Average Error: 6.3 → 0.1
Time: 4.1s
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 r928382 = x;
        double r928383 = y;
        double r928384 = r928383 * r928383;
        double r928385 = z;
        double r928386 = r928384 / r928385;
        double r928387 = r928382 + r928386;
        return r928387;
}
↓
double f(double x, double y, double z) {
        double r928388 = y;
        double r928389 = z;
        double r928390 = r928388 / r928389;
        double r928391 = x;
        double r928392 = fma(r928390, r928388, r928391);
        return r928392;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original6.3
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z}\]

Derivation

  1. Initial program 6.3

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

  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 2020036 +o rules:numerics
(FPCore (x y z)
  :name "Crypto.Random.Test:calculate from crypto-random-0.0.9"
  :precision binary64

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

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