Average Error: 0.1 → 0.1
Time: 14.6s
Precision: 64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[\left(y + x\right) + \left(-\mathsf{fma}\left(y + 0.5, \log y, z\right)\right)\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
\left(y + x\right) + \left(-\mathsf{fma}\left(y + 0.5, \log y, z\right)\right)
double f(double x, double y, double z) {
        double r196009 = x;
        double r196010 = y;
        double r196011 = 0.5;
        double r196012 = r196010 + r196011;
        double r196013 = log(r196010);
        double r196014 = r196012 * r196013;
        double r196015 = r196009 - r196014;
        double r196016 = r196015 + r196010;
        double r196017 = z;
        double r196018 = r196016 - r196017;
        return r196018;
}
↓
double f(double x, double y, double z) {
        double r196019 = y;
        double r196020 = x;
        double r196021 = r196019 + r196020;
        double r196022 = 0.5;
        double r196023 = r196019 + r196022;
        double r196024 = log(r196019);
        double r196025 = z;
        double r196026 = fma(r196023, r196024, r196025);
        double r196027 = -r196026;
        double r196028 = r196021 + r196027;
        return r196028;
}

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

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

  4. Applied sub-neg0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019198 +o rules:numerics
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"

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

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