Average Error: 0.1 → 0.1
Time: 16.3s
Precision: 64
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
↓
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
↓
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
double f(double x, double y, double z) {
        double r24277018 = x;
        double r24277019 = y;
        double r24277020 = r24277018 * r24277019;
        double r24277021 = z;
        double r24277022 = r24277021 * r24277021;
        double r24277023 = r24277020 + r24277022;
        double r24277024 = r24277023 + r24277022;
        double r24277025 = r24277024 + r24277022;
        return r24277025;
}
↓
double f(double x, double y, double z) {
        double r24277026 = x;
        double r24277027 = y;
        double r24277028 = r24277026 * r24277027;
        double r24277029 = z;
        double r24277030 = r24277029 * r24277029;
        double r24277031 = r24277028 + r24277030;
        double r24277032 = r24277031 + r24277030;
        double r24277033 = r24277032 + r24277030;
        return r24277033;
}

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

Derivation

  1. Initial program 0.1

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

  2. Final simplification0.1

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

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, A"

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

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