Average Error: 0.1 → 0.1
Time: 32.7s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(t + \left(\left(\log \left(\sqrt[3]{\sqrt[3]{y}}\right) \cdot x + x \cdot \left(\log \left(\sqrt[3]{{y}^{\frac{2}{3}}}\right) + \log y \cdot \frac{2}{3}\right)\right) + z\right)\right)\right)\right) + y \cdot i\]
\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(\log c \cdot \left(b - 0.5\right) + \left(a + \left(t + \left(\left(\log \left(\sqrt[3]{\sqrt[3]{y}}\right) \cdot x + x \cdot \left(\log \left(\sqrt[3]{{y}^{\frac{2}{3}}}\right) + \log y \cdot \frac{2}{3}\right)\right) + z\right)\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 r77553 = x;
        double r77554 = y;
        double r77555 = log(r77554);
        double r77556 = r77553 * r77555;
        double r77557 = z;
        double r77558 = r77556 + r77557;
        double r77559 = t;
        double r77560 = r77558 + r77559;
        double r77561 = a;
        double r77562 = r77560 + r77561;
        double r77563 = b;
        double r77564 = 0.5;
        double r77565 = r77563 - r77564;
        double r77566 = c;
        double r77567 = log(r77566);
        double r77568 = r77565 * r77567;
        double r77569 = r77562 + r77568;
        double r77570 = i;
        double r77571 = r77554 * r77570;
        double r77572 = r77569 + r77571;
        return r77572;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r77573 = c;
        double r77574 = log(r77573);
        double r77575 = b;
        double r77576 = 0.5;
        double r77577 = r77575 - r77576;
        double r77578 = r77574 * r77577;
        double r77579 = a;
        double r77580 = t;
        double r77581 = y;
        double r77582 = cbrt(r77581);
        double r77583 = cbrt(r77582);
        double r77584 = log(r77583);
        double r77585 = x;
        double r77586 = r77584 * r77585;
        double r77587 = 0.6666666666666666;
        double r77588 = pow(r77581, r77587);
        double r77589 = cbrt(r77588);
        double r77590 = log(r77589);
        double r77591 = log(r77581);
        double r77592 = r77591 * r77587;
        double r77593 = r77590 + r77592;
        double r77594 = r77585 * r77593;
        double r77595 = r77586 + r77594;
        double r77596 = z;
        double r77597 = r77595 + r77596;
        double r77598 = r77580 + r77597;
        double r77599 = r77579 + r77598;
        double r77600 = r77578 + r77599;
        double r77601 = i;
        double r77602 = r77581 * r77601;
        double r77603 = r77600 + r77602;
        return r77603;
}

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

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

  8. Applied add-cube-cbrt0.1

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

  9. Applied cbrt-prod0.1

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

  10. Applied log-prod0.1

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

  11. Applied distribute-lft-in0.1

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

  12. Applied associate-+r+0.1

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

  13. Simplified0.1

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

  14. Final simplification0.1

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

Reproduce

herbie shell --seed 2019194 
(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)))