Average Error: 0.1 → 0.1
Time: 11.1s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{c}\right)\right) + \left(b - 0.5\right) \cdot \log \left(e^{\log \left({c}^{\frac{1}{3}}\right)}\right)\right)\right) + y \cdot i\]
\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(e^{\log \left({c}^{\frac{1}{3}}\right)}\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 r62028 = x;
        double r62029 = y;
        double r62030 = log(r62029);
        double r62031 = r62028 * r62030;
        double r62032 = z;
        double r62033 = r62031 + r62032;
        double r62034 = t;
        double r62035 = r62033 + r62034;
        double r62036 = a;
        double r62037 = r62035 + r62036;
        double r62038 = b;
        double r62039 = 0.5;
        double r62040 = r62038 - r62039;
        double r62041 = c;
        double r62042 = log(r62041);
        double r62043 = r62040 * r62042;
        double r62044 = r62037 + r62043;
        double r62045 = i;
        double r62046 = r62029 * r62045;
        double r62047 = r62044 + r62046;
        return r62047;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r62048 = x;
        double r62049 = y;
        double r62050 = log(r62049);
        double r62051 = r62048 * r62050;
        double r62052 = z;
        double r62053 = r62051 + r62052;
        double r62054 = t;
        double r62055 = r62053 + r62054;
        double r62056 = a;
        double r62057 = r62055 + r62056;
        double r62058 = b;
        double r62059 = 0.5;
        double r62060 = r62058 - r62059;
        double r62061 = 2.0;
        double r62062 = c;
        double r62063 = cbrt(r62062);
        double r62064 = log(r62063);
        double r62065 = r62061 * r62064;
        double r62066 = r62060 * r62065;
        double r62067 = 0.3333333333333333;
        double r62068 = pow(r62062, r62067);
        double r62069 = log(r62068);
        double r62070 = exp(r62069);
        double r62071 = log(r62070);
        double r62072 = r62060 * r62071;
        double r62073 = r62066 + r62072;
        double r62074 = r62057 + r62073;
        double r62075 = i;
        double r62076 = r62049 * r62075;
        double r62077 = r62074 + r62076;
        return r62077;
}

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. Using strategy rm

  8. Applied add-exp-log0.1

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

  9. Simplified0.1

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{c}\right)\right) + \left(b - 0.5\right) \cdot \log \left(e^{\color{blue}{\log \left({c}^{\frac{1}{3}}\right)}}\right)\right)\right) + y \cdot i\]

  10. Final simplification0.1

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{c}\right)\right) + \left(b - 0.5\right) \cdot \log \left(e^{\log \left({c}^{\frac{1}{3}}\right)}\right)\right)\right) + y \cdot i\]

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)))