Average Error: 0.0 → 0.0
Time: 12.5s
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 r26470229 = x;
        double r26470230 = y;
        double r26470231 = r26470230 - r26470229;
        double r26470232 = z;
        double r26470233 = r26470231 * r26470232;
        double r26470234 = r26470229 + r26470233;
        return r26470234;
}
↓
double f(double x, double y, double z) {
        double r26470235 = z;
        double r26470236 = y;
        double r26470237 = x;
        double r26470238 = r26470236 - r26470237;
        double r26470239 = fma(r26470235, r26470238, r26470237);
        return r26470239;
}

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 2019173 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  (+ x (* (- y x) z)))