Average Error: 0.4 → 0.4
Time: 2.8m
Precision: 64
Internal Precision: 384
\[\left(35000000.0 + \left(0.401 \cdot \frac{1000}{v}\right) \cdot \frac{1000}{v}\right) \cdot \left(v - 1000 \cdot 4.27 \cdot 10^{-05}\right) - \left(1.3806503 \cdot 10^{-23} \cdot 1000\right) \cdot 300\]
↓
\[\left(\left(\frac{1000}{v} \cdot \frac{1000}{v}\right) \cdot 0.401 + 35000000.0\right) \cdot \left(v - 1000 \cdot 4.27 \cdot 10^{-05}\right) - \left(1.3806503 \cdot 10^{-23} \cdot 1000\right) \cdot 300\]

Error

Bits error versus v

Derivation

  1. Initial program 0.4

    \[\left(35000000.0 + \left(0.401 \cdot \frac{1000}{v}\right) \cdot \frac{1000}{v}\right) \cdot \left(v - 1000 \cdot 4.27 \cdot 10^{-05}\right) - \left(1.3806503 \cdot 10^{-23} \cdot 1000\right) \cdot 300\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.4

    \[\leadsto \left(35000000.0 + \left(0.401 \cdot \frac{1000}{v}\right) \cdot \frac{1000}{v}\right) \cdot \color{blue}{\left(1 \cdot \left(v - 1000 \cdot 4.27 \cdot 10^{-05}\right)\right)} - \left(1.3806503 \cdot 10^{-23} \cdot 1000\right) \cdot 300\]

  4. Applied associate-*r*0.4

    \[\leadsto \color{blue}{\left(\left(35000000.0 + \left(0.401 \cdot \frac{1000}{v}\right) \cdot \frac{1000}{v}\right) \cdot 1\right) \cdot \left(v - 1000 \cdot 4.27 \cdot 10^{-05}\right)} - \left(1.3806503 \cdot 10^{-23} \cdot 1000\right) \cdot 300\]

  5. Applied simplify0.4

    \[\leadsto \color{blue}{\left(\left(\frac{1000}{v} \cdot \frac{1000}{v}\right) \cdot 0.401 + 35000000.0\right)} \cdot \left(v - 1000 \cdot 4.27 \cdot 10^{-05}\right) - \left(1.3806503 \cdot 10^{-23} \cdot 1000\right) \cdot 300\]

Runtime

Time bar (total: 2.8m)Debug log

herbie shell --seed '#(1743936871 1855164119 3668777427 1254258049 132811564 1366975197)' 
(FPCore (v)
  :name "carbonGas"
  :pre (<= 0.1 v 0.5)
  (- (* (+ 35000000.0 (* (* 0.401 (/ 1000 v)) (/ 1000 v))) (- v (* 1000 4.27e-05))) (* (* 1.3806503e-23 1000) 300)))