Average Error: 2.4 → 0.1
Time: 15.3s
Precision: 64
Internal Precision: 576
$\frac{inflow}{lam} + \left(1.0 - \frac{outflow}{lam}\right) \cdot p$
$\begin{array}{l} \mathbf{if}\;p \le -9.435390504479849 \cdot 10^{-35} \lor \neg \left(p \le 59947.37659807981\right):\\ \;\;\;\;\left(p \cdot 1.0 + \frac{inflow}{lam}\right) - \frac{1}{\frac{\frac{lam}{outflow}}{p}}\\ \mathbf{else}:\\ \;\;\;\;\left(p \cdot 1.0 + \frac{inflow}{lam}\right) - \frac{outflow \cdot p}{lam}\\ \end{array}$

# Try it out

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# Derivation

1. Split input into 2 regimes
2. ## if p < -9.435390504479849e-35 or 59947.37659807981 < p

1. Initial program 0.1

$\frac{inflow}{lam} + \left(1.0 - \frac{outflow}{lam}\right) \cdot p$
2. Initial simplification0.1

$\leadsto \left(\frac{inflow}{lam} + p \cdot 1.0\right) - \frac{p}{\frac{lam}{outflow}}$
3. Using strategy rm
4. Applied clear-num0.1

$\leadsto \left(\frac{inflow}{lam} + p \cdot 1.0\right) - \color{blue}{\frac{1}{\frac{\frac{lam}{outflow}}{p}}}$

## if -9.435390504479849e-35 < p < 59947.37659807981

1. Initial program 4.3

$\frac{inflow}{lam} + \left(1.0 - \frac{outflow}{lam}\right) \cdot p$
2. Taylor expanded around -inf 0.1

$\leadsto \color{blue}{\left(\frac{inflow}{lam} + 1.0 \cdot p\right) - \frac{outflow \cdot p}{lam}}$
3. Recombined 2 regimes into one program.
4. Final simplification0.1

$\leadsto \begin{array}{l} \mathbf{if}\;p \le -9.435390504479849 \cdot 10^{-35} \lor \neg \left(p \le 59947.37659807981\right):\\ \;\;\;\;\left(p \cdot 1.0 + \frac{inflow}{lam}\right) - \frac{1}{\frac{\frac{lam}{outflow}}{p}}\\ \mathbf{else}:\\ \;\;\;\;\left(p \cdot 1.0 + \frac{inflow}{lam}\right) - \frac{outflow \cdot p}{lam}\\ \end{array}$

# Runtime

Time bar (total: 15.3s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)'
(FPCore (inflow lam outflow p)
:name "inflow / lam + (1.0 - outflow / lam) * p"
(+ (/ inflow lam) (* (- 1.0 (/ outflow lam)) p)))