Average Error: 0.1 → 0.1
Time: 21.7s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - \frac{1}{2}\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{c}\right) + \log \left({\left(\frac{1}{c}\right)}^{\frac{-1}{3}}\right)\right) + y \cdot i\right)\]
\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(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - \frac{1}{2}\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{c}\right) + \log \left({\left(\frac{1}{c}\right)}^{\frac{-1}{3}}\right)\right) + y \cdot i\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r67466 = x;
        double r67467 = y;
        double r67468 = log(r67467);
        double r67469 = r67466 * r67468;
        double r67470 = z;
        double r67471 = r67469 + r67470;
        double r67472 = t;
        double r67473 = r67471 + r67472;
        double r67474 = a;
        double r67475 = r67473 + r67474;
        double r67476 = b;
        double r67477 = 0.5;
        double r67478 = r67476 - r67477;
        double r67479 = c;
        double r67480 = log(r67479);
        double r67481 = r67478 * r67480;
        double r67482 = r67475 + r67481;
        double r67483 = i;
        double r67484 = r67467 * r67483;
        double r67485 = r67482 + r67484;
        return r67485;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r67486 = x;
        double r67487 = y;
        double r67488 = log(r67487);
        double r67489 = r67486 * r67488;
        double r67490 = z;
        double r67491 = r67489 + r67490;
        double r67492 = t;
        double r67493 = r67491 + r67492;
        double r67494 = a;
        double r67495 = r67493 + r67494;
        double r67496 = b;
        double r67497 = 1.0;
        double r67498 = 2.0;
        double r67499 = r67497 / r67498;
        double r67500 = r67496 - r67499;
        double r67501 = 2.0;
        double r67502 = c;
        double r67503 = cbrt(r67502);
        double r67504 = log(r67503);
        double r67505 = r67501 * r67504;
        double r67506 = 1.0;
        double r67507 = r67506 / r67502;
        double r67508 = -0.3333333333333333;
        double r67509 = pow(r67507, r67508);
        double r67510 = log(r67509);
        double r67511 = r67505 + r67510;
        double r67512 = r67500 * r67511;
        double r67513 = i;
        double r67514 = r67487 * r67513;
        double r67515 = r67512 + r67514;
        double r67516 = r67495 + r67515;
        return r67516;
}

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

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

  7. Simplified0.1

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

  8. Taylor expanded around inf 0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019304 
(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)))