Average Error: 0.3 → 0.3
Time: 12.5s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot \log \left({t}^{\frac{1}{3}}\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot \log \left({t}^{\frac{1}{3}}\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r67537 = x;
        double r67538 = y;
        double r67539 = r67537 + r67538;
        double r67540 = log(r67539);
        double r67541 = z;
        double r67542 = log(r67541);
        double r67543 = r67540 + r67542;
        double r67544 = t;
        double r67545 = r67543 - r67544;
        double r67546 = a;
        double r67547 = 0.5;
        double r67548 = r67546 - r67547;
        double r67549 = log(r67544);
        double r67550 = r67548 * r67549;
        double r67551 = r67545 + r67550;
        return r67551;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r67552 = x;
        double r67553 = y;
        double r67554 = r67552 + r67553;
        double r67555 = log(r67554);
        double r67556 = z;
        double r67557 = log(r67556);
        double r67558 = r67555 + r67557;
        double r67559 = t;
        double r67560 = r67558 - r67559;
        double r67561 = a;
        double r67562 = 0.5;
        double r67563 = r67561 - r67562;
        double r67564 = 2.0;
        double r67565 = cbrt(r67559);
        double r67566 = log(r67565);
        double r67567 = r67564 * r67566;
        double r67568 = r67563 * r67567;
        double r67569 = 0.3333333333333333;
        double r67570 = pow(r67559, r67569);
        double r67571 = log(r67570);
        double r67572 = r67563 * r67571;
        double r67573 = r67568 + r67572;
        double r67574 = r67560 + r67573;
        return r67574;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.3

    \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.3

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

  4. Applied log-prod0.3

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

  5. Applied distribute-lft-in0.3

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

  6. Simplified0.3

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

  8. Applied pow1/30.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2020064 +o rules:numerics
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))