Average Error: 0.1 → 0.1
Time: 30.4s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(a + y \cdot i\right) + \left(\left(z + x \cdot \log y\right) + t\right)\right) + \left(\left(b - 0.5\right) \cdot \left(\log \left(\sqrt[3]{c}\right) \cdot 2\right) + \left(b - 0.5\right) \cdot \log \left({\left({c}^{\left(\sqrt{\frac{1}{3}}\right)}\right)}^{\left(\sqrt{\frac{1}{3}}\right)}\right)\right)\]
\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(a + y \cdot i\right) + \left(\left(z + x \cdot \log y\right) + t\right)\right) + \left(\left(b - 0.5\right) \cdot \left(\log \left(\sqrt[3]{c}\right) \cdot 2\right) + \left(b - 0.5\right) \cdot \log \left({\left({c}^{\left(\sqrt{\frac{1}{3}}\right)}\right)}^{\left(\sqrt{\frac{1}{3}}\right)}\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r113083 = x;
        double r113084 = y;
        double r113085 = log(r113084);
        double r113086 = r113083 * r113085;
        double r113087 = z;
        double r113088 = r113086 + r113087;
        double r113089 = t;
        double r113090 = r113088 + r113089;
        double r113091 = a;
        double r113092 = r113090 + r113091;
        double r113093 = b;
        double r113094 = 0.5;
        double r113095 = r113093 - r113094;
        double r113096 = c;
        double r113097 = log(r113096);
        double r113098 = r113095 * r113097;
        double r113099 = r113092 + r113098;
        double r113100 = i;
        double r113101 = r113084 * r113100;
        double r113102 = r113099 + r113101;
        return r113102;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r113103 = a;
        double r113104 = y;
        double r113105 = i;
        double r113106 = r113104 * r113105;
        double r113107 = r113103 + r113106;
        double r113108 = z;
        double r113109 = x;
        double r113110 = log(r113104);
        double r113111 = r113109 * r113110;
        double r113112 = r113108 + r113111;
        double r113113 = t;
        double r113114 = r113112 + r113113;
        double r113115 = r113107 + r113114;
        double r113116 = b;
        double r113117 = 0.5;
        double r113118 = r113116 - r113117;
        double r113119 = c;
        double r113120 = cbrt(r113119);
        double r113121 = log(r113120);
        double r113122 = 2.0;
        double r113123 = r113121 * r113122;
        double r113124 = r113118 * r113123;
        double r113125 = 0.3333333333333333;
        double r113126 = sqrt(r113125);
        double r113127 = pow(r113119, r113126);
        double r113128 = pow(r113127, r113126);
        double r113129 = log(r113128);
        double r113130 = r113118 * r113129;
        double r113131 = r113124 + r113130;
        double r113132 = r113115 + r113131;
        return r113132;
}

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. Simplified0.1

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

  4. Applied add-cube-cbrt0.1

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

  5. Applied log-prod0.1

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

  6. Applied distribute-lft-in0.1

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

  7. Simplified0.1

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

  8. Simplified0.1

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

  10. Applied pow1/30.1

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

  12. Applied add-sqr-sqrt0.1

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

  13. Applied pow-unpow0.1

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

  14. Final simplification0.1

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

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B"
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))