Average Error: 0.1 → 0.2
Time: 9.6s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \left(\log \left(\frac{1}{c}\right) \cdot \frac{-5}{6}\right) + \log \left(\sqrt[3]{\sqrt{c}}\right) \cdot \left(b - 0.5\right)\right)\right) + y \cdot i\]
\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(\log \left(\frac{1}{c}\right) \cdot \frac{-5}{6}\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 r80024 = x;
        double r80025 = y;
        double r80026 = log(r80025);
        double r80027 = r80024 * r80026;
        double r80028 = z;
        double r80029 = r80027 + r80028;
        double r80030 = t;
        double r80031 = r80029 + r80030;
        double r80032 = a;
        double r80033 = r80031 + r80032;
        double r80034 = b;
        double r80035 = 0.5;
        double r80036 = r80034 - r80035;
        double r80037 = c;
        double r80038 = log(r80037);
        double r80039 = r80036 * r80038;
        double r80040 = r80033 + r80039;
        double r80041 = i;
        double r80042 = r80025 * r80041;
        double r80043 = r80040 + r80042;
        return r80043;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r80044 = x;
        double r80045 = y;
        double r80046 = log(r80045);
        double r80047 = r80044 * r80046;
        double r80048 = z;
        double r80049 = r80047 + r80048;
        double r80050 = t;
        double r80051 = r80049 + r80050;
        double r80052 = a;
        double r80053 = r80051 + r80052;
        double r80054 = b;
        double r80055 = 0.5;
        double r80056 = r80054 - r80055;
        double r80057 = 1.0;
        double r80058 = c;
        double r80059 = r80057 / r80058;
        double r80060 = log(r80059);
        double r80061 = -0.8333333333333334;
        double r80062 = r80060 * r80061;
        double r80063 = r80056 * r80062;
        double r80064 = sqrt(r80058);
        double r80065 = cbrt(r80064);
        double r80066 = log(r80065);
        double r80067 = r80066 * r80056;
        double r80068 = r80063 + r80067;
        double r80069 = r80053 + r80068;
        double r80070 = i;
        double r80071 = r80045 * r80070;
        double r80072 = r80069 + r80071;
        return r80072;
}

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. Taylor expanded around inf 0.2

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \color{blue}{\left(\log \left({\left(\frac{1}{c}\right)}^{\frac{-1}{6}}\right) + 2 \cdot \log \left({\left(\frac{1}{c}\right)}^{\frac{-1}{3}}\right)\right)} + \log \left(\sqrt[3]{\sqrt{c}}\right) \cdot \left(b - 0.5\right)\right)\right) + y \cdot i\]

  15. Simplified0.2

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \color{blue}{\left(\log \left(\frac{1}{c}\right) \cdot \frac{-5}{6}\right)} + \log \left(\sqrt[3]{\sqrt{c}}\right) \cdot \left(b - 0.5\right)\right)\right) + y \cdot i\]

  16. Final simplification0.2

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \left(\log \left(\frac{1}{c}\right) \cdot \frac{-5}{6}\right) + \log \left(\sqrt[3]{\sqrt{c}}\right) \cdot \left(b - 0.5\right)\right)\right) + y \cdot i\]

Reproduce

herbie shell --seed 2020049 
(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)))