Average Error: 6.4 → 0.1
Time: 11.8s
Precision: 64
\[x + \frac{y \cdot y}{z}\]
↓
\[x + \frac{y}{\frac{z}{y}}\]
x + \frac{y \cdot y}{z}
↓
x + \frac{y}{\frac{z}{y}}
double f(double x, double y, double z) {
        double r542026 = x;
        double r542027 = y;
        double r542028 = r542027 * r542027;
        double r542029 = z;
        double r542030 = r542028 / r542029;
        double r542031 = r542026 + r542030;
        return r542031;
}
↓
double f(double x, double y, double z) {
        double r542032 = x;
        double r542033 = y;
        double r542034 = z;
        double r542035 = r542034 / r542033;
        double r542036 = r542033 / r542035;
        double r542037 = r542032 + r542036;
        return r542037;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.4
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z}\]

Derivation

  1. Initial program 6.4

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

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{z}, y, x\right)}\]
  3. Using strategy rm

  4. Applied fma-udef0.1

    \[\leadsto \color{blue}{\frac{y}{z} \cdot y + x}\]

  5. Simplified6.4

    \[\leadsto \color{blue}{\frac{{y}^{2}}{z}} + x\]
  6. Using strategy rm

  7. Applied sqr-pow6.4

    \[\leadsto \frac{\color{blue}{{y}^{\left(\frac{2}{2}\right)} \cdot {y}^{\left(\frac{2}{2}\right)}}}{z} + x\]

  8. Applied associate-/l*0.1

    \[\leadsto \color{blue}{\frac{{y}^{\left(\frac{2}{2}\right)}}{\frac{z}{{y}^{\left(\frac{2}{2}\right)}}}} + x\]

  9. Simplified0.1

    \[\leadsto \frac{{y}^{\left(\frac{2}{2}\right)}}{\color{blue}{\frac{z}{y}}} + x\]

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019303 +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)))