Average Error: 0.0 → 0.0
Time: 1.0s
Precision: 64
\[x + y \cdot \left(z - x\right)\]
↓
\[x + \left(y \cdot z + y \cdot \left(-x\right)\right)\]
x + y \cdot \left(z - x\right)
↓
x + \left(y \cdot z + y \cdot \left(-x\right)\right)
double f(double x, double y, double z) {
        double r1165 = x;
        double r1166 = y;
        double r1167 = z;
        double r1168 = r1167 - r1165;
        double r1169 = r1166 * r1168;
        double r1170 = r1165 + r1169;
        return r1170;
}
↓
double f(double x, double y, double z) {
        double r1171 = x;
        double r1172 = y;
        double r1173 = z;
        double r1174 = r1172 * r1173;
        double r1175 = -r1171;
        double r1176 = r1172 * r1175;
        double r1177 = r1174 + r1176;
        double r1178 = r1171 + r1177;
        return r1178;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020059 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))