Average Error: 0.0 → 0.0
Time: 18.9s
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 r29134434 = x;
        double r29134435 = y;
        double r29134436 = r29134434 * r29134435;
        double r29134437 = z;
        double r29134438 = 1.0;
        double r29134439 = r29134438 - r29134435;
        double r29134440 = r29134437 * r29134439;
        double r29134441 = r29134436 + r29134440;
        return r29134441;
}
↓
double f(double x, double y, double z) {
        double r29134442 = x;
        double r29134443 = y;
        double r29134444 = 1.0;
        double r29134445 = r29134444 - r29134443;
        double r29134446 = z;
        double r29134447 = r29134445 * r29134446;
        double r29134448 = fma(r29134442, r29134443, r29134447);
        return r29134448;
}

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 2019168 +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))))