Average Error: 0.1 → 0.1
Time: 46.7s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(x \cdot \log \left(\sqrt{y}\right) + \left(\log \left(\sqrt{y}\right) \cdot x + z\right)\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{c}\right)\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right)\right)\right) + y \cdot i\]
\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 \left(\sqrt{y}\right) + \left(\log \left(\sqrt{y}\right) \cdot x + z\right)\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 r82033 = x;
        double r82034 = y;
        double r82035 = log(r82034);
        double r82036 = r82033 * r82035;
        double r82037 = z;
        double r82038 = r82036 + r82037;
        double r82039 = t;
        double r82040 = r82038 + r82039;
        double r82041 = a;
        double r82042 = r82040 + r82041;
        double r82043 = b;
        double r82044 = 0.5;
        double r82045 = r82043 - r82044;
        double r82046 = c;
        double r82047 = log(r82046);
        double r82048 = r82045 * r82047;
        double r82049 = r82042 + r82048;
        double r82050 = i;
        double r82051 = r82034 * r82050;
        double r82052 = r82049 + r82051;
        return r82052;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r82053 = x;
        double r82054 = y;
        double r82055 = sqrt(r82054);
        double r82056 = log(r82055);
        double r82057 = r82053 * r82056;
        double r82058 = r82056 * r82053;
        double r82059 = z;
        double r82060 = r82058 + r82059;
        double r82061 = r82057 + r82060;
        double r82062 = t;
        double r82063 = r82061 + r82062;
        double r82064 = a;
        double r82065 = r82063 + r82064;
        double r82066 = b;
        double r82067 = 0.5;
        double r82068 = r82066 - r82067;
        double r82069 = 2.0;
        double r82070 = c;
        double r82071 = cbrt(r82070);
        double r82072 = log(r82071);
        double r82073 = r82069 * r82072;
        double r82074 = r82068 * r82073;
        double r82075 = r82068 * r82072;
        double r82076 = r82074 + r82075;
        double r82077 = r82065 + r82076;
        double r82078 = i;
        double r82079 = r82054 * r82078;
        double r82080 = r82077 + r82079;
        return r82080;
}

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-sqr-sqrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Applied associate-+l+0.1

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

  7. Simplified0.1

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

  9. Applied add-cube-cbrt0.1

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

  10. Applied log-prod0.1

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

  11. Applied distribute-lft-in0.1

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

  12. Simplified0.1

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

  13. Final simplification0.1

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

Reproduce

herbie shell --seed 2019303 
(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)))