Average Error: 0.0 → 0.0
Time: 897.0ms
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 r183199 = x;
        double r183200 = y;
        double r183201 = r183200 - r183199;
        double r183202 = z;
        double r183203 = r183201 * r183202;
        double r183204 = r183199 + r183203;
        return r183204;
}
↓
double f(double x, double y, double z) {
        double r183205 = z;
        double r183206 = y;
        double r183207 = x;
        double r183208 = r183206 - r183207;
        double r183209 = fma(r183205, r183208, r183207);
        return r183209;
}

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 2020033 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))