Average Error: 0.5 → 0.4
Time: 15.0s
Precision: 64
\[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]
↓
\[\mathsf{fma}\left(\frac{3}{\mathsf{fma}\left(x1, x1, 1\right)}, \mathsf{fma}\left(3, x1 \cdot x1, -\mathsf{fma}\left(x2, 2, x1\right)\right), \left(x1 + \frac{\mathsf{fma}\left(3, x1 \cdot x1, 2 \cdot x2 - x1\right) \cdot \left(\left(3 \cdot x1\right) \cdot x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \mathsf{fma}\left(\mathsf{fma}\left(\left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot 2, \frac{x1 \cdot \mathsf{fma}\left(3, x1 \cdot x1, 2 \cdot x2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, \left(\left(x1 \cdot x1\right) \cdot \left(\sqrt[3]{\mathsf{fma}\left(4 \cdot \left(\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1\right), \frac{1}{x1 \cdot x1 + 1}, -6 \cdot 1\right)} \cdot \sqrt[3]{\mathsf{fma}\left(4 \cdot \left(\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1\right), \frac{1}{x1 \cdot x1 + 1}, -6 \cdot 1\right)}\right)\right) \cdot \sqrt[3]{\mathsf{fma}\left(4 \cdot \left(\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1\right), \frac{1}{x1 \cdot x1 + 1}, -6 \cdot 1\right)} + \left(\mathsf{fma}\left(-6, 1, 6\right) \cdot x1\right) \cdot x1\right), \mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot x1, x1\right)\right)\right)\]
x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)
↓
\mathsf{fma}\left(\frac{3}{\mathsf{fma}\left(x1, x1, 1\right)}, \mathsf{fma}\left(3, x1 \cdot x1, -\mathsf{fma}\left(x2, 2, x1\right)\right), \left(x1 + \frac{\mathsf{fma}\left(3, x1 \cdot x1, 2 \cdot x2 - x1\right) \cdot \left(\left(3 \cdot x1\right) \cdot x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \mathsf{fma}\left(\mathsf{fma}\left(\left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot 2, \frac{x1 \cdot \mathsf{fma}\left(3, x1 \cdot x1, 2 \cdot x2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, \left(\left(x1 \cdot x1\right) \cdot \left(\sqrt[3]{\mathsf{fma}\left(4 \cdot \left(\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1\right), \frac{1}{x1 \cdot x1 + 1}, -6 \cdot 1\right)} \cdot \sqrt[3]{\mathsf{fma}\left(4 \cdot \left(\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1\right), \frac{1}{x1 \cdot x1 + 1}, -6 \cdot 1\right)}\right)\right) \cdot \sqrt[3]{\mathsf{fma}\left(4 \cdot \left(\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1\right), \frac{1}{x1 \cdot x1 + 1}, -6 \cdot 1\right)} + \left(\mathsf{fma}\left(-6, 1, 6\right) \cdot x1\right) \cdot x1\right), \mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot x1, x1\right)\right)\right)
double code(double x1, double x2) {
	return ((double) (x1 + ((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (2.0 * x1)) * ((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0)))))) * ((double) (((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0)))) - 3.0)))) + ((double) (((double) (x1 * x1)) * ((double) (((double) (4.0 * ((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0)))))) - 6.0)))))) * ((double) (((double) (x1 * x1)) + 1.0)))) + ((double) (((double) (((double) (3.0 * x1)) * x1)) * ((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0)))))))) + ((double) (((double) (x1 * x1)) * x1)))) + x1)) + ((double) (3.0 * ((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) - ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0))))))))));
}
↓
double code(double x1, double x2) {
	return ((double) fma(((double) (3.0 / ((double) fma(x1, x1, 1.0)))), ((double) fma(3.0, ((double) (x1 * x1)), ((double) -(((double) fma(x2, 2.0, x1)))))), ((double) (((double) (x1 + ((double) (((double) (((double) fma(3.0, ((double) (x1 * x1)), ((double) (((double) (2.0 * x2)) - x1)))) * ((double) (((double) (3.0 * x1)) * x1)))) / ((double) fma(x1, x1, 1.0)))))) + ((double) fma(((double) fma(((double) (((double) (((double) (((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)) / ((double) (((double) (x1 * x1)) + 1.0)))) - 3.0)) * 2.0)), ((double) (((double) (x1 * ((double) fma(3.0, ((double) (x1 * x1)), ((double) (((double) (2.0 * x2)) - x1)))))) / ((double) fma(x1, x1, 1.0)))), ((double) (((double) (((double) (((double) (x1 * x1)) * ((double) (((double) cbrt(((double) fma(((double) (4.0 * ((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)))), ((double) (1.0 / ((double) (((double) (x1 * x1)) + 1.0)))), ((double) -(((double) (6.0 * 1.0)))))))) * ((double) cbrt(((double) fma(((double) (4.0 * ((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)))), ((double) (1.0 / ((double) (((double) (x1 * x1)) + 1.0)))), ((double) -(((double) (6.0 * 1.0)))))))))))) * ((double) cbrt(((double) fma(((double) (4.0 * ((double) (((double) (((double) (((double) (3.0 * x1)) * x1)) + ((double) (2.0 * x2)))) - x1)))), ((double) (1.0 / ((double) (((double) (x1 * x1)) + 1.0)))), ((double) -(((double) (6.0 * 1.0)))))))))) + ((double) (((double) (((double) fma(((double) -(6.0)), 1.0, 6.0)) * x1)) * x1)))))), ((double) fma(x1, x1, 1.0)), ((double) fma(x1, ((double) (x1 * x1)), x1))))))));
}

Error

Bits error versus x1

Bits error versus x2

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.5

    \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]

  2. Simplified0.3

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{3}{\mathsf{fma}\left(x1, x1, 1\right)}, \mathsf{fma}\left(3, x1 \cdot x1, -\mathsf{fma}\left(x2, 2, x1\right)\right), \left(x1 + \frac{\mathsf{fma}\left(3, x1 \cdot x1, 2 \cdot x2 - x1\right) \cdot \left(\left(3 \cdot x1\right) \cdot x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \mathsf{fma}\left(\mathsf{fma}\left(\left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot 2, \frac{x1 \cdot \mathsf{fma}\left(3, x1 \cdot x1, 2 \cdot x2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot x1, x1\right)\right)\right)}\]
  3. Using strategy rm

  4. Applied add-cube-cbrt0.4

    \[\leadsto \mathsf{fma}\left(\frac{3}{\mathsf{fma}\left(x1, x1, 1\right)}, \mathsf{fma}\left(3, x1 \cdot x1, -\mathsf{fma}\left(x2, 2, x1\right)\right), \left(x1 + \frac{\mathsf{fma}\left(3, x1 \cdot x1, 2 \cdot x2 - x1\right) \cdot \left(\left(3 \cdot x1\right) \cdot x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \mathsf{fma}\left(\mathsf{fma}\left(\left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot 2, \frac{x1 \cdot \mathsf{fma}\left(3, x1 \cdot x1, 2 \cdot x2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - \color{blue}{\left(\sqrt[3]{6} \cdot \sqrt[3]{6}\right) \cdot \sqrt[3]{6}}\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot x1, x1\right)\right)\right)\]

  5. Applied div-inv0.4

    \[\leadsto \mathsf{fma}\left(\frac{3}{\mathsf{fma}\left(x1, x1, 1\right)}, \mathsf{fma}\left(3, x1 \cdot x1, -\mathsf{fma}\left(x2, 2, x1\right)\right), \left(x1 + \frac{\mathsf{fma}\left(3, x1 \cdot x1, 2 \cdot x2 - x1\right) \cdot \left(\left(3 \cdot x1\right) \cdot x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \mathsf{fma}\left(\mathsf{fma}\left(\left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot 2, \frac{x1 \cdot \mathsf{fma}\left(3, x1 \cdot x1, 2 \cdot x2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \color{blue}{\left(\left(\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1\right) \cdot \frac{1}{x1 \cdot x1 + 1}\right)} - \left(\sqrt[3]{6} \cdot \sqrt[3]{6}\right) \cdot \sqrt[3]{6}\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot x1, x1\right)\right)\right)\]

  6. Applied associate-*r*0.4

    \[\leadsto \mathsf{fma}\left(\frac{3}{\mathsf{fma}\left(x1, x1, 1\right)}, \mathsf{fma}\left(3, x1 \cdot x1, -\mathsf{fma}\left(x2, 2, x1\right)\right), \left(x1 + \frac{\mathsf{fma}\left(3, x1 \cdot x1, 2 \cdot x2 - x1\right) \cdot \left(\left(3 \cdot x1\right) \cdot x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \mathsf{fma}\left(\mathsf{fma}\left(\left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot 2, \frac{x1 \cdot \mathsf{fma}\left(3, x1 \cdot x1, 2 \cdot x2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, \left(x1 \cdot x1\right) \cdot \left(\color{blue}{\left(4 \cdot \left(\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1\right)\right) \cdot \frac{1}{x1 \cdot x1 + 1}} - \left(\sqrt[3]{6} \cdot \sqrt[3]{6}\right) \cdot \sqrt[3]{6}\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot x1, x1\right)\right)\right)\]

  7. Applied prod-diff0.4

    \[\leadsto \mathsf{fma}\left(\frac{3}{\mathsf{fma}\left(x1, x1, 1\right)}, \mathsf{fma}\left(3, x1 \cdot x1, -\mathsf{fma}\left(x2, 2, x1\right)\right), \left(x1 + \frac{\mathsf{fma}\left(3, x1 \cdot x1, 2 \cdot x2 - x1\right) \cdot \left(\left(3 \cdot x1\right) \cdot x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \mathsf{fma}\left(\mathsf{fma}\left(\left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot 2, \frac{x1 \cdot \mathsf{fma}\left(3, x1 \cdot x1, 2 \cdot x2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, \left(x1 \cdot x1\right) \cdot \color{blue}{\left(\mathsf{fma}\left(4 \cdot \left(\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1\right), \frac{1}{x1 \cdot x1 + 1}, -\sqrt[3]{6} \cdot \left(\sqrt[3]{6} \cdot \sqrt[3]{6}\right)\right) + \mathsf{fma}\left(-\sqrt[3]{6}, \sqrt[3]{6} \cdot \sqrt[3]{6}, \sqrt[3]{6} \cdot \left(\sqrt[3]{6} \cdot \sqrt[3]{6}\right)\right)\right)}\right), \mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot x1, x1\right)\right)\right)\]

  8. Applied distribute-lft-in0.4

    \[\leadsto \mathsf{fma}\left(\frac{3}{\mathsf{fma}\left(x1, x1, 1\right)}, \mathsf{fma}\left(3, x1 \cdot x1, -\mathsf{fma}\left(x2, 2, x1\right)\right), \left(x1 + \frac{\mathsf{fma}\left(3, x1 \cdot x1, 2 \cdot x2 - x1\right) \cdot \left(\left(3 \cdot x1\right) \cdot x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \mathsf{fma}\left(\mathsf{fma}\left(\left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot 2, \frac{x1 \cdot \mathsf{fma}\left(3, x1 \cdot x1, 2 \cdot x2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, \color{blue}{\left(x1 \cdot x1\right) \cdot \mathsf{fma}\left(4 \cdot \left(\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1\right), \frac{1}{x1 \cdot x1 + 1}, -\sqrt[3]{6} \cdot \left(\sqrt[3]{6} \cdot \sqrt[3]{6}\right)\right) + \left(x1 \cdot x1\right) \cdot \mathsf{fma}\left(-\sqrt[3]{6}, \sqrt[3]{6} \cdot \sqrt[3]{6}, \sqrt[3]{6} \cdot \left(\sqrt[3]{6} \cdot \sqrt[3]{6}\right)\right)}\right), \mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot x1, x1\right)\right)\right)\]

  9. Simplified0.3

    \[\leadsto \mathsf{fma}\left(\frac{3}{\mathsf{fma}\left(x1, x1, 1\right)}, \mathsf{fma}\left(3, x1 \cdot x1, -\mathsf{fma}\left(x2, 2, x1\right)\right), \left(x1 + \frac{\mathsf{fma}\left(3, x1 \cdot x1, 2 \cdot x2 - x1\right) \cdot \left(\left(3 \cdot x1\right) \cdot x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \mathsf{fma}\left(\mathsf{fma}\left(\left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot 2, \frac{x1 \cdot \mathsf{fma}\left(3, x1 \cdot x1, 2 \cdot x2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, \color{blue}{\left(x1 \cdot x1\right) \cdot \mathsf{fma}\left(4 \cdot \left(\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1\right), \frac{1}{x1 \cdot x1 + 1}, -6 \cdot 1\right)} + \left(x1 \cdot x1\right) \cdot \mathsf{fma}\left(-\sqrt[3]{6}, \sqrt[3]{6} \cdot \sqrt[3]{6}, \sqrt[3]{6} \cdot \left(\sqrt[3]{6} \cdot \sqrt[3]{6}\right)\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot x1, x1\right)\right)\right)\]

  10. Simplified0.3

    \[\leadsto \mathsf{fma}\left(\frac{3}{\mathsf{fma}\left(x1, x1, 1\right)}, \mathsf{fma}\left(3, x1 \cdot x1, -\mathsf{fma}\left(x2, 2, x1\right)\right), \left(x1 + \frac{\mathsf{fma}\left(3, x1 \cdot x1, 2 \cdot x2 - x1\right) \cdot \left(\left(3 \cdot x1\right) \cdot x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \mathsf{fma}\left(\mathsf{fma}\left(\left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot 2, \frac{x1 \cdot \mathsf{fma}\left(3, x1 \cdot x1, 2 \cdot x2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, \left(x1 \cdot x1\right) \cdot \mathsf{fma}\left(4 \cdot \left(\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1\right), \frac{1}{x1 \cdot x1 + 1}, -6 \cdot 1\right) + \color{blue}{\left(\mathsf{fma}\left(-6, 1, 6\right) \cdot x1\right) \cdot x1}\right), \mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot x1, x1\right)\right)\right)\]
  11. Using strategy rm

  12. Applied add-cube-cbrt0.4

    \[\leadsto \mathsf{fma}\left(\frac{3}{\mathsf{fma}\left(x1, x1, 1\right)}, \mathsf{fma}\left(3, x1 \cdot x1, -\mathsf{fma}\left(x2, 2, x1\right)\right), \left(x1 + \frac{\mathsf{fma}\left(3, x1 \cdot x1, 2 \cdot x2 - x1\right) \cdot \left(\left(3 \cdot x1\right) \cdot x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \mathsf{fma}\left(\mathsf{fma}\left(\left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot 2, \frac{x1 \cdot \mathsf{fma}\left(3, x1 \cdot x1, 2 \cdot x2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, \left(x1 \cdot x1\right) \cdot \color{blue}{\left(\left(\sqrt[3]{\mathsf{fma}\left(4 \cdot \left(\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1\right), \frac{1}{x1 \cdot x1 + 1}, -6 \cdot 1\right)} \cdot \sqrt[3]{\mathsf{fma}\left(4 \cdot \left(\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1\right), \frac{1}{x1 \cdot x1 + 1}, -6 \cdot 1\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(4 \cdot \left(\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1\right), \frac{1}{x1 \cdot x1 + 1}, -6 \cdot 1\right)}\right)} + \left(\mathsf{fma}\left(-6, 1, 6\right) \cdot x1\right) \cdot x1\right), \mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot x1, x1\right)\right)\right)\]

  13. Applied associate-*r*0.4

    \[\leadsto \mathsf{fma}\left(\frac{3}{\mathsf{fma}\left(x1, x1, 1\right)}, \mathsf{fma}\left(3, x1 \cdot x1, -\mathsf{fma}\left(x2, 2, x1\right)\right), \left(x1 + \frac{\mathsf{fma}\left(3, x1 \cdot x1, 2 \cdot x2 - x1\right) \cdot \left(\left(3 \cdot x1\right) \cdot x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \mathsf{fma}\left(\mathsf{fma}\left(\left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot 2, \frac{x1 \cdot \mathsf{fma}\left(3, x1 \cdot x1, 2 \cdot x2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, \color{blue}{\left(\left(x1 \cdot x1\right) \cdot \left(\sqrt[3]{\mathsf{fma}\left(4 \cdot \left(\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1\right), \frac{1}{x1 \cdot x1 + 1}, -6 \cdot 1\right)} \cdot \sqrt[3]{\mathsf{fma}\left(4 \cdot \left(\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1\right), \frac{1}{x1 \cdot x1 + 1}, -6 \cdot 1\right)}\right)\right) \cdot \sqrt[3]{\mathsf{fma}\left(4 \cdot \left(\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1\right), \frac{1}{x1 \cdot x1 + 1}, -6 \cdot 1\right)}} + \left(\mathsf{fma}\left(-6, 1, 6\right) \cdot x1\right) \cdot x1\right), \mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot x1, x1\right)\right)\right)\]

  14. Final simplification0.4

    \[\leadsto \mathsf{fma}\left(\frac{3}{\mathsf{fma}\left(x1, x1, 1\right)}, \mathsf{fma}\left(3, x1 \cdot x1, -\mathsf{fma}\left(x2, 2, x1\right)\right), \left(x1 + \frac{\mathsf{fma}\left(3, x1 \cdot x1, 2 \cdot x2 - x1\right) \cdot \left(\left(3 \cdot x1\right) \cdot x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + \mathsf{fma}\left(\mathsf{fma}\left(\left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot 2, \frac{x1 \cdot \mathsf{fma}\left(3, x1 \cdot x1, 2 \cdot x2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, \left(\left(x1 \cdot x1\right) \cdot \left(\sqrt[3]{\mathsf{fma}\left(4 \cdot \left(\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1\right), \frac{1}{x1 \cdot x1 + 1}, -6 \cdot 1\right)} \cdot \sqrt[3]{\mathsf{fma}\left(4 \cdot \left(\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1\right), \frac{1}{x1 \cdot x1 + 1}, -6 \cdot 1\right)}\right)\right) \cdot \sqrt[3]{\mathsf{fma}\left(4 \cdot \left(\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1\right), \frac{1}{x1 \cdot x1 + 1}, -6 \cdot 1\right)} + \left(\mathsf{fma}\left(-6, 1, 6\right) \cdot x1\right) \cdot x1\right), \mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot x1, x1\right)\right)\right)\]

Reproduce

herbie shell --seed 2020114 +o rules:numerics
(FPCore (x1 x2)
  :name "Rosa's FloatVsDoubleBenchmark"
  :precision binary64
  (+ x1 (+ (+ (+ (+ (* (+ (* (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (- (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) 3)) (* (* x1 x1) (- (* 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) 6))) (+ (* x1 x1) 1)) (* (* (* 3 x1) x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)))) (* (* x1 x1) x1)) x1) (* 3 (/ (- (- (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))))))