Average Error: 0.1 → 0.1
Time: 29.4s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(y \cdot i + \left(x \cdot \log y + z\right)\right) + \left(3 \cdot \log \left(\sqrt[3]{c}\right)\right) \cdot \left(b - 0.5\right)\right) + \left(t + a\right)\]
\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(\left(y \cdot i + \left(x \cdot \log y + z\right)\right) + \left(3 \cdot \log \left(\sqrt[3]{c}\right)\right) \cdot \left(b - 0.5\right)\right) + \left(t + a\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r79575 = x;
        double r79576 = y;
        double r79577 = log(r79576);
        double r79578 = r79575 * r79577;
        double r79579 = z;
        double r79580 = r79578 + r79579;
        double r79581 = t;
        double r79582 = r79580 + r79581;
        double r79583 = a;
        double r79584 = r79582 + r79583;
        double r79585 = b;
        double r79586 = 0.5;
        double r79587 = r79585 - r79586;
        double r79588 = c;
        double r79589 = log(r79588);
        double r79590 = r79587 * r79589;
        double r79591 = r79584 + r79590;
        double r79592 = i;
        double r79593 = r79576 * r79592;
        double r79594 = r79591 + r79593;
        return r79594;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r79595 = y;
        double r79596 = i;
        double r79597 = r79595 * r79596;
        double r79598 = x;
        double r79599 = log(r79595);
        double r79600 = r79598 * r79599;
        double r79601 = z;
        double r79602 = r79600 + r79601;
        double r79603 = r79597 + r79602;
        double r79604 = 3.0;
        double r79605 = c;
        double r79606 = cbrt(r79605);
        double r79607 = log(r79606);
        double r79608 = r79604 * r79607;
        double r79609 = b;
        double r79610 = 0.5;
        double r79611 = r79609 - r79610;
        double r79612 = r79608 * r79611;
        double r79613 = r79603 + r79612;
        double r79614 = t;
        double r79615 = a;
        double r79616 = r79614 + r79615;
        double r79617 = r79613 + r79616;
        return r79617;
}

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-rgt-in0.1

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

  6. Applied associate-+r+0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019294 
(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)))