Average Error: 61.0 → 31.7
Time: 5.6s
Precision: 64
Internal Precision: 2368
$(\left(\frac{x}{y}\right) \cdot y + \left(-x\right))_*$
$\log \left(\sqrt{e^{(\left(\frac{x}{y}\right) \cdot y + \left(-x\right))_*}}\right) + \log \left(\sqrt{e^{(\left(\frac{x}{y}\right) \cdot y + \left(-x\right))_*}}\right)$

# Derivation

1. Initial program 61.0

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

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

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

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

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

# Runtime

Time bar (total: 5.6s)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)))