\[(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]

↓

\[\begin{array}{l} \mathbf{if}\;z \le -379930112174.3745:\\ \;\;\;\;\left(\sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)} \cdot \sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)}\right) \cdot \sqrt[3]{\left(\sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)} \cdot \sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)}\right) \cdot \sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)}}\\ \mathbf{if}\;z \le 3.962180353379337 \cdot 10^{+17}:\\ \;\;\;\;\left((x \cdot y + z)_* - y \cdot x\right) - \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)} \cdot \sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)}\right) \cdot \sqrt[3]{\left(\sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)} \cdot \sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)}\right) \cdot \sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)}}\\ \end{array}\]

Original	45.7
Target	0
Herbie	20.2

Derivation

Split input into 2 regimes
if z < -379930112174.3745 or 3.962180353379337e+17 < z
1. Initial program 62.0
  \[(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
2. Using strategy rm
3. Applied add-cube-cbrt62.0
  \[\leadsto \color{blue}{\left(\sqrt[3]{(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)} \cdot \sqrt[3]{(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)}\right) \cdot \sqrt[3]{(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)}}\]
4. Taylor expanded around 0 62.0
  \[\leadsto \left(\sqrt[3]{(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)} \cdot \sqrt[3]{\color{blue}{(x \cdot y + z)_* - \left(z + \left(1 + y \cdot x\right)\right)}}\right) \cdot \sqrt[3]{(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)}\]
5. Applied simplify31.5
  \[\leadsto \color{blue}{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)}\]
6. Using strategy rm
7. Applied add-cube-cbrt31.5
  \[\leadsto \color{blue}{\left(\sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)} \cdot \sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)}\right) \cdot \sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)}}\]
8. Using strategy rm
9. Applied add-cube-cbrt31.5
  \[\leadsto \left(\sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)} \cdot \sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)}\right) \cdot \sqrt[3]{\color{blue}{\left(\sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)} \cdot \sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)}\right) \cdot \sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)}}}\]
if -379930112174.3745 < z < 3.962180353379337e+17
1. Initial program 30.3
  \[(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
2. Using strategy rm
3. Applied add-cube-cbrt30.3
  \[\leadsto \color{blue}{\left(\sqrt[3]{(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)} \cdot \sqrt[3]{(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)}\right) \cdot \sqrt[3]{(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)}}\]
4. Taylor expanded around 0 30.3
  \[\leadsto \left(\sqrt[3]{(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)} \cdot \sqrt[3]{\color{blue}{(x \cdot y + z)_* - \left(z + \left(1 + y \cdot x\right)\right)}}\right) \cdot \sqrt[3]{(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)}\]
5. Applied simplify30.3
  \[\leadsto \color{blue}{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)}\]
6. Using strategy rm
7. Applied add-cube-cbrt30.3
  \[\leadsto \color{blue}{\left(\sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)} \cdot \sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)}\right) \cdot \sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)}}\]
8. Taylor expanded around 0 30.3
  \[\leadsto \left(\sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)} \cdot \sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)}\right) \cdot \sqrt[3]{\color{blue}{(x \cdot y + z)_* - \left(z + \left(1 + y \cdot x\right)\right)}}\]
9. Applied simplify9.5
  \[\leadsto \color{blue}{\left((x \cdot y + z)_* - y \cdot x\right) - \left(z + 1\right)}\]
Recombined 2 regimes into one program.
Removed slow pow expressions.

Error

Target

Derivation

`if z < -379930112174.3745 or 3.962180353379337e+17 < z`

`if -379930112174.3745 < z < 3.962180353379337e+17`

Runtime