Average Error: 0.1 → 0.1
Time: 11.2s
Precision: 64
\[\left(x \cdot 3\right) \cdot y - z\]
↓
\[3 \cdot \left(x \cdot y\right) - z\]
\left(x \cdot 3\right) \cdot y - z
↓
3 \cdot \left(x \cdot y\right) - z
double f(double x, double y, double z) {
        double r642118 = x;
        double r642119 = 3.0;
        double r642120 = r642118 * r642119;
        double r642121 = y;
        double r642122 = r642120 * r642121;
        double r642123 = z;
        double r642124 = r642122 - r642123;
        return r642124;
}
↓
double f(double x, double y, double z) {
        double r642125 = 3.0;
        double r642126 = x;
        double r642127 = y;
        double r642128 = r642126 * r642127;
        double r642129 = r642125 * r642128;
        double r642130 = z;
        double r642131 = r642129 - r642130;
        return r642131;
}

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. Taylor expanded around 0 0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2020045 
(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))