Average Error: 0.1 → 0.1
Time: 35.0s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(z + \left(\left(\log \left(\sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right) \cdot x + x \cdot \log \left({y}^{\frac{1}{3}}\right)\right)\right) + t\right) + a\right) + \log c \cdot \left(b - 0.5\right)\right) + y \cdot i\]
\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(z + \left(\left(\log \left(\sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right) \cdot x + x \cdot \log \left({y}^{\frac{1}{3}}\right)\right)\right) + t\right) + a\right) + \log c \cdot \left(b - 0.5\right)\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3684575 = x;
        double r3684576 = y;
        double r3684577 = log(r3684576);
        double r3684578 = r3684575 * r3684577;
        double r3684579 = z;
        double r3684580 = r3684578 + r3684579;
        double r3684581 = t;
        double r3684582 = r3684580 + r3684581;
        double r3684583 = a;
        double r3684584 = r3684582 + r3684583;
        double r3684585 = b;
        double r3684586 = 0.5;
        double r3684587 = r3684585 - r3684586;
        double r3684588 = c;
        double r3684589 = log(r3684588);
        double r3684590 = r3684587 * r3684589;
        double r3684591 = r3684584 + r3684590;
        double r3684592 = i;
        double r3684593 = r3684576 * r3684592;
        double r3684594 = r3684591 + r3684593;
        return r3684594;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3684595 = z;
        double r3684596 = y;
        double r3684597 = cbrt(r3684596);
        double r3684598 = log(r3684597);
        double r3684599 = r3684598 + r3684598;
        double r3684600 = x;
        double r3684601 = r3684599 * r3684600;
        double r3684602 = 0.3333333333333333;
        double r3684603 = pow(r3684596, r3684602);
        double r3684604 = log(r3684603);
        double r3684605 = r3684600 * r3684604;
        double r3684606 = r3684601 + r3684605;
        double r3684607 = r3684595 + r3684606;
        double r3684608 = t;
        double r3684609 = r3684607 + r3684608;
        double r3684610 = a;
        double r3684611 = r3684609 + r3684610;
        double r3684612 = c;
        double r3684613 = log(r3684612);
        double r3684614 = b;
        double r3684615 = 0.5;
        double r3684616 = r3684614 - r3684615;
        double r3684617 = r3684613 * r3684616;
        double r3684618 = r3684611 + r3684617;
        double r3684619 = i;
        double r3684620 = r3684596 * r3684619;
        double r3684621 = r3684618 + r3684620;
        return r3684621;
}

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-rgt-in0.1

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

  6. Simplified0.1

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

  8. Applied pow1/30.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019158 
(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)))