Average Error: 45.7 → 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 r57600 = x;
        double r57601 = y;
        double r57602 = z;
        double r57603 = fma(r57600, r57601, r57602);
        double r57604 = 1.0;
        double r57605 = r57600 * r57601;
        double r57606 = r57605 + r57602;
        double r57607 = r57604 + r57606;
        double r57608 = r57603 - r57607;
        return r57608;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r57609 = 1.0;
        double r57610 = -r57609;
        return r57610;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original45.7
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 45.7

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2020018 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"
  :precision binary64

  :herbie-target
  -1

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