Average Error: 0.1 → 0.1
Time: 10.5s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{c}\right)\right) + \left(b - 0.5\right) \cdot \log \left(e^{\log \left({c}^{\frac{1}{3}}\right)}\right)\right)\right) + y \cdot i\]
\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(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{c}\right)\right) + \left(b - 0.5\right) \cdot \log \left(e^{\log \left({c}^{\frac{1}{3}}\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 r62588 = x;
        double r62589 = y;
        double r62590 = log(r62589);
        double r62591 = r62588 * r62590;
        double r62592 = z;
        double r62593 = r62591 + r62592;
        double r62594 = t;
        double r62595 = r62593 + r62594;
        double r62596 = a;
        double r62597 = r62595 + r62596;
        double r62598 = b;
        double r62599 = 0.5;
        double r62600 = r62598 - r62599;
        double r62601 = c;
        double r62602 = log(r62601);
        double r62603 = r62600 * r62602;
        double r62604 = r62597 + r62603;
        double r62605 = i;
        double r62606 = r62589 * r62605;
        double r62607 = r62604 + r62606;
        return r62607;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r62608 = x;
        double r62609 = y;
        double r62610 = log(r62609);
        double r62611 = r62608 * r62610;
        double r62612 = z;
        double r62613 = r62611 + r62612;
        double r62614 = t;
        double r62615 = r62613 + r62614;
        double r62616 = a;
        double r62617 = r62615 + r62616;
        double r62618 = b;
        double r62619 = 0.5;
        double r62620 = r62618 - r62619;
        double r62621 = 2.0;
        double r62622 = c;
        double r62623 = cbrt(r62622);
        double r62624 = log(r62623);
        double r62625 = r62621 * r62624;
        double r62626 = r62620 * r62625;
        double r62627 = 0.3333333333333333;
        double r62628 = pow(r62622, r62627);
        double r62629 = log(r62628);
        double r62630 = exp(r62629);
        double r62631 = log(r62630);
        double r62632 = r62620 * r62631;
        double r62633 = r62626 + r62632;
        double r62634 = r62617 + r62633;
        double r62635 = i;
        double r62636 = r62609 * r62635;
        double r62637 = r62634 + r62636;
        return r62637;
}

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-lft-in0.1

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

  6. Simplified0.1

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

  8. Applied add-exp-log0.1

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

  9. Simplified0.1

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{c}\right)\right) + \left(b - 0.5\right) \cdot \log \left(e^{\color{blue}{\log \left({c}^{\frac{1}{3}}\right)}}\right)\right)\right) + y \cdot i\]

  10. Final simplification0.1

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{c}\right)\right) + \left(b - 0.5\right) \cdot \log \left(e^{\log \left({c}^{\frac{1}{3}}\right)}\right)\right)\right) + y \cdot i\]

Reproduce

herbie shell --seed 2020046 
(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)))