Average Error: 0.1 → 0.1
Time: 21.9s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(y + \mathsf{fma}\left(b, a - 0.5, x\right)\right) + \left(1 - \log t\right) \cdot z\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(y + \mathsf{fma}\left(b, a - 0.5, x\right)\right) + \left(1 - \log t\right) \cdot z
double f(double x, double y, double z, double t, double a, double b) {
        double r18043373 = x;
        double r18043374 = y;
        double r18043375 = r18043373 + r18043374;
        double r18043376 = z;
        double r18043377 = r18043375 + r18043376;
        double r18043378 = t;
        double r18043379 = log(r18043378);
        double r18043380 = r18043376 * r18043379;
        double r18043381 = r18043377 - r18043380;
        double r18043382 = a;
        double r18043383 = 0.5;
        double r18043384 = r18043382 - r18043383;
        double r18043385 = b;
        double r18043386 = r18043384 * r18043385;
        double r18043387 = r18043381 + r18043386;
        return r18043387;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r18043388 = y;
        double r18043389 = b;
        double r18043390 = a;
        double r18043391 = 0.5;
        double r18043392 = r18043390 - r18043391;
        double r18043393 = x;
        double r18043394 = fma(r18043389, r18043392, r18043393);
        double r18043395 = r18043388 + r18043394;
        double r18043396 = 1.0;
        double r18043397 = t;
        double r18043398 = log(r18043397);
        double r18043399 = r18043396 - r18043398;
        double r18043400 = z;
        double r18043401 = r18043399 * r18043400;
        double r18043402 = r18043395 + r18043401;
        return r18043402;
}

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

Target

Original0.1
Target0.4
Herbie0.1
\[\left(\left(x + y\right) + \frac{\left(1 - {\left(\log t\right)}^{2}\right) \cdot z}{1 + \log t}\right) + \left(a - 0.5\right) \cdot b\]

Derivation

  1. Initial program 0.1

    \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(1 - \log t, z, \mathsf{fma}\left(b, a - 0.5, x\right) + y\right)}\]
  3. Using strategy rm

  4. Applied fma-udef0.1

    \[\leadsto \color{blue}{\left(1 - \log t\right) \cdot z + \left(\mathsf{fma}\left(b, a - 0.5, x\right) + y\right)}\]

  5. Final simplification0.1

    \[\leadsto \left(y + \mathsf{fma}\left(b, a - 0.5, x\right)\right) + \left(1 - \log t\right) \cdot z\]

Reproduce

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

  :herbie-target
  (+ (+ (+ x y) (/ (* (- 1.0 (pow (log t) 2.0)) z) (+ 1.0 (log t)))) (* (- a 0.5) b))

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