Average Error: 0.1 → 0.1
Time: 37.0s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(\left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right)\right) + \log \left({\left({c}^{\left(\sqrt{\frac{1}{3}}\right)}\right)}^{\left(\sqrt{\frac{1}{3}}\right)}\right) \cdot \left(b - 0.5\right)\right)\right) + i \cdot y\]
\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(\left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right)\right) + \log \left({\left({c}^{\left(\sqrt{\frac{1}{3}}\right)}\right)}^{\left(\sqrt{\frac{1}{3}}\right)}\right) \cdot \left(b - 0.5\right)\right)\right) + i \cdot y
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3873560 = x;
        double r3873561 = y;
        double r3873562 = log(r3873561);
        double r3873563 = r3873560 * r3873562;
        double r3873564 = z;
        double r3873565 = r3873563 + r3873564;
        double r3873566 = t;
        double r3873567 = r3873565 + r3873566;
        double r3873568 = a;
        double r3873569 = r3873567 + r3873568;
        double r3873570 = b;
        double r3873571 = 0.5;
        double r3873572 = r3873570 - r3873571;
        double r3873573 = c;
        double r3873574 = log(r3873573);
        double r3873575 = r3873572 * r3873574;
        double r3873576 = r3873569 + r3873575;
        double r3873577 = i;
        double r3873578 = r3873561 * r3873577;
        double r3873579 = r3873576 + r3873578;
        return r3873579;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3873580 = x;
        double r3873581 = y;
        double r3873582 = log(r3873581);
        double r3873583 = r3873580 * r3873582;
        double r3873584 = z;
        double r3873585 = r3873583 + r3873584;
        double r3873586 = t;
        double r3873587 = r3873585 + r3873586;
        double r3873588 = a;
        double r3873589 = r3873587 + r3873588;
        double r3873590 = b;
        double r3873591 = 0.5;
        double r3873592 = r3873590 - r3873591;
        double r3873593 = c;
        double r3873594 = cbrt(r3873593);
        double r3873595 = log(r3873594);
        double r3873596 = r3873592 * r3873595;
        double r3873597 = r3873596 + r3873596;
        double r3873598 = 0.3333333333333333;
        double r3873599 = sqrt(r3873598);
        double r3873600 = pow(r3873593, r3873599);
        double r3873601 = pow(r3873600, r3873599);
        double r3873602 = log(r3873601);
        double r3873603 = r3873602 * r3873592;
        double r3873604 = r3873597 + r3873603;
        double r3873605 = r3873589 + r3873604;
        double r3873606 = i;
        double r3873607 = r3873606 * r3873581;
        double r3873608 = r3873605 + r3873607;
        return r3873608;
}

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

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

  7. Simplified0.1

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

  9. Applied pow1/30.1

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

  11. Applied add-sqr-sqrt0.1

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

  12. Applied pow-unpow0.1

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

  13. Final simplification0.1

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

Reproduce

herbie shell --seed 2019179 
(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)))