Average Error: 45.1 → 0
Time: 10.3s
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 r36331 = x;
        double r36332 = y;
        double r36333 = z;
        double r36334 = fma(r36331, r36332, r36333);
        double r36335 = 1.0;
        double r36336 = r36331 * r36332;
        double r36337 = r36336 + r36333;
        double r36338 = r36335 + r36337;
        double r36339 = r36334 - r36338;
        return r36339;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r36340 = 1.0;
        double r36341 = -r36340;
        return r36341;
}

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

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

  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))))