Average Error: 61.0 → 31.7
Time: 4.6s
Precision: 64
Internal Precision: 2368
$(\left(\frac{x}{y}\right) \cdot \left(-y\right) + x)_*$
$\log \left(\sqrt[3]{e^{(\left(\frac{x}{y}\right) \cdot \left(-y\right) + x)_*}}\right) + \log \left(\sqrt[3]{e^{(\left(\frac{x}{y}\right) \cdot \left(-y\right) + x)_*}} \cdot \sqrt[3]{e^{(\left(\frac{x}{y}\right) \cdot \left(-y\right) + x)_*}}\right)$

# Derivation

1. Initial program 61.0

$(\left(\frac{x}{y}\right) \cdot \left(-y\right) + x)_*$
2. Initial simplification61.0

$\leadsto (\left(\frac{x}{y}\right) \cdot \left(-y\right) + x)_*$
3. Using strategy rm

$\leadsto \color{blue}{\log \left(e^{(\left(\frac{x}{y}\right) \cdot \left(-y\right) + x)_*}\right)}$
5. Using strategy rm

$\leadsto \log \color{blue}{\left(\left(\sqrt[3]{e^{(\left(\frac{x}{y}\right) \cdot \left(-y\right) + x)_*}} \cdot \sqrt[3]{e^{(\left(\frac{x}{y}\right) \cdot \left(-y\right) + x)_*}}\right) \cdot \sqrt[3]{e^{(\left(\frac{x}{y}\right) \cdot \left(-y\right) + x)_*}}\right)}$
7. Applied log-prod31.7

$\leadsto \color{blue}{\log \left(\sqrt[3]{e^{(\left(\frac{x}{y}\right) \cdot \left(-y\right) + x)_*}} \cdot \sqrt[3]{e^{(\left(\frac{x}{y}\right) \cdot \left(-y\right) + x)_*}}\right) + \log \left(\sqrt[3]{e^{(\left(\frac{x}{y}\right) \cdot \left(-y\right) + x)_*}}\right)}$
8. Final simplification31.7

$\leadsto \log \left(\sqrt[3]{e^{(\left(\frac{x}{y}\right) \cdot \left(-y\right) + x)_*}}\right) + \log \left(\sqrt[3]{e^{(\left(\frac{x}{y}\right) \cdot \left(-y\right) + x)_*}} \cdot \sqrt[3]{e^{(\left(\frac{x}{y}\right) \cdot \left(-y\right) + x)_*}}\right)$

# Runtime

Time bar (total: 4.6s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)'
(FPCore (x y)
:name "fma(x/y,-y,x)"
(fma (/ x y) (- y) x))