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

# Try it out

Results

 In Out
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))))