Average Error: 0.3 → 0.3
Time: 1.1m
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log t \cdot \left(a - 0.5\right) + \left(\left(\left(\log z + \log \left(\sqrt{y + x}\right)\right) + \log \left(\sqrt{y + x}\right)\right) - t\right)\]
double f(double x, double y, double z, double t, double a) {
        double r4346537 = x;
        double r4346538 = y;
        double r4346539 = r4346537 + r4346538;
        double r4346540 = log(r4346539);
        double r4346541 = z;
        double r4346542 = log(r4346541);
        double r4346543 = r4346540 + r4346542;
        double r4346544 = t;
        double r4346545 = r4346543 - r4346544;
        double r4346546 = a;
        double r4346547 = 0.5;
        double r4346548 = r4346546 - r4346547;
        double r4346549 = log(r4346544);
        double r4346550 = r4346548 * r4346549;
        double r4346551 = r4346545 + r4346550;
        return r4346551;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r4346552 = t;
        double r4346553 = log(r4346552);
        double r4346554 = a;
        double r4346555 = 0.5;
        double r4346556 = r4346554 - r4346555;
        double r4346557 = r4346553 * r4346556;
        double r4346558 = z;
        double r4346559 = log(r4346558);
        double r4346560 = y;
        double r4346561 = x;
        double r4346562 = r4346560 + r4346561;
        double r4346563 = sqrt(r4346562);
        double r4346564 = log(r4346563);
        double r4346565 = r4346559 + r4346564;
        double r4346566 = r4346565 + r4346564;
        double r4346567 = r4346566 - r4346552;
        double r4346568 = r4346557 + r4346567;
        return r4346568;
}


\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log t \cdot \left(a - 0.5\right) + \left(\left(\left(\log z + \log \left(\sqrt{y + x}\right)\right) + \log \left(\sqrt{y + x}\right)\right) - t\right)

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

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-sqr-sqrt0.3

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

  4. Applied log-prod0.3

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

  5. Applied associate-+l+0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019102 +o rules:numerics
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))