Average Error: 0.1 → 0.1
Time: 9.8s
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 r620133 = x;
        double r620134 = 3.0;
        double r620135 = r620133 * r620134;
        double r620136 = y;
        double r620137 = r620135 * r620136;
        double r620138 = z;
        double r620139 = r620137 - r620138;
        return r620139;
}
↓
double f(double x, double y, double z) {
        double r620140 = 3.0;
        double r620141 = x;
        double r620142 = y;
        double r620143 = r620141 * r620142;
        double r620144 = r620140 * r620143;
        double r620145 = z;
        double r620146 = r620144 - r620145;
        return r620146;
}

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
Target0.2
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 2019198 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, B"

  :herbie-target
  (- (* x (* 3.0 y)) z)

  (- (* (* x 3.0) y) z))