Average Error: 0.1 → 0.1
Time: 22.6s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(2 \cdot \log \left(\left(\sqrt[3]{\sqrt[3]{c}} \cdot \sqrt[3]{\sqrt[3]{c}}\right) \cdot \sqrt[3]{\sqrt[3]{c}}\right)\right) \cdot \left(b - 0.5\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right)\right)\right) + y \cdot i\]
\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 y + z\right) + t\right) + a\right) + \left(\left(2 \cdot \log \left(\left(\sqrt[3]{\sqrt[3]{c}} \cdot \sqrt[3]{\sqrt[3]{c}}\right) \cdot \sqrt[3]{\sqrt[3]{c}}\right)\right) \cdot \left(b - 0.5\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 r118921 = x;
        double r118922 = y;
        double r118923 = log(r118922);
        double r118924 = r118921 * r118923;
        double r118925 = z;
        double r118926 = r118924 + r118925;
        double r118927 = t;
        double r118928 = r118926 + r118927;
        double r118929 = a;
        double r118930 = r118928 + r118929;
        double r118931 = b;
        double r118932 = 0.5;
        double r118933 = r118931 - r118932;
        double r118934 = c;
        double r118935 = log(r118934);
        double r118936 = r118933 * r118935;
        double r118937 = r118930 + r118936;
        double r118938 = i;
        double r118939 = r118922 * r118938;
        double r118940 = r118937 + r118939;
        return r118940;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r118941 = x;
        double r118942 = y;
        double r118943 = log(r118942);
        double r118944 = r118941 * r118943;
        double r118945 = z;
        double r118946 = r118944 + r118945;
        double r118947 = t;
        double r118948 = r118946 + r118947;
        double r118949 = a;
        double r118950 = r118948 + r118949;
        double r118951 = 2.0;
        double r118952 = c;
        double r118953 = cbrt(r118952);
        double r118954 = cbrt(r118953);
        double r118955 = r118954 * r118954;
        double r118956 = r118955 * r118954;
        double r118957 = log(r118956);
        double r118958 = r118951 * r118957;
        double r118959 = b;
        double r118960 = 0.5;
        double r118961 = r118959 - r118960;
        double r118962 = r118958 * r118961;
        double r118963 = log(r118953);
        double r118964 = r118961 * r118963;
        double r118965 = r118962 + r118964;
        double r118966 = r118950 + r118965;
        double r118967 = i;
        double r118968 = r118942 * r118967;
        double r118969 = r118966 + r118968;
        return r118969;
}

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

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

  8. Applied add-cube-cbrt0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020042 
(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)))