Average Error: 6.1 → 0.1
Time: 11.5s
Precision: 64
\[x + \frac{y \cdot y}{z}\]
↓
\[\mathsf{fma}\left(\frac{y}{z}, y, x\right)\]
x + \frac{y \cdot y}{z}
↓
\mathsf{fma}\left(\frac{y}{z}, y, x\right)
double f(double x, double y, double z) {
        double r39450523 = x;
        double r39450524 = y;
        double r39450525 = r39450524 * r39450524;
        double r39450526 = z;
        double r39450527 = r39450525 / r39450526;
        double r39450528 = r39450523 + r39450527;
        return r39450528;
}
↓
double f(double x, double y, double z) {
        double r39450529 = y;
        double r39450530 = z;
        double r39450531 = r39450529 / r39450530;
        double r39450532 = x;
        double r39450533 = fma(r39450531, r39450529, r39450532);
        return r39450533;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original6.1
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z}\]

Derivation

  1. Initial program 6.1

    \[x + \frac{y \cdot y}{z}\]

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y z)
  :name "Crypto.Random.Test:calculate from crypto-random-0.0.9"

  :herbie-target
  (+ x (* y (/ y z)))

  (+ x (/ (* y y) z)))