Average Error: 0.1 → 0.2
Time: 3.0s
Precision: binary64
\[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z\]
↓
\[\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \left(\sqrt[3]{\sqrt{3}} \cdot \left(\sqrt[3]{\sqrt{3}} \cdot \left(z \cdot z\right)\right)\right) + x \cdot y\]
\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z
↓
\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \left(\sqrt[3]{\sqrt{3}} \cdot \left(\sqrt[3]{\sqrt{3}} \cdot \left(z \cdot z\right)\right)\right) + x \cdot y
double code(double x, double y, double z) {
	return ((double) (((double) (((double) (((double) (x * y)) + ((double) (z * z)))) + ((double) (z * z)))) + ((double) (z * z))));
}
↓
double code(double x, double y, double z) {
	return ((double) (((double) (((double) (((double) cbrt(3.0)) * ((double) cbrt(3.0)))) * ((double) (((double) cbrt(((double) sqrt(3.0)))) * ((double) (((double) cbrt(((double) sqrt(3.0)))) * ((double) (z * z)))))))) + ((double) (x * y))));
}

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
Herbie0.2
\[\left(3 \cdot z\right) \cdot z + y \cdot x\]

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 add-cube-cbrt0.1

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

  5. Applied associate-*l*0.2

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

  7. Applied add-sqr-sqrt0.2

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

  8. Applied cbrt-prod0.2

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

  9. Applied associate-*l*0.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2020161 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (+ (* (* 3.0 z) z) (* y x))

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