Average Error: 0.3 → 0.3
Time: 34.0s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\mathsf{fma}\left(\log t, a - 0.5, \left(\left(-t\right) + \log z\right) + \log \left(y + x\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\mathsf{fma}\left(\log t, a - 0.5, \left(\left(-t\right) + \log z\right) + \log \left(y + x\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r14636364 = x;
        double r14636365 = y;
        double r14636366 = r14636364 + r14636365;
        double r14636367 = log(r14636366);
        double r14636368 = z;
        double r14636369 = log(r14636368);
        double r14636370 = r14636367 + r14636369;
        double r14636371 = t;
        double r14636372 = r14636370 - r14636371;
        double r14636373 = a;
        double r14636374 = 0.5;
        double r14636375 = r14636373 - r14636374;
        double r14636376 = log(r14636371);
        double r14636377 = r14636375 * r14636376;
        double r14636378 = r14636372 + r14636377;
        return r14636378;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r14636379 = t;
        double r14636380 = log(r14636379);
        double r14636381 = a;
        double r14636382 = 0.5;
        double r14636383 = r14636381 - r14636382;
        double r14636384 = -r14636379;
        double r14636385 = z;
        double r14636386 = log(r14636385);
        double r14636387 = r14636384 + r14636386;
        double r14636388 = y;
        double r14636389 = x;
        double r14636390 = r14636388 + r14636389;
        double r14636391 = log(r14636390);
        double r14636392 = r14636387 + r14636391;
        double r14636393 = fma(r14636380, r14636383, r14636392);
        return r14636393;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original0.3
Target0.3
Herbie0.3
\[\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]

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. Simplified0.3

    \[\leadsto \color{blue}{\mathsf{fma}\left(\log t, a - 0.5, \log \left(y + x\right) + \left(\log z - t\right)\right)}\]
  3. Using strategy rm

  4. Applied sub-neg0.3

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

  5. Final simplification0.3

    \[\leadsto \mathsf{fma}\left(\log t, a - 0.5, \left(\left(-t\right) + \log z\right) + \log \left(y + x\right)\right)\]

Reproduce

herbie shell --seed 2019192 +o rules:numerics
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"

  :herbie-target
  (+ (log (+ x y)) (+ (- (log z) t) (* (- a 0.5) (log t))))

  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))