Average Error: 0.1 → 0.1
Time: 27.8s
Precision: 64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[x - \mathsf{fma}\left(\log y, y + 0.5, z - y\right)\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
x - \mathsf{fma}\left(\log y, y + 0.5, z - y\right)
double f(double x, double y, double z) {
        double r12213754 = x;
        double r12213755 = y;
        double r12213756 = 0.5;
        double r12213757 = r12213755 + r12213756;
        double r12213758 = log(r12213755);
        double r12213759 = r12213757 * r12213758;
        double r12213760 = r12213754 - r12213759;
        double r12213761 = r12213760 + r12213755;
        double r12213762 = z;
        double r12213763 = r12213761 - r12213762;
        return r12213763;
}
↓
double f(double x, double y, double z) {
        double r12213764 = x;
        double r12213765 = y;
        double r12213766 = log(r12213765);
        double r12213767 = 0.5;
        double r12213768 = r12213765 + r12213767;
        double r12213769 = z;
        double r12213770 = r12213769 - r12213765;
        double r12213771 = fma(r12213766, r12213768, r12213770);
        double r12213772 = r12213764 - r12213771;
        return r12213772;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019170 +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))