Average Error: 0.0 → 0.0
Time: 10.9s
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 r7266578 = x;
        double r7266579 = y;
        double r7266580 = r7266579 - r7266578;
        double r7266581 = z;
        double r7266582 = r7266580 * r7266581;
        double r7266583 = r7266578 + r7266582;
        return r7266583;
}
↓
double f(double x, double y, double z) {
        double r7266584 = z;
        double r7266585 = y;
        double r7266586 = x;
        double r7266587 = r7266585 - r7266586;
        double r7266588 = fma(r7266584, r7266587, r7266586);
        return r7266588;
}

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 2019174 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  (+ x (* (- y x) z)))