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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -7136802653565914.0:\\ \;\;\;\;\left(\sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)} \cdot \sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)}\right) \cdot \sqrt[3]{\left(\sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)} \cdot \sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)}\right) \cdot \sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)}}\\ \mathbf{if}\;z \le 8.418307185260896 \cdot 10^{-08}:\\ \;\;\;\;\left((x \cdot y + z)_* - y \cdot x\right) - \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)} \cdot \sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)}\right) \cdot \sqrt[3]{\left(\sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)} \cdot \sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)}\right) \cdot \sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)}}\\ \end{array}\]

Original	45.2
Target	0
Herbie	20.1

Derivation

Split input into 2 regimes
if z < -7136802653565914.0 or 8.418307185260896e-08 < z
1. Initial program 60.9
  \[(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
2. Using strategy rm
3. Applied add-cube-cbrt60.9
  \[\leadsto \color{blue}{\left(\sqrt[3]{(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)} \cdot \sqrt[3]{(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)}\right) \cdot \sqrt[3]{(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)}}\]
4. Taylor expanded around 0 60.9
  \[\leadsto \left(\sqrt[3]{(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)} \cdot \sqrt[3]{\color{blue}{(x \cdot y + z)_* - \left(z + \left(1 + y \cdot x\right)\right)}}\right) \cdot \sqrt[3]{(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)}\]
5. Applied simplify31.7
  \[\leadsto \color{blue}{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)}\]
6. Using strategy rm
7. Applied add-cube-cbrt31.7
  \[\leadsto \color{blue}{\left(\sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)} \cdot \sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)}\right) \cdot \sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)}}\]
8. Using strategy rm
9. Applied add-cube-cbrt31.7
  \[\leadsto \left(\sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)} \cdot \sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)}\right) \cdot \sqrt[3]{\color{blue}{\left(\sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)} \cdot \sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)}\right) \cdot \sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)}}}\]
if -7136802653565914.0 < z < 8.418307185260896e-08
1. Initial program 29.8
  \[(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
2. Using strategy rm
3. Applied add-cube-cbrt29.8
  \[\leadsto \color{blue}{\left(\sqrt[3]{(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)} \cdot \sqrt[3]{(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)}\right) \cdot \sqrt[3]{(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)}}\]
4. Taylor expanded around 0 29.8
  \[\leadsto \left(\sqrt[3]{(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)} \cdot \sqrt[3]{\color{blue}{(x \cdot y + z)_* - \left(z + \left(1 + y \cdot x\right)\right)}}\right) \cdot \sqrt[3]{(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)}\]
5. Applied simplify29.9
  \[\leadsto \color{blue}{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)}\]
6. Using strategy rm
7. Applied add-cube-cbrt29.9
  \[\leadsto \color{blue}{\left(\sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)} \cdot \sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)}\right) \cdot \sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)}}\]
8. Taylor expanded around 0 29.9
  \[\leadsto \left(\sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)} \cdot \sqrt[3]{\left((x \cdot y + z)_* - z\right) - \left(1 + y \cdot x\right)}\right) \cdot \sqrt[3]{\color{blue}{(x \cdot y + z)_* - \left(z + \left(1 + y \cdot x\right)\right)}}\]
9. Applied simplify8.7
  \[\leadsto \color{blue}{\left((x \cdot y + z)_* - y \cdot x\right) - \left(z + 1\right)}\]
Recombined 2 regimes into one program.

Error

Target

Derivation

`if z < -7136802653565914.0 or 8.418307185260896e-08 < z`

`if -7136802653565914.0 < z < 8.418307185260896e-08`

Runtime