Average Error: 45.8 → 0
Time: 1.1s
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 r60572 = x;
        double r60573 = y;
        double r60574 = z;
        double r60575 = fma(r60572, r60573, r60574);
        double r60576 = 1.0;
        double r60577 = r60572 * r60573;
        double r60578 = r60577 + r60574;
        double r60579 = r60576 + r60578;
        double r60580 = r60575 - r60579;
        return r60580;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r60581 = 1.0;
        double r60582 = -r60581;
        return r60582;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original45.8
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 45.8

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2020002 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"
  :precision binary64

  :herbie-target
  -1

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