Average Error: 0.1 → 0.1
Time: 44.4s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(\left(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot x + \log \left(\sqrt[3]{y}\right) \cdot x\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i
↓
\left(\left(\left(\left(\left(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot x + \log \left(\sqrt[3]{y}\right) \cdot x\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r82695 = x;
        double r82696 = y;
        double r82697 = log(r82696);
        double r82698 = r82695 * r82697;
        double r82699 = z;
        double r82700 = r82698 + r82699;
        double r82701 = t;
        double r82702 = r82700 + r82701;
        double r82703 = a;
        double r82704 = r82702 + r82703;
        double r82705 = b;
        double r82706 = 0.5;
        double r82707 = r82705 - r82706;
        double r82708 = c;
        double r82709 = log(r82708);
        double r82710 = r82707 * r82709;
        double r82711 = r82704 + r82710;
        double r82712 = i;
        double r82713 = r82696 * r82712;
        double r82714 = r82711 + r82713;
        return r82714;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r82715 = 2.0;
        double r82716 = y;
        double r82717 = cbrt(r82716);
        double r82718 = log(r82717);
        double r82719 = r82715 * r82718;
        double r82720 = x;
        double r82721 = r82719 * r82720;
        double r82722 = r82718 * r82720;
        double r82723 = r82721 + r82722;
        double r82724 = z;
        double r82725 = r82723 + r82724;
        double r82726 = t;
        double r82727 = r82725 + r82726;
        double r82728 = a;
        double r82729 = r82727 + r82728;
        double r82730 = b;
        double r82731 = 0.5;
        double r82732 = r82730 - r82731;
        double r82733 = c;
        double r82734 = log(r82733);
        double r82735 = r82732 * r82734;
        double r82736 = r82729 + r82735;
        double r82737 = i;
        double r82738 = r82716 * r82737;
        double r82739 = r82736 + r82738;
        return r82739;
}

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

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Simplified0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019323 
(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)))