Average Error: 45.1 → 0
Time: 32.0s
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 r60373 = x;
        double r60374 = y;
        double r60375 = z;
        double r60376 = fma(r60373, r60374, r60375);
        double r60377 = 1.0;
        double r60378 = r60373 * r60374;
        double r60379 = r60378 + r60375;
        double r60380 = r60377 + r60379;
        double r60381 = r60376 - r60380;
        return r60381;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r60382 = 1.0;
        double r60383 = -r60382;
        return r60383;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original45.1
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 45.1

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

  2. Simplified0

    \[\leadsto \color{blue}{0 - 1}\]

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"
  :precision binary64

  :herbie-target
  -1

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