Average Error: 0.0 → 0.0
Time: 10.0s
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 r15089 = x;
        double r15090 = y;
        double r15091 = z;
        double r15092 = r15091 - r15089;
        double r15093 = r15090 * r15092;
        double r15094 = r15089 + r15093;
        return r15094;
}
↓
double f(double x, double y, double z) {
        double r15095 = x;
        double r15096 = z;
        double r15097 = y;
        double r15098 = r15096 * r15097;
        double r15099 = r15095 + r15098;
        double r15100 = -r15095;
        double r15101 = r15097 * r15100;
        double r15102 = r15099 + r15101;
        return r15102;
}

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 2019350 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))