Average Error: 0.1 → 0.1
Time: 10.9s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left({y}^{\frac{1}{3}}\right)\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i
↓
\left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left({y}^{\frac{1}{3}}\right)\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r81457 = x;
        double r81458 = y;
        double r81459 = log(r81458);
        double r81460 = r81457 * r81459;
        double r81461 = z;
        double r81462 = r81460 + r81461;
        double r81463 = t;
        double r81464 = r81462 + r81463;
        double r81465 = a;
        double r81466 = r81464 + r81465;
        double r81467 = b;
        double r81468 = 0.5;
        double r81469 = r81467 - r81468;
        double r81470 = c;
        double r81471 = log(r81470);
        double r81472 = r81469 * r81471;
        double r81473 = r81466 + r81472;
        double r81474 = i;
        double r81475 = r81458 * r81474;
        double r81476 = r81473 + r81475;
        return r81476;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r81477 = x;
        double r81478 = 2.0;
        double r81479 = y;
        double r81480 = cbrt(r81479);
        double r81481 = log(r81480);
        double r81482 = r81478 * r81481;
        double r81483 = r81477 * r81482;
        double r81484 = 0.3333333333333333;
        double r81485 = pow(r81479, r81484);
        double r81486 = log(r81485);
        double r81487 = r81477 * r81486;
        double r81488 = r81483 + r81487;
        double r81489 = z;
        double r81490 = r81488 + r81489;
        double r81491 = t;
        double r81492 = r81490 + r81491;
        double r81493 = a;
        double r81494 = r81492 + r81493;
        double r81495 = b;
        double r81496 = 0.5;
        double r81497 = r81495 - r81496;
        double r81498 = c;
        double r81499 = log(r81498);
        double r81500 = r81497 * r81499;
        double r81501 = r81494 + r81500;
        double r81502 = i;
        double r81503 = r81479 * r81502;
        double r81504 = r81501 + r81503;
        return r81504;
}

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

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Simplified0.1

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

  8. Applied pow1/30.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020060 
(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)))