Average Error: 0.0 → 0.0
Time: 13.2s
Precision: 64
\[x + y \cdot \left(z + x\right)\]
↓
\[\mathsf{fma}\left(y, z + x, x\right)\]
x + y \cdot \left(z + x\right)
↓
\mathsf{fma}\left(y, z + x, x\right)
double f(double x, double y, double z) {
        double r8968524 = x;
        double r8968525 = y;
        double r8968526 = z;
        double r8968527 = r8968526 + r8968524;
        double r8968528 = r8968525 * r8968527;
        double r8968529 = r8968524 + r8968528;
        return r8968529;
}
↓
double f(double x, double y, double z) {
        double r8968530 = y;
        double r8968531 = z;
        double r8968532 = x;
        double r8968533 = r8968531 + r8968532;
        double r8968534 = fma(r8968530, r8968533, r8968532);
        return r8968534;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  (+ x (* y (+ z x))))