Average Error: 0.0 → 0.0
Time: 1.1s
Precision: 64
\[\left(1 - x\right) \cdot y + x \cdot z\]
↓
\[\mathsf{fma}\left(1 - x, y, x \cdot z\right)\]
\left(1 - x\right) \cdot y + x \cdot z
↓
\mathsf{fma}\left(1 - x, y, x \cdot z\right)
double f(double x, double y, double z) {
        double r511220 = 1.0;
        double r511221 = x;
        double r511222 = r511220 - r511221;
        double r511223 = y;
        double r511224 = r511222 * r511223;
        double r511225 = z;
        double r511226 = r511221 * r511225;
        double r511227 = r511224 + r511226;
        return r511227;
}
↓
double f(double x, double y, double z) {
        double r511228 = 1.0;
        double r511229 = x;
        double r511230 = r511228 - r511229;
        double r511231 = y;
        double r511232 = z;
        double r511233 = r511229 * r511232;
        double r511234 = fma(r511230, r511231, r511233);
        return r511234;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Color.HSV:lerp  from diagrams-contrib-1.3.0.5"
  :precision binary64

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

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