Average Error: 44.6 → 0
Time: 4.8s
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 r12680137 = x;
        double r12680138 = y;
        double r12680139 = z;
        double r12680140 = fma(r12680137, r12680138, r12680139);
        double r12680141 = 1.0;
        double r12680142 = r12680137 * r12680138;
        double r12680143 = r12680142 + r12680139;
        double r12680144 = r12680141 + r12680143;
        double r12680145 = r12680140 - r12680144;
        return r12680145;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r12680146 = -1.0;
        return r12680146;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original44.6
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 44.6

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2019125 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1

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