Average Error: 0.0 → 0.0
Time: 2.4s
Precision: 64
\[x + y \cdot \left(z - x\right)\]
↓
\[\left(x + z \cdot y\right) + y \cdot \left(-x\right)\]
x + y \cdot \left(z - x\right)
↓
\left(x + z \cdot y\right) + y \cdot \left(-x\right)
double f(double x, double y, double z) {
        double r12293 = x;
        double r12294 = y;
        double r12295 = z;
        double r12296 = r12295 - r12293;
        double r12297 = r12294 * r12296;
        double r12298 = r12293 + r12297;
        return r12298;
}
↓
double f(double x, double y, double z) {
        double r12299 = x;
        double r12300 = z;
        double r12301 = y;
        double r12302 = r12300 * r12301;
        double r12303 = r12299 + r12302;
        double r12304 = -r12299;
        double r12305 = r12301 * r12304;
        double r12306 = r12303 + r12305;
        return r12306;
}

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-lft-in0.0

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

  5. Applied associate-+r+0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019322 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))