Average Error: 3.7 → 0.8
Time: 12.6s
Precision: 64
Internal Precision: 320
$\frac{x \cdot y}{a} + z$
$\begin{array}{l} \mathbf{if}\;\frac{x \cdot y}{a} = -\infty:\\ \;\;\;\;z + x \cdot \frac{y}{a}\\ \mathbf{elif}\;\frac{x \cdot y}{a} \le 2.3984251035498995 \cdot 10^{+284}:\\ \;\;\;\;\frac{x \cdot y}{a} + z\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot \frac{y}{a}\\ \end{array}$

# Try it out

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# Derivation

1. Split input into 2 regimes
2. ## if (/ (* x y) a) < -inf.0 or 2.3984251035498995e+284 < (/ (* x y) a)

1. Initial program 52.4

$\frac{x \cdot y}{a} + z$
2. Initial simplification3.4

$\leadsto z + x \cdot \frac{y}{a}$

## if -inf.0 < (/ (* x y) a) < 2.3984251035498995e+284

1. Initial program 0.7

$\frac{x \cdot y}{a} + z$
2. Initial simplification3.8

$\leadsto z + x \cdot \frac{y}{a}$
3. Taylor expanded around -inf 0.7

$\leadsto z + \color{blue}{\frac{x \cdot y}{a}}$
3. Recombined 2 regimes into one program.
4. Final simplification0.8

$\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y}{a} = -\infty:\\ \;\;\;\;z + x \cdot \frac{y}{a}\\ \mathbf{elif}\;\frac{x \cdot y}{a} \le 2.3984251035498995 \cdot 10^{+284}:\\ \;\;\;\;\frac{x \cdot y}{a} + z\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot \frac{y}{a}\\ \end{array}$

# Runtime

Time bar (total: 12.6s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)'
(FPCore (x y a z)
:name "x*y/a+z"
(+ (/ (* x y) a) z))