Average Error: 0.0 → 0.1
Time: 1.8s
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 r181537 = x;
        double r181538 = y;
        double r181539 = 4.0;
        double r181540 = r181538 * r181539;
        double r181541 = z;
        double r181542 = r181540 * r181541;
        double r181543 = r181537 - r181542;
        return r181543;
}
↓
double f(double x, double y, double z) {
        double r181544 = x;
        double r181545 = y;
        double r181546 = 4.0;
        double r181547 = z;
        double r181548 = r181546 * r181547;
        double r181549 = r181545 * r181548;
        double r181550 = r181544 - r181549;
        return r181550;
}

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)))