Average Error: 22.3 → 22.3
Time: 4.1s
Precision: binary64
\[{10}^{\left(\frac{\left(-1\right) \cdot calb + \sqrt{{calb}^{2} - \left(4 \cdot cala\right) \cdot \left(calc - Tcor_RCO2\right)}}{2 \cdot cala}\right)}\]
↓
\[{10}^{\left(\frac{\left(-1\right) \cdot calb + \sqrt{{calb}^{2} - \left(4 \cdot cala\right) \cdot \left(calc - Tcor_RCO2\right)}}{2 \cdot cala}\right)}\]

Error

Bits error versus calb

Bits error versus cala

Bits error versus calc

Bits error versus Tcor_RCO2

Derivation

  1. Initial program 22.3

    \[{10}^{\left(\frac{\left(-1\right) \cdot calb + \sqrt{{calb}^{2} - \left(4 \cdot cala\right) \cdot \left(calc - Tcor_RCO2\right)}}{2 \cdot cala}\right)}\]

  2. Final simplification22.3

    \[\leadsto {10}^{\left(\frac{\left(-1\right) \cdot calb + \sqrt{{calb}^{2} - \left(4 \cdot cala\right) \cdot \left(calc - Tcor_RCO2\right)}}{2 \cdot cala}\right)}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (calb cala calc Tcor_RCO2)
  :name "(pow 10.0 (/ (+ (* (- 1.0) calb) (sqrt (- (pow calb 2) (* (* 4.0 cala) (- calc Tcor_RCO2))))) (* 2.0 cala)))"
  :precision binary64
  (pow 10.0 (/ (+ (* (neg 1.0) calb) (sqrt (- (pow calb 2.0) (* (* 4.0 cala) (- calc Tcor_RCO2))))) (* 2.0 cala))))