Average Error: 0.0 → 0.0
Time: 2.4s
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 r544063 = x;
        double r544064 = y;
        double r544065 = r544063 * r544064;
        double r544066 = z;
        double r544067 = 1.0;
        double r544068 = r544067 - r544064;
        double r544069 = r544066 * r544068;
        double r544070 = r544065 + r544069;
        return r544070;
}
↓
double f(double x, double y, double z) {
        double r544071 = x;
        double r544072 = y;
        double r544073 = z;
        double r544074 = 1.0;
        double r544075 = r544074 - r544072;
        double r544076 = r544073 * r544075;
        double r544077 = fma(r544071, r544072, r544076);
        return r544077;
}

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 2019351 +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))))