Average Error: 0.1 → 0.1
Time: 19.9s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(y \cdot i + \left(\left(t + x \cdot \left(\left(\log \left(\sqrt[3]{\sqrt[3]{y}}\right) \cdot 2 + \log \left(\sqrt[3]{y}\right)\right) + 2 \cdot \log \left(\sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right)\right)\right) + z\right)\right) + \left(a + \left(b - 0.5\right) \cdot \log c\right)\]
\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(y \cdot i + \left(\left(t + x \cdot \left(\left(\log \left(\sqrt[3]{\sqrt[3]{y}}\right) \cdot 2 + \log \left(\sqrt[3]{y}\right)\right) + 2 \cdot \log \left(\sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right)\right)\right) + z\right)\right) + \left(a + \left(b - 0.5\right) \cdot \log c\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r56641 = x;
        double r56642 = y;
        double r56643 = log(r56642);
        double r56644 = r56641 * r56643;
        double r56645 = z;
        double r56646 = r56644 + r56645;
        double r56647 = t;
        double r56648 = r56646 + r56647;
        double r56649 = a;
        double r56650 = r56648 + r56649;
        double r56651 = b;
        double r56652 = 0.5;
        double r56653 = r56651 - r56652;
        double r56654 = c;
        double r56655 = log(r56654);
        double r56656 = r56653 * r56655;
        double r56657 = r56650 + r56656;
        double r56658 = i;
        double r56659 = r56642 * r56658;
        double r56660 = r56657 + r56659;
        return r56660;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r56661 = y;
        double r56662 = i;
        double r56663 = r56661 * r56662;
        double r56664 = t;
        double r56665 = x;
        double r56666 = cbrt(r56661);
        double r56667 = cbrt(r56666);
        double r56668 = log(r56667);
        double r56669 = 2.0;
        double r56670 = r56668 * r56669;
        double r56671 = log(r56666);
        double r56672 = r56670 + r56671;
        double r56673 = r56666 * r56666;
        double r56674 = cbrt(r56673);
        double r56675 = log(r56674);
        double r56676 = r56669 * r56675;
        double r56677 = r56672 + r56676;
        double r56678 = r56665 * r56677;
        double r56679 = r56664 + r56678;
        double r56680 = z;
        double r56681 = r56679 + r56680;
        double r56682 = r56663 + r56681;
        double r56683 = a;
        double r56684 = b;
        double r56685 = 0.5;
        double r56686 = r56684 - r56685;
        double r56687 = c;
        double r56688 = log(r56687);
        double r56689 = r56686 * r56688;
        double r56690 = r56683 + r56689;
        double r56691 = r56682 + r56690;
        return r56691;
}

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

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

  9. Applied cbrt-prod0.1

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

  10. Applied log-prod0.1

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

  11. Applied distribute-lft-in0.1

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

  12. Applied distribute-rgt-in0.1

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

  13. Applied associate-+l+0.1

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

  14. Simplified0.1

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

  15. Final simplification0.1

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

Reproduce

herbie shell --seed 1978988140 
(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)))