r72109 = r72085 * r72108;
        double r72110 = r72107 + r72109;
        return r72110;
}

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. Applied associate-+l+0.1

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

  7. Simplified0.1

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

  9. Applied pow1/30.1

    \[\leadsto \left(\left(\left(\left(x \cdot \log \left(\sqrt[3]{y} \cdot \color{blue}{{y}^{\frac{1}{3}}}\right) + \left(\log \left(\sqrt[3]{y}\right) \cdot x + z\right)\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  10. Final simplification0.1

    \[\leadsto \left(\left(\left(\left(x \cdot \log \left(\sqrt[3]{y} \cdot {y}^{\frac{1}{3}}\right) + \left(\log \left(\sqrt[3]{y}\right) \cdot x + z\right)\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

Reproduce

herbie shell --seed 2020064 
(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)))