Average Error: 0.1 → 0.1
Time: 3.0s
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 r883941 = x;
        double r883942 = 3.0;
        double r883943 = r883941 * r883942;
        double r883944 = y;
        double r883945 = r883943 * r883944;
        double r883946 = z;
        double r883947 = r883945 - r883946;
        return r883947;
}
↓
double f(double x, double y, double z) {
        double r883948 = x;
        double r883949 = 3.0;
        double r883950 = y;
        double r883951 = r883949 * r883950;
        double r883952 = r883948 * r883951;
        double r883953 = z;
        double r883954 = r883952 - r883953;
        return r883954;
}

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 2020089 
(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))