Average Error: 0.0 → 0.0
Time: 12.3s
Precision: 64
\[x \cdot y + z \cdot \left(1 - y\right)\]
↓
\[\mathsf{fma}\left(x, y, \left(1 - y\right) \cdot z\right)\]
x \cdot y + z \cdot \left(1 - y\right)
↓
\mathsf{fma}\left(x, y, \left(1 - y\right) \cdot z\right)
double f(double x, double y, double z) {
        double r28740234 = x;
        double r28740235 = y;
        double r28740236 = r28740234 * r28740235;
        double r28740237 = z;
        double r28740238 = 1.0;
        double r28740239 = r28740238 - r28740235;
        double r28740240 = r28740237 * r28740239;
        double r28740241 = r28740236 + r28740240;
        return r28740241;
}
↓
double f(double x, double y, double z) {
        double r28740242 = x;
        double r28740243 = y;
        double r28740244 = 1.0;
        double r28740245 = r28740244 - r28740243;
        double r28740246 = z;
        double r28740247 = r28740245 * r28740246;
        double r28740248 = fma(r28740242, r28740243, r28740247);
        return r28740248;
}

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

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

Reproduce

herbie shell --seed 2019192 +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))))