Average Error: 0.0 → 0.0
Time: 12.9s
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 r31416067 = 1.0;
        double r31416068 = x;
        double r31416069 = r31416067 - r31416068;
        double r31416070 = y;
        double r31416071 = r31416069 * r31416070;
        double r31416072 = z;
        double r31416073 = r31416068 * r31416072;
        double r31416074 = r31416071 + r31416073;
        return r31416074;
}
↓
double f(double x, double y, double z) {
        double r31416075 = x;
        double r31416076 = z;
        double r31416077 = y;
        double r31416078 = r31416076 - r31416077;
        double r31416079 = 1.0;
        double r31416080 = r31416079 * r31416077;
        double r31416081 = fma(r31416075, r31416078, r31416080);
        return r31416081;
}

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 2019179 +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)))