Average Error: 0.0 → 0.0
Time: 3.4s
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 r14557 = x;
        double r14558 = y;
        double r14559 = z;
        double r14560 = r14559 - r14557;
        double r14561 = r14558 * r14560;
        double r14562 = r14557 + r14561;
        return r14562;
}
↓
double f(double x, double y, double z) {
        double r14563 = x;
        double r14564 = z;
        double r14565 = y;
        double r14566 = r14564 * r14565;
        double r14567 = r14563 + r14566;
        double r14568 = -r14563;
        double r14569 = r14568 * r14565;
        double r14570 = r14567 + r14569;
        return r14570;
}

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 2020065 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))