Average Error: 45.2 → 0
Time: 4.3s
Precision: 64
\[(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
↓
\[-1\]
double f(double x, double y, double z) {
        double r5679825 = x;
        double r5679826 = y;
        double r5679827 = z;
        double r5679828 = fma(r5679825, r5679826, r5679827);
        double r5679829 = 1.0;
        double r5679830 = r5679825 * r5679826;
        double r5679831 = r5679830 + r5679827;
        double r5679832 = r5679829 + r5679831;
        double r5679833 = r5679828 - r5679832;
        return r5679833;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r5679834 = -1.0;
        return r5679834;
}


(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)
↓
-1

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original45.2
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 45.2

    \[(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2019101 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1

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