Average Error: 0.1 → 0.1
Time: 25.1s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(2 \cdot \log \left(\left(\sqrt[3]{\sqrt[3]{c}} \cdot \sqrt[3]{\sqrt[3]{c}}\right) \cdot \sqrt[3]{\sqrt[3]{c}}\right)\right) \cdot \left(b - 0.5\right) + \left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right)\right) + \log \left(\sqrt[3]{c}\right) \cdot \left(b - 0.5\right)\right) + y \cdot i\]
\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(2 \cdot \log \left(\left(\sqrt[3]{\sqrt[3]{c}} \cdot \sqrt[3]{\sqrt[3]{c}}\right) \cdot \sqrt[3]{\sqrt[3]{c}}\right)\right) \cdot \left(b - 0.5\right) + \left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right)\right) + \log \left(\sqrt[3]{c}\right) \cdot \left(b - 0.5\right)\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r77486 = x;
        double r77487 = y;
        double r77488 = log(r77487);
        double r77489 = r77486 * r77488;
        double r77490 = z;
        double r77491 = r77489 + r77490;
        double r77492 = t;
        double r77493 = r77491 + r77492;
        double r77494 = a;
        double r77495 = r77493 + r77494;
        double r77496 = b;
        double r77497 = 0.5;
        double r77498 = r77496 - r77497;
        double r77499 = c;
        double r77500 = log(r77499);
        double r77501 = r77498 * r77500;
        double r77502 = r77495 + r77501;
        double r77503 = i;
        double r77504 = r77487 * r77503;
        double r77505 = r77502 + r77504;
        return r77505;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r77506 = 2.0;
        double r77507 = c;
        double r77508 = cbrt(r77507);
        double r77509 = cbrt(r77508);
        double r77510 = r77509 * r77509;
        double r77511 = r77510 * r77509;
        double r77512 = log(r77511);
        double r77513 = r77506 * r77512;
        double r77514 = b;
        double r77515 = 0.5;
        double r77516 = r77514 - r77515;
        double r77517 = r77513 * r77516;
        double r77518 = x;
        double r77519 = y;
        double r77520 = log(r77519);
        double r77521 = r77518 * r77520;
        double r77522 = z;
        double r77523 = r77521 + r77522;
        double r77524 = t;
        double r77525 = r77523 + r77524;
        double r77526 = a;
        double r77527 = r77525 + r77526;
        double r77528 = r77517 + r77527;
        double r77529 = log(r77508);
        double r77530 = r77529 * r77516;
        double r77531 = r77528 + r77530;
        double r77532 = i;
        double r77533 = r77519 * r77532;
        double r77534 = r77531 + r77533;
        return r77534;
}

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. Simplified0.1

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

  9. Applied add-cube-cbrt0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2020047 
(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)))