Average Error: 22.4 → 17.3
Time: 53.0s
Precision: 64
Internal Precision: 2368
\[{10.0}^{\left(\frac{\left(-1.0\right) \cdot calb + \sqrt{{calb}^{2} - \left(4.0 \cdot cala\right) \cdot \left(calc - Tcor_RCO2\right)}}{2.0 \cdot cala}\right)}\]
\[\begin{array}{l} \mathbf{if}\;cala \le -1.325846820001231 \cdot 10^{+233} \lor \neg \left(cala \le 9.430427809853857 \cdot 10^{-206}\right):\\ \;\;\;\;{10.0}^{\left(\frac{calb \cdot \left(-1.0\right)}{2.0 \cdot cala}\right)}\\ \mathbf{else}:\\ \;\;\;\;{10.0}^{\left(\frac{calb \cdot \left(-1.0\right) + \sqrt{{calb}^{2} - \left(cala \cdot 4.0\right) \cdot \left(calc - Tcor_RCO2\right)}}{2.0 \cdot cala}\right)}\\ \end{array}\]

Error

Bits error versus calb

Bits error versus cala

Bits error versus calc

Bits error versus Tcor_RCO2

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes
  2. if cala < -1.325846820001231e+233 or 9.430427809853857e-206 < cala

    1. Initial program 36.5

      \[{10.0}^{\left(\frac{\left(-1.0\right) \cdot calb + \sqrt{{calb}^{2} - \left(4.0 \cdot cala\right) \cdot \left(calc - Tcor_RCO2\right)}}{2.0 \cdot cala}\right)}\]
    2. Taylor expanded around 0 21.9

      \[\leadsto {10.0}^{\left(\frac{\left(-1.0\right) \cdot calb + \color{blue}{0}}{2.0 \cdot cala}\right)}\]

    if -1.325846820001231e+233 < cala < 9.430427809853857e-206

    1. Initial program 14.8

      \[{10.0}^{\left(\frac{\left(-1.0\right) \cdot calb + \sqrt{{calb}^{2} - \left(4.0 \cdot cala\right) \cdot \left(calc - Tcor_RCO2\right)}}{2.0 \cdot cala}\right)}\]
  3. Recombined 2 regimes into one program.
  4. Final simplification17.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;cala \le -1.325846820001231 \cdot 10^{+233} \lor \neg \left(cala \le 9.430427809853857 \cdot 10^{-206}\right):\\ \;\;\;\;{10.0}^{\left(\frac{calb \cdot \left(-1.0\right)}{2.0 \cdot cala}\right)}\\ \mathbf{else}:\\ \;\;\;\;{10.0}^{\left(\frac{calb \cdot \left(-1.0\right) + \sqrt{{calb}^{2} - \left(cala \cdot 4.0\right) \cdot \left(calc - Tcor_RCO2\right)}}{2.0 \cdot cala}\right)}\\ \end{array}\]

Runtime

Time bar (total: 53.0s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (calb cala calc Tcor_RCO2)
  :name "pow(10.,((-1. * calb + sqrt(pow(calb,2) - (4. * cala * (calc - Tcor_RCO2)))) / (2. * cala)))"
  (pow 10.0 (/ (+ (* (- 1.0) calb) (sqrt (- (pow calb 2) (* (* 4.0 cala) (- calc Tcor_RCO2))))) (* 2.0 cala))))