Average Error: 0.1 → 0.1
Time: 10.1s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{c}\right) + \log \left(\sqrt[3]{\sqrt{c}}\right)\right) + \log \left(\sqrt[3]{\sqrt{c}}\right) \cdot \left(b - 0.5\right)\right)\right) + y \cdot i\]
\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) + \log \left(\sqrt[3]{\sqrt{c}}\right)\right) + \log \left(\sqrt[3]{\sqrt{c}}\right) \cdot \left(b - 0.5\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 r86028 = x;
        double r86029 = y;
        double r86030 = log(r86029);
        double r86031 = r86028 * r86030;
        double r86032 = z;
        double r86033 = r86031 + r86032;
        double r86034 = t;
        double r86035 = r86033 + r86034;
        double r86036 = a;
        double r86037 = r86035 + r86036;
        double r86038 = b;
        double r86039 = 0.5;
        double r86040 = r86038 - r86039;
        double r86041 = c;
        double r86042 = log(r86041);
        double r86043 = r86040 * r86042;
        double r86044 = r86037 + r86043;
        double r86045 = i;
        double r86046 = r86029 * r86045;
        double r86047 = r86044 + r86046;
        return r86047;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r86048 = x;
        double r86049 = y;
        double r86050 = log(r86049);
        double r86051 = r86048 * r86050;
        double r86052 = z;
        double r86053 = r86051 + r86052;
        double r86054 = t;
        double r86055 = r86053 + r86054;
        double r86056 = a;
        double r86057 = r86055 + r86056;
        double r86058 = b;
        double r86059 = 0.5;
        double r86060 = r86058 - r86059;
        double r86061 = 2.0;
        double r86062 = c;
        double r86063 = cbrt(r86062);
        double r86064 = log(r86063);
        double r86065 = r86061 * r86064;
        double r86066 = sqrt(r86062);
        double r86067 = cbrt(r86066);
        double r86068 = log(r86067);
        double r86069 = r86065 + r86068;
        double r86070 = r86060 * r86069;
        double r86071 = r86068 * r86060;
        double r86072 = r86070 + r86071;
        double r86073 = r86057 + r86072;
        double r86074 = i;
        double r86075 = r86049 * r86074;
        double r86076 = r86073 + r86075;
        return r86076;
}

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-sqr-sqrt0.1

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

  9. Applied cbrt-prod0.1

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

  10. Applied log-prod0.1

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

  11. Applied distribute-rgt-in0.1

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

  12. Applied associate-+r+0.1

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

  13. Simplified0.1

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

  14. Final simplification0.1

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

Reproduce

herbie shell --seed 2020062 
(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)))