Average Error: 0.0 → 0.0
Time: 2.2s
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 r6227 = x;
        double r6228 = y;
        double r6229 = z;
        double r6230 = r6229 - r6227;
        double r6231 = r6228 * r6230;
        double r6232 = r6227 + r6231;
        return r6232;
}
↓
double f(double x, double y, double z) {
        double r6233 = x;
        double r6234 = z;
        double r6235 = y;
        double r6236 = r6234 * r6235;
        double r6237 = r6233 + r6236;
        double r6238 = -r6233;
        double r6239 = r6235 * r6238;
        double r6240 = r6237 + r6239;
        return r6240;
}

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 2020049 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))