Average Error: 0.0 → 0.0
Time: 13.5s
Precision: 64
\[\left(1 - x\right) \cdot y + x \cdot z\]
↓
\[\mathsf{fma}\left(x, z - y, 1 \cdot y\right)\]
\left(1 - x\right) \cdot y + x \cdot z
↓
\mathsf{fma}\left(x, z - y, 1 \cdot y\right)
double f(double x, double y, double z) {
        double r32505661 = 1.0;
        double r32505662 = x;
        double r32505663 = r32505661 - r32505662;
        double r32505664 = y;
        double r32505665 = r32505663 * r32505664;
        double r32505666 = z;
        double r32505667 = r32505662 * r32505666;
        double r32505668 = r32505665 + r32505667;
        return r32505668;
}
↓
double f(double x, double y, double z) {
        double r32505669 = x;
        double r32505670 = z;
        double r32505671 = y;
        double r32505672 = r32505670 - r32505671;
        double r32505673 = 1.0;
        double r32505674 = r32505673 * r32505671;
        double r32505675 = fma(r32505669, r32505672, r32505674);
        return r32505675;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

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

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Color.HSV:lerp  from diagrams-contrib-1.3.0.5"

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

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