Average Error: 44.9 → 0
Time: 1.9s
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 r62454 = x;
        double r62455 = y;
        double r62456 = z;
        double r62457 = fma(r62454, r62455, r62456);
        double r62458 = 1.0;
        double r62459 = r62454 * r62455;
        double r62460 = r62459 + r62456;
        double r62461 = r62458 + r62460;
        double r62462 = r62457 - r62461;
        return r62462;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r62463 = 1.0;
        double r62464 = -r62463;
        return r62464;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original44.9
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 44.9

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2020083 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"
  :precision binary64

  :herbie-target
  -1

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