Average Error: 3.6 → 0.1
Time: 16.6s
Precision: 64
Internal Precision: 320
\[\left(p + \frac{inflow}{lam}\right) - \frac{outflow \cdot p}{lam}\]
\[\begin{array}{l} \mathbf{if}\;\left(\frac{inflow}{lam} + p\right) - \frac{outflow \cdot p}{lam} = -\infty:\\ \;\;\;\;\left(\frac{inflow}{lam} + p\right) - p \cdot \frac{outflow}{lam}\\ \mathbf{elif}\;\left(\frac{inflow}{lam} + p\right) - \frac{outflow \cdot p}{lam} \le 1.1484297405980849 \cdot 10^{+305}:\\ \;\;\;\;\left(\frac{inflow}{lam} + p\right) - \frac{outflow \cdot p}{lam}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{inflow}{lam} + p\right) - \frac{p}{lam} \cdot outflow\\ \end{array}\]

Error

Bits error versus p

Bits error versus inflow

Bits error versus lam

Bits error versus outflow

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes
  2. if (- (+ p (/ inflow lam)) (/ (* outflow p) lam)) < -inf.0

    1. Initial program 60.8

      \[\left(p + \frac{inflow}{lam}\right) - \frac{outflow \cdot p}{lam}\]
    2. Using strategy rm
    3. Applied div-inv60.8

      \[\leadsto \left(p + \frac{inflow}{lam}\right) - \color{blue}{\left(outflow \cdot p\right) \cdot \frac{1}{lam}}\]
    4. Using strategy rm
    5. Applied pow160.8

      \[\leadsto \left(p + \frac{inflow}{lam}\right) - \left(outflow \cdot p\right) \cdot \color{blue}{{\left(\frac{1}{lam}\right)}^{1}}\]
    6. Applied pow160.8

      \[\leadsto \left(p + \frac{inflow}{lam}\right) - \color{blue}{{\left(outflow \cdot p\right)}^{1}} \cdot {\left(\frac{1}{lam}\right)}^{1}\]
    7. Applied pow-prod-down60.8

      \[\leadsto \left(p + \frac{inflow}{lam}\right) - \color{blue}{{\left(\left(outflow \cdot p\right) \cdot \frac{1}{lam}\right)}^{1}}\]
    8. Simplified0.1

      \[\leadsto \left(p + \frac{inflow}{lam}\right) - {\color{blue}{\left(\frac{outflow}{lam} \cdot p\right)}}^{1}\]

    if -inf.0 < (- (+ p (/ inflow lam)) (/ (* outflow p) lam)) < 1.1484297405980849e+305

    1. Initial program 0.1

      \[\left(p + \frac{inflow}{lam}\right) - \frac{outflow \cdot p}{lam}\]

    if 1.1484297405980849e+305 < (- (+ p (/ inflow lam)) (/ (* outflow p) lam))

    1. Initial program 54.6

      \[\left(p + \frac{inflow}{lam}\right) - \frac{outflow \cdot p}{lam}\]
    2. Initial simplification0.8

      \[\leadsto \left(\frac{inflow}{lam} + p\right) - \frac{p}{lam} \cdot outflow\]
  3. Recombined 3 regimes into one program.
  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\frac{inflow}{lam} + p\right) - \frac{outflow \cdot p}{lam} = -\infty:\\ \;\;\;\;\left(\frac{inflow}{lam} + p\right) - p \cdot \frac{outflow}{lam}\\ \mathbf{elif}\;\left(\frac{inflow}{lam} + p\right) - \frac{outflow \cdot p}{lam} \le 1.1484297405980849 \cdot 10^{+305}:\\ \;\;\;\;\left(\frac{inflow}{lam} + p\right) - \frac{outflow \cdot p}{lam}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{inflow}{lam} + p\right) - \frac{p}{lam} \cdot outflow\\ \end{array}\]

Runtime

Time bar (total: 16.6s)Debug log

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