Average Error: 3.2 → 0.3
Time: 15.4s
Precision: 64
Internal Precision: 576
$\left(\frac{inflow}{lam} + p\right) - \frac{outflow \cdot p}{lam}$
$\begin{array}{l} \mathbf{if}\;p \le -4.1600516230761307 \cdot 10^{+113} \lor \neg \left(p \le 1.0818115154476408 \cdot 10^{+35}\right):\\ \;\;\;\;\left(p + \frac{inflow}{lam}\right) - \frac{\frac{1}{\frac{lam}{outflow}}}{\frac{1}{p}}\\ \mathbf{else}:\\ \;\;\;\;\left(p + \frac{inflow}{lam}\right) - \frac{p \cdot outflow}{lam}\\ \end{array}$

# Try it out

Results

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# Derivation

1. Split input into 2 regimes
2. ## if p < -4.1600516230761307e+113 or 1.0818115154476408e+35 < p

1. Initial program 9.3

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

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

$\leadsto \left(p + \frac{inflow}{lam}\right) - \color{blue}{\frac{1}{\frac{\frac{lam}{outflow}}{p}}}$
5. Using strategy rm
6. Applied div-inv0.1

$\leadsto \left(p + \frac{inflow}{lam}\right) - \frac{1}{\color{blue}{\frac{lam}{outflow} \cdot \frac{1}{p}}}$
7. Applied associate-/r*0.1

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

## if -4.1600516230761307e+113 < p < 1.0818115154476408e+35

1. Initial program 0.4

$\left(\frac{inflow}{lam} + p\right) - \frac{outflow \cdot p}{lam}$
2. Initial simplification3.2

$\leadsto \left(p + \frac{inflow}{lam}\right) - \frac{p}{\frac{lam}{outflow}}$
3. Using strategy rm
4. Applied clear-num3.2

$\leadsto \left(p + \frac{inflow}{lam}\right) - \color{blue}{\frac{1}{\frac{\frac{lam}{outflow}}{p}}}$
5. Taylor expanded around 0 0.4

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

$\leadsto \begin{array}{l} \mathbf{if}\;p \le -4.1600516230761307 \cdot 10^{+113} \lor \neg \left(p \le 1.0818115154476408 \cdot 10^{+35}\right):\\ \;\;\;\;\left(p + \frac{inflow}{lam}\right) - \frac{\frac{1}{\frac{lam}{outflow}}}{\frac{1}{p}}\\ \mathbf{else}:\\ \;\;\;\;\left(p + \frac{inflow}{lam}\right) - \frac{p \cdot outflow}{lam}\\ \end{array}$

# Runtime

Time bar (total: 15.4s)Debug log

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