Average Error: 45.1 → 0
Time: 4.2s
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 r3112067 = x;
        double r3112068 = y;
        double r3112069 = z;
        double r3112070 = fma(r3112067, r3112068, r3112069);
        double r3112071 = 1.0;
        double r3112072 = r3112067 * r3112068;
        double r3112073 = r3112072 + r3112069;
        double r3112074 = r3112071 + r3112073;
        double r3112075 = r3112070 - r3112074;
        return r3112075;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r3112076 = -1.0;
        return r3112076;
}

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 2019121 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1

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