Average Error: 45.4 → 0
Time: 4.1s
Precision: 64
\[\mathsf{fma}\left(x, y, z\right) - \left(1 + \left(x \cdot y + z\right)\right)\]
↓
\[-1\]
\mathsf{fma}\left(x, y, z\right) - \left(1 + \left(x \cdot y + z\right)\right)
↓
-1
double f(double x, double y, double z) {
        double r46838 = x;
        double r46839 = y;
        double r46840 = z;
        double r46841 = fma(r46838, r46839, r46840);
        double r46842 = 1.0;
        double r46843 = r46838 * r46839;
        double r46844 = r46843 + r46840;
        double r46845 = r46842 + r46844;
        double r46846 = r46841 - r46845;
        return r46846;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r46847 = 1.0;
        double r46848 = -r46847;
        return r46848;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original45.4
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 45.4

    \[\mathsf{fma}\left(x, y, z\right) - \left(1 + \left(x \cdot y + z\right)\right)\]

  2. Simplified0

    \[\leadsto \color{blue}{-1}\]

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2019212 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"
  :precision binary64

  :herbie-target
  -1

  (- (fma x y z) (+ 1 (+ (* x y) z))))