Average Error: 0.0 → 0.0
Time: 18.8s
Precision: 64
\[x \cdot y + z \cdot \left(1.0 - y\right)\]
↓
\[\mathsf{fma}\left(x, y, \left(1.0 - y\right) \cdot z\right)\]
x \cdot y + z \cdot \left(1.0 - y\right)
↓
\mathsf{fma}\left(x, y, \left(1.0 - y\right) \cdot z\right)
double f(double x, double y, double z) {
        double r23025004 = x;
        double r23025005 = y;
        double r23025006 = r23025004 * r23025005;
        double r23025007 = z;
        double r23025008 = 1.0;
        double r23025009 = r23025008 - r23025005;
        double r23025010 = r23025007 * r23025009;
        double r23025011 = r23025006 + r23025010;
        return r23025011;
}
↓
double f(double x, double y, double z) {
        double r23025012 = x;
        double r23025013 = y;
        double r23025014 = 1.0;
        double r23025015 = r23025014 - r23025013;
        double r23025016 = z;
        double r23025017 = r23025015 * r23025016;
        double r23025018 = fma(r23025012, r23025013, r23025017);
        return r23025018;
}

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

    \[x \cdot y + z \cdot \left(1.0 - y\right)\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \left(1.0 - y\right) \cdot z\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, y, \left(1.0 - y\right) \cdot z\right)\]

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment:bezierClip from diagrams-lib-1.3.0.3"

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

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