Average Error: 0.1 → 0.1
Time: 25.9s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(y \cdot i + \left(b - 0.5\right) \cdot \left(\log \left({\left(\frac{1}{c}\right)}^{\frac{-1}{3}}\right) + 2 \cdot \log \left(\sqrt[3]{c}\right)\right)\right) + \left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right)\]
\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(y \cdot i + \left(b - 0.5\right) \cdot \left(\log \left({\left(\frac{1}{c}\right)}^{\frac{-1}{3}}\right) + 2 \cdot \log \left(\sqrt[3]{c}\right)\right)\right) + \left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r64550 = x;
        double r64551 = y;
        double r64552 = log(r64551);
        double r64553 = r64550 * r64552;
        double r64554 = z;
        double r64555 = r64553 + r64554;
        double r64556 = t;
        double r64557 = r64555 + r64556;
        double r64558 = a;
        double r64559 = r64557 + r64558;
        double r64560 = b;
        double r64561 = 0.5;
        double r64562 = r64560 - r64561;
        double r64563 = c;
        double r64564 = log(r64563);
        double r64565 = r64562 * r64564;
        double r64566 = r64559 + r64565;
        double r64567 = i;
        double r64568 = r64551 * r64567;
        double r64569 = r64566 + r64568;
        return r64569;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r64570 = y;
        double r64571 = i;
        double r64572 = r64570 * r64571;
        double r64573 = b;
        double r64574 = 0.5;
        double r64575 = r64573 - r64574;
        double r64576 = 1.0;
        double r64577 = c;
        double r64578 = r64576 / r64577;
        double r64579 = -0.3333333333333333;
        double r64580 = pow(r64578, r64579);
        double r64581 = log(r64580);
        double r64582 = 2.0;
        double r64583 = cbrt(r64577);
        double r64584 = log(r64583);
        double r64585 = r64582 * r64584;
        double r64586 = r64581 + r64585;
        double r64587 = r64575 * r64586;
        double r64588 = r64572 + r64587;
        double r64589 = x;
        double r64590 = log(r64570);
        double r64591 = r64589 * r64590;
        double r64592 = z;
        double r64593 = r64591 + r64592;
        double r64594 = t;
        double r64595 = r64593 + r64594;
        double r64596 = a;
        double r64597 = r64595 + r64596;
        double r64598 = r64588 + r64597;
        return r64598;
}

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. Applied associate-+r+0.1

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

  7. Simplified0.1

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

  8. Taylor expanded around inf 0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019298 
(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)))