Average Error: 0.1 → 0.1
Time: 11.9s
Precision: 64
\[\left(x \cdot 3\right) \cdot y - z\]
↓
\[x \cdot \left(3 \cdot y\right) - z\]
\left(x \cdot 3\right) \cdot y - z
↓
x \cdot \left(3 \cdot y\right) - z
double f(double x, double y, double z) {
        double r824169 = x;
        double r824170 = 3.0;
        double r824171 = r824169 * r824170;
        double r824172 = y;
        double r824173 = r824171 * r824172;
        double r824174 = z;
        double r824175 = r824173 - r824174;
        return r824175;
}
↓
double f(double x, double y, double z) {
        double r824176 = x;
        double r824177 = 3.0;
        double r824178 = y;
        double r824179 = r824177 * r824178;
        double r824180 = r824176 * r824179;
        double r824181 = z;
        double r824182 = r824180 - r824181;
        return r824182;
}

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

Target

Original0.1
Target0.1
Herbie0.1
\[x \cdot \left(3 \cdot y\right) - z\]

Derivation

  1. Initial program 0.1

    \[\left(x \cdot 3\right) \cdot y - z\]
  2. Using strategy rm

  3. Applied associate-*l*0.1

    \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right)} - z\]

  4. Final simplification0.1

    \[\leadsto x \cdot \left(3 \cdot y\right) - z\]

Reproduce

herbie shell --seed 2019209 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (- (* x (* 3 y)) z)

  (- (* (* x 3) y) z))