Average Error: 0.0 → 0.0
Time: 8.4s
Precision: 64
\[x + \left(y - x\right) \cdot z\]
↓
\[\mathsf{fma}\left(z, y - x, x\right)\]
x + \left(y - x\right) \cdot z
↓
\mathsf{fma}\left(z, y - x, x\right)
double f(double x, double y, double z) {
        double r7015542 = x;
        double r7015543 = y;
        double r7015544 = r7015543 - r7015542;
        double r7015545 = z;
        double r7015546 = r7015544 * r7015545;
        double r7015547 = r7015542 + r7015546;
        return r7015547;
}
↓
double f(double x, double y, double z) {
        double r7015548 = z;
        double r7015549 = y;
        double r7015550 = x;
        double r7015551 = r7015549 - r7015550;
        double r7015552 = fma(r7015548, r7015551, r7015550);
        return r7015552;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  (+ x (* (- y x) z)))