Average Error: 0.0 → 0.0
Time: 12.8s
Precision: 64
\[x \cdot y + z \cdot \left(1 - y\right)\]
↓
\[\mathsf{fma}\left(z, 1 - y, x \cdot y\right)\]
x \cdot y + z \cdot \left(1 - y\right)
↓
\mathsf{fma}\left(z, 1 - y, x \cdot y\right)
double f(double x, double y, double z) {
        double r33545182 = x;
        double r33545183 = y;
        double r33545184 = r33545182 * r33545183;
        double r33545185 = z;
        double r33545186 = 1.0;
        double r33545187 = r33545186 - r33545183;
        double r33545188 = r33545185 * r33545187;
        double r33545189 = r33545184 + r33545188;
        return r33545189;
}
↓
double f(double x, double y, double z) {
        double r33545190 = z;
        double r33545191 = 1.0;
        double r33545192 = y;
        double r33545193 = r33545191 - r33545192;
        double r33545194 = x;
        double r33545195 = r33545194 * r33545192;
        double r33545196 = fma(r33545190, r33545193, r33545195);
        return r33545196;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.0
Target0.0
Herbie0.0
\[z - \left(z - x\right) \cdot y\]

Derivation

  1. Initial program 0.0

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

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(1 \cdot z + x \cdot y\right) - z \cdot y}\]

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment:bezierClip from diagrams-lib-1.3.0.3"

  :herbie-target
  (- z (* (- z x) y))

  (+ (* x y) (* z (- 1.0 y))))