Average Error: 0.0 → 0.0
Time: 5.7s
Precision: 64
\[x \cdot y + z \cdot \left(1 - y\right)\]
↓
\[\mathsf{fma}\left(x, y, z \cdot \left(1 - y\right)\right)\]
x \cdot y + z \cdot \left(1 - y\right)
↓
\mathsf{fma}\left(x, y, z \cdot \left(1 - y\right)\right)
double f(double x, double y, double z) {
        double r517026 = x;
        double r517027 = y;
        double r517028 = r517026 * r517027;
        double r517029 = z;
        double r517030 = 1.0;
        double r517031 = r517030 - r517027;
        double r517032 = r517029 * r517031;
        double r517033 = r517028 + r517032;
        return r517033;
}
↓
double f(double x, double y, double z) {
        double r517034 = x;
        double r517035 = y;
        double r517036 = z;
        double r517037 = 1.0;
        double r517038 = r517037 - r517035;
        double r517039 = r517036 * r517038;
        double r517040 = fma(r517034, r517035, r517039);
        return r517040;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019209 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment:bezierClip from diagrams-lib-1.3.0.3"
  :precision binary64

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

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