Average Error: 45.0 → 45.2
Time: 15.0s
Precision: binary64
\[\mathsf{fma}\left(x, y, z\right) - \left(1 + \left(x \cdot y + z\right)\right)\]
↓
\[\left(\sqrt[3]{\left(\mathsf{fma}\left(x, y, z\right) - 1\right) - x \cdot y} \cdot \sqrt[3]{\left(\mathsf{fma}\left(x, y, z\right) - 1\right) - x \cdot y}\right) \cdot \sqrt[3]{\left(\sqrt[3]{\left(\mathsf{fma}\left(x, y, z\right) - 1\right) - x \cdot y} \cdot \sqrt[3]{\left(\mathsf{fma}\left(x, y, z\right) - 1\right) - x \cdot y}\right) \cdot \sqrt[3]{\left(\mathsf{fma}\left(x, y, z\right) - 1\right) - x \cdot y}} - z\]
\mathsf{fma}\left(x, y, z\right) - \left(1 + \left(x \cdot y + z\right)\right)
↓
\left(\sqrt[3]{\left(\mathsf{fma}\left(x, y, z\right) - 1\right) - x \cdot y} \cdot \sqrt[3]{\left(\mathsf{fma}\left(x, y, z\right) - 1\right) - x \cdot y}\right) \cdot \sqrt[3]{\left(\sqrt[3]{\left(\mathsf{fma}\left(x, y, z\right) - 1\right) - x \cdot y} \cdot \sqrt[3]{\left(\mathsf{fma}\left(x, y, z\right) - 1\right) - x \cdot y}\right) \cdot \sqrt[3]{\left(\mathsf{fma}\left(x, y, z\right) - 1\right) - x \cdot y}} - z
double code(double x, double y, double z) {
	return ((double) (((double) fma(x, y, z)) - ((double) (1.0 + ((double) (((double) (x * y)) + z))))));
}
↓
double code(double x, double y, double z) {
	return ((double) (((double) (((double) (((double) cbrt(((double) (((double) (((double) fma(x, y, z)) - 1.0)) - ((double) (x * y)))))) * ((double) cbrt(((double) (((double) (((double) fma(x, y, z)) - 1.0)) - ((double) (x * y)))))))) * ((double) cbrt(((double) (((double) (((double) cbrt(((double) (((double) (((double) fma(x, y, z)) - 1.0)) - ((double) (x * y)))))) * ((double) cbrt(((double) (((double) (((double) fma(x, y, z)) - 1.0)) - ((double) (x * y)))))))) * ((double) cbrt(((double) (((double) (((double) fma(x, y, z)) - 1.0)) - ((double) (x * y)))))))))))) - z));
}

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

Original45.0
Target0
Herbie45.2
\[-1\]

Derivation

  1. Initial program 45.0

    \[\mathsf{fma}\left(x, y, z\right) - \left(1 + \left(x \cdot y + z\right)\right)\]
  2. Using strategy rm

  3. Applied associate--r+45.0

    \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, y, z\right) - 1\right) - \left(x \cdot y + z\right)}\]
  4. Using strategy rm

  5. Applied associate--r+44.9

    \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, z\right) - 1\right) - x \cdot y\right) - z}\]
  6. Using strategy rm

  7. Applied add-cube-cbrt45.2

    \[\leadsto \color{blue}{\left(\sqrt[3]{\left(\mathsf{fma}\left(x, y, z\right) - 1\right) - x \cdot y} \cdot \sqrt[3]{\left(\mathsf{fma}\left(x, y, z\right) - 1\right) - x \cdot y}\right) \cdot \sqrt[3]{\left(\mathsf{fma}\left(x, y, z\right) - 1\right) - x \cdot y}} - z\]
  8. Using strategy rm

  9. Applied add-cube-cbrt45.2

    \[\leadsto \left(\sqrt[3]{\left(\mathsf{fma}\left(x, y, z\right) - 1\right) - x \cdot y} \cdot \sqrt[3]{\left(\mathsf{fma}\left(x, y, z\right) - 1\right) - x \cdot y}\right) \cdot \sqrt[3]{\color{blue}{\left(\sqrt[3]{\left(\mathsf{fma}\left(x, y, z\right) - 1\right) - x \cdot y} \cdot \sqrt[3]{\left(\mathsf{fma}\left(x, y, z\right) - 1\right) - x \cdot y}\right) \cdot \sqrt[3]{\left(\mathsf{fma}\left(x, y, z\right) - 1\right) - x \cdot y}}} - z\]

  10. Final simplification45.2

    \[\leadsto \left(\sqrt[3]{\left(\mathsf{fma}\left(x, y, z\right) - 1\right) - x \cdot y} \cdot \sqrt[3]{\left(\mathsf{fma}\left(x, y, z\right) - 1\right) - x \cdot y}\right) \cdot \sqrt[3]{\left(\sqrt[3]{\left(\mathsf{fma}\left(x, y, z\right) - 1\right) - x \cdot y} \cdot \sqrt[3]{\left(\mathsf{fma}\left(x, y, z\right) - 1\right) - x \cdot y}\right) \cdot \sqrt[3]{\left(\mathsf{fma}\left(x, y, z\right) - 1\right) - x \cdot y}} - z\]

Reproduce

herbie shell --seed 2020163 
(FPCore (x y z)
  :name "simple fma test"
  :precision binary64

  :herbie-target
  -1.0

  (- (fma x y z) (+ 1.0 (+ (* x y) z))))