Average Error: 0.2 → 0.1
Time: 20.1s
Precision: 64
\[\left(x \cdot 3\right) \cdot y - z\]
↓
\[x \cdot \left(y \cdot 3\right) - z\]
\left(x \cdot 3\right) \cdot y - z
↓
x \cdot \left(y \cdot 3\right) - z
double f(double x, double y, double z) {
        double r500148 = x;
        double r500149 = 3.0;
        double r500150 = r500148 * r500149;
        double r500151 = y;
        double r500152 = r500150 * r500151;
        double r500153 = z;
        double r500154 = r500152 - r500153;
        return r500154;
}
↓
double f(double x, double y, double z) {
        double r500155 = x;
        double r500156 = y;
        double r500157 = 3.0;
        double r500158 = r500156 * r500157;
        double r500159 = r500155 * r500158;
        double r500160 = z;
        double r500161 = r500159 - r500160;
        return r500161;
}

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

Original0.2
Target0.1
Herbie0.1
\[x \cdot \left(3 \cdot y\right) - z\]

Derivation

  1. Initial program 0.2

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

  3. Applied associate-*l*0.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019323 
(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))