Average Error: 0.0 → 0.0
Time: 12.7s
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 r17418497 = x;
        double r17418498 = y;
        double r17418499 = r17418497 * r17418498;
        double r17418500 = z;
        double r17418501 = 1.0;
        double r17418502 = r17418501 - r17418498;
        double r17418503 = r17418500 * r17418502;
        double r17418504 = r17418499 + r17418503;
        return r17418504;
}
↓
double f(double x, double y, double z) {
        double r17418505 = x;
        double r17418506 = y;
        double r17418507 = 1.0;
        double r17418508 = r17418507 - r17418506;
        double r17418509 = z;
        double r17418510 = r17418508 * r17418509;
        double r17418511 = fma(r17418505, r17418506, r17418510);
        return r17418511;
}

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))))