Average Error: 0.1 → 0.1
Time: 13.9s
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 r781473 = x;
        double r781474 = 3.0;
        double r781475 = r781473 * r781474;
        double r781476 = y;
        double r781477 = r781475 * r781476;
        double r781478 = z;
        double r781479 = r781477 - r781478;
        return r781479;
}
↓
double f(double x, double y, double z) {
        double r781480 = 3.0;
        double r781481 = x;
        double r781482 = y;
        double r781483 = r781481 * r781482;
        double r781484 = r781480 * r781483;
        double r781485 = z;
        double r781486 = r781484 - r781485;
        return r781486;
}

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 2019350 
(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))