Average Error: 0.0 → 0.0
Time: 14.2s
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 r33827947 = x;
        double r33827948 = y;
        double r33827949 = r33827947 * r33827948;
        double r33827950 = z;
        double r33827951 = 1.0;
        double r33827952 = r33827951 - r33827948;
        double r33827953 = r33827950 * r33827952;
        double r33827954 = r33827949 + r33827953;
        return r33827954;
}
↓
double f(double x, double y, double z) {
        double r33827955 = x;
        double r33827956 = y;
        double r33827957 = 1.0;
        double r33827958 = r33827957 - r33827956;
        double r33827959 = z;
        double r33827960 = r33827958 * r33827959;
        double r33827961 = fma(r33827955, r33827956, r33827960);
        return r33827961;
}

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 2019163 +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))))