Average Error: 0.1 → 0.1
Time: 14.3s
Precision: 64
\[x - \left(y \cdot 4\right) \cdot z\]
↓
\[\frac{x + \left(y \cdot 4\right) \cdot z}{\frac{x + \left(y \cdot 4\right) \cdot z}{x - \left(y \cdot 4\right) \cdot z}}\]
x - \left(y \cdot 4\right) \cdot z
↓
\frac{x + \left(y \cdot 4\right) \cdot z}{\frac{x + \left(y \cdot 4\right) \cdot z}{x - \left(y \cdot 4\right) \cdot z}}
double f(double x, double y, double z) {
        double r185393 = x;
        double r185394 = y;
        double r185395 = 4.0;
        double r185396 = r185394 * r185395;
        double r185397 = z;
        double r185398 = r185396 * r185397;
        double r185399 = r185393 - r185398;
        return r185399;
}
↓
double f(double x, double y, double z) {
        double r185400 = x;
        double r185401 = y;
        double r185402 = 4.0;
        double r185403 = r185401 * r185402;
        double r185404 = z;
        double r185405 = r185403 * r185404;
        double r185406 = r185400 + r185405;
        double r185407 = r185400 - r185405;
        double r185408 = r185406 / r185407;
        double r185409 = r185406 / r185408;
        return r185409;
}

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 0.1

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

  3. Applied flip--29.0

    \[\leadsto \color{blue}{\frac{x \cdot x - \left(\left(y \cdot 4\right) \cdot z\right) \cdot \left(\left(y \cdot 4\right) \cdot z\right)}{x + \left(y \cdot 4\right) \cdot z}}\]
  4. Using strategy rm

  5. Applied difference-of-squares29.0

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

  6. Applied associate-/l*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019198 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, A"
  (- x (* (* y 4.0) z)))