Average Error: 0.1 → 0.1
Time: 2.5s
Precision: 64
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
↓
\[\left(3 \cdot z\right) \cdot z + x \cdot y\]
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
↓
\left(3 \cdot z\right) \cdot z + x \cdot y
double f(double x, double y, double z) {
        double r566719 = x;
        double r566720 = y;
        double r566721 = r566719 * r566720;
        double r566722 = z;
        double r566723 = r566722 * r566722;
        double r566724 = r566721 + r566723;
        double r566725 = r566724 + r566723;
        double r566726 = r566725 + r566723;
        return r566726;
}
↓
double f(double x, double y, double z) {
        double r566727 = 3.0;
        double r566728 = z;
        double r566729 = r566727 * r566728;
        double r566730 = r566729 * r566728;
        double r566731 = x;
        double r566732 = y;
        double r566733 = r566731 * r566732;
        double r566734 = r566730 + r566733;
        return r566734;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 0.1

    \[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]

  2. Simplified0.1

    \[\leadsto \color{blue}{3 \cdot \left(z \cdot z\right) + x \cdot y}\]
  3. Using strategy rm

  4. Applied associate-*r*0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020036 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (+ (* (* 3 z) z) (* y x))

  (+ (+ (+ (* x y) (* z z)) (* z z)) (* z z)))