Average Error: 0.1 → 0.1
Time: 10.3s
Precision: 64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[x - \left(\mathsf{fma}\left(\log y, y + 0.5, z\right) - y\right)\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
x - \left(\mathsf{fma}\left(\log y, y + 0.5, z\right) - y\right)
double f(double x, double y, double z) {
        double r381449 = x;
        double r381450 = y;
        double r381451 = 0.5;
        double r381452 = r381450 + r381451;
        double r381453 = log(r381450);
        double r381454 = r381452 * r381453;
        double r381455 = r381449 - r381454;
        double r381456 = r381455 + r381450;
        double r381457 = z;
        double r381458 = r381456 - r381457;
        return r381458;
}
↓
double f(double x, double y, double z) {
        double r381459 = x;
        double r381460 = y;
        double r381461 = log(r381460);
        double r381462 = 0.5;
        double r381463 = r381460 + r381462;
        double r381464 = z;
        double r381465 = fma(r381461, r381463, r381464);
        double r381466 = r381465 - r381460;
        double r381467 = r381459 - r381466;
        return r381467;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.1
Target0.1
Herbie0.1
\[\left(\left(y + x\right) - z\right) - \left(y + 0.5\right) \cdot \log y\]

Derivation

  1. Initial program 0.1

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2020002 +o rules:numerics
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"
  :precision binary64

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

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