Average Error: 0.0 → 0.1
Time: 1.9s
Precision: 64
\[x - \left(y \cdot 4\right) \cdot z\]
↓
\[x - y \cdot \left(4 \cdot z\right)\]
x - \left(y \cdot 4\right) \cdot z
↓
x - y \cdot \left(4 \cdot z\right)
double f(double x, double y, double z) {
        double r221124 = x;
        double r221125 = y;
        double r221126 = 4.0;
        double r221127 = r221125 * r221126;
        double r221128 = z;
        double r221129 = r221127 * r221128;
        double r221130 = r221124 - r221129;
        return r221130;
}
↓
double f(double x, double y, double z) {
        double r221131 = x;
        double r221132 = y;
        double r221133 = 4.0;
        double r221134 = z;
        double r221135 = r221133 * r221134;
        double r221136 = r221132 * r221135;
        double r221137 = r221131 - r221136;
        return r221137;
}

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

    \[x - \left(y \cdot 4\right) \cdot z\]
  2. Using strategy rm

  3. Applied associate-*l*0.1

    \[\leadsto x - \color{blue}{y \cdot \left(4 \cdot z\right)}\]

  4. Final simplification0.1

    \[\leadsto x - y \cdot \left(4 \cdot z\right)\]

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, A"
  :precision binary64
  (- x (* (* y 4) z)))