Average Error: 0.0 → 0.0
Time: 9.5s
Precision: 64
\[x + y \cdot \left(z - x\right)\]
↓
\[\left(x + z \cdot y\right) + \left(-x\right) \cdot y\]
x + y \cdot \left(z - x\right)
↓
\left(x + z \cdot y\right) + \left(-x\right) \cdot y
double f(double x, double y, double z) {
        double r14190 = x;
        double r14191 = y;
        double r14192 = z;
        double r14193 = r14192 - r14190;
        double r14194 = r14191 * r14193;
        double r14195 = r14190 + r14194;
        return r14195;
}
↓
double f(double x, double y, double z) {
        double r14196 = x;
        double r14197 = z;
        double r14198 = y;
        double r14199 = r14197 * r14198;
        double r14200 = r14196 + r14199;
        double r14201 = -r14196;
        double r14202 = r14201 * r14198;
        double r14203 = r14200 + r14202;
        return r14203;
}

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

Derivation

  1. Initial program 0.0

    \[x + y \cdot \left(z - x\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.0

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

  4. Applied distribute-rgt-in0.0

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

  5. Applied associate-+r+0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020045 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))