Average Error: 19.5 → 19.5
Time: 11.3s
Precision: binary64
\[\frac{\left(0.0100000000000000002 \cdot e^{\left(\left(\left(\left(\left(\left(\frac{-2991.2728999999999}{{K}^{2}} - \frac{6017.0128000000004}{K}\right) + 18.876428539999999\right) - 0.028354720999999999 \cdot K\right) + 1.7838301000000001 \cdot 10^{-5} \cdot {K}^{2}\right) - 8.4150417000000001 \cdot 10^{-10} \cdot {K}^{3}\right) + 4.44125430000000024 \cdot 10^{-13} \cdot {K}^{4}\right) + 2.8584870000000002 \cdot \log K}\right) \cdot \left(\left(1 + 7.20000000000000045 \cdot 10^{-4}\right) + \left(\left(\left(\left(\frac{P}{1013.25} - 1.19000000000000006 \cdot 10^{-4} \cdot e\right) + 3.5088000000000001 \cdot 10^{-9} \cdot {e}^{2}\right) + 1.16959999999999998 \cdot 10^{-12} \cdot {e}^{3}\right) \cdot 1.01324999999999998\right) \cdot \left(3.1999999999999999 \cdot 10^{-6} + 5.9000000000000003 \cdot 10^{-10} \cdot {C}^{2}\right)\right)}{1013.25}\]
↓
\[\frac{\left(0.0100000000000000002 \cdot e^{\left(\left(\left(\left(\left(\left(\frac{-2991.2728999999999}{{K}^{2}} - \frac{6017.0128000000004}{K}\right) + 18.876428539999999\right) - 0.028354720999999999 \cdot K\right) + 1.7838301000000001 \cdot 10^{-5} \cdot {K}^{2}\right) - 8.4150417000000001 \cdot 10^{-10} \cdot {K}^{3}\right) + 4.44125430000000024 \cdot 10^{-13} \cdot {K}^{4}\right) + 2.8584870000000002 \cdot \log K}\right) \cdot \left(\left(1 + 7.20000000000000045 \cdot 10^{-4}\right) + \left(\left(\left(\left(\frac{P}{1013.25} - 1.19000000000000006 \cdot 10^{-4} \cdot e\right) + 3.5088000000000001 \cdot 10^{-9} \cdot {e}^{2}\right) + 1.16959999999999998 \cdot 10^{-12} \cdot {e}^{3}\right) \cdot 1.01324999999999998\right) \cdot \left(3.1999999999999999 \cdot 10^{-6} + 5.9000000000000003 \cdot 10^{-10} \cdot {C}^{2}\right)\right)}{1013.25}\]

Error

Bits error versus K

Bits error versus P

Bits error versus C

Derivation

  1. Initial program 19.5

    \[\frac{\left(0.0100000000000000002 \cdot e^{\left(\left(\left(\left(\left(\left(\frac{-2991.2728999999999}{{K}^{2}} - \frac{6017.0128000000004}{K}\right) + 18.876428539999999\right) - 0.028354720999999999 \cdot K\right) + 1.7838301000000001 \cdot 10^{-5} \cdot {K}^{2}\right) - 8.4150417000000001 \cdot 10^{-10} \cdot {K}^{3}\right) + 4.44125430000000024 \cdot 10^{-13} \cdot {K}^{4}\right) + 2.8584870000000002 \cdot \log K}\right) \cdot \left(\left(1 + 7.20000000000000045 \cdot 10^{-4}\right) + \left(\left(\left(\left(\frac{P}{1013.25} - 1.19000000000000006 \cdot 10^{-4} \cdot e\right) + 3.5088000000000001 \cdot 10^{-9} \cdot {e}^{2}\right) + 1.16959999999999998 \cdot 10^{-12} \cdot {e}^{3}\right) \cdot 1.01324999999999998\right) \cdot \left(3.1999999999999999 \cdot 10^{-6} + 5.9000000000000003 \cdot 10^{-10} \cdot {C}^{2}\right)\right)}{1013.25}\]

  2. Final simplification19.5

    \[\leadsto \frac{\left(0.0100000000000000002 \cdot e^{\left(\left(\left(\left(\left(\left(\frac{-2991.2728999999999}{{K}^{2}} - \frac{6017.0128000000004}{K}\right) + 18.876428539999999\right) - 0.028354720999999999 \cdot K\right) + 1.7838301000000001 \cdot 10^{-5} \cdot {K}^{2}\right) - 8.4150417000000001 \cdot 10^{-10} \cdot {K}^{3}\right) + 4.44125430000000024 \cdot 10^{-13} \cdot {K}^{4}\right) + 2.8584870000000002 \cdot \log K}\right) \cdot \left(\left(1 + 7.20000000000000045 \cdot 10^{-4}\right) + \left(\left(\left(\left(\frac{P}{1013.25} - 1.19000000000000006 \cdot 10^{-4} \cdot e\right) + 3.5088000000000001 \cdot 10^{-9} \cdot {e}^{2}\right) + 1.16959999999999998 \cdot 10^{-12} \cdot {e}^{3}\right) \cdot 1.01324999999999998\right) \cdot \left(3.1999999999999999 \cdot 10^{-6} + 5.9000000000000003 \cdot 10^{-10} \cdot {C}^{2}\right)\right)}{1013.25}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (K P C)
  :name "(/ (* (* 0.01 (exp (+ (+ (- (+ (- (+ (- (/ (- 2991.2729) (pow K 2)) (/ 6017.0128 K)) 18.87642854) (* 0.028354721 K)) (* 1.7838301e-05 (pow K 2))) (* 8.4150417e-10 (pow K 3))) (* 4.4412543e-13 (pow K 4))) (* 2.8584870000000002 (log K))))) (+ (+ 1 0.00072) (* (* (+ (+ (- (/ P 1013.25) (* 0.000119 E)) (* 3.5088e-09 (pow E 2))) (* 1.1696e-12 (pow E 3))) 1.01325) (+ 3.2e-06 (* 5.9e-10 (pow C 2)))))) 1013.25)"
  :precision binary64
  (/ (* (* 0.01 (exp (+ (+ (- (+ (- (+ (- (/ (neg 2991.2729) (pow K 2.0)) (/ 6017.0128 K)) 18.87642854) (* 0.028354721 K)) (* 1.7838301e-05 (pow K 2.0))) (* 8.4150417e-10 (pow K 3.0))) (* 4.4412543e-13 (pow K 4.0))) (* 2.8584870000000002 (log K))))) (+ (+ 1.0 0.00072) (* (* (+ (+ (- (/ P 1013.25) (* 0.000119 E)) (* 3.5088e-09 (pow E 2.0))) (* 1.1696e-12 (pow E 3.0))) 1.01325) (+ 3.2e-06 (* 5.9e-10 (pow C 2.0)))))) 1013.25))