Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B

Average Error: 0.0 → 0.0

Time: 11.5s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z) {
        double r9047956 = x;
        double r9047957 = y;
        double r9047958 = r9047957 - r9047956;
        double r9047959 = z;
        double r9047960 = r9047958 * r9047959;
        double r9047961 = r9047956 + r9047960;
        return r9047961;
}

↓

double f(double x, double y, double z) {
        double r9047962 = y;
        double r9047963 = x;
        double r9047964 = r9047962 - r9047963;
        double r9047965 = z;
        double r9047966 = fma(r9047964, r9047965, r9047963);
        return r9047966;
}

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. Simplified 0.0

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

3. Final simplification 0.0

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  (+ x (* (- y x) z)))