Average Error: 0.0 → 0.1
Time: 37.1s
Precision: 64
Internal Precision: 320
\[\frac{1}{\left(\left(a0 + a1 \cdot \log r\right) + a2 \cdot {\left(\log r\right)}^{2}\right) + a3 \cdot {\left(\log r\right)}^{3}} - 273.15\]
\[\left(\sqrt[3]{\frac{1}{a3 \cdot {\left(\log r\right)}^{3} + \left(a2 \cdot {\left(\log r\right)}^{2} + \left(\log r \cdot a1 + a0\right)\right)}} \cdot \sqrt[3]{\frac{1}{a3 \cdot {\left(\log r\right)}^{3} + \left(a2 \cdot {\left(\log r\right)}^{2} + \left(\log r \cdot a1 + a0\right)\right)}}\right) \cdot \sqrt[3]{\frac{1}{a3 \cdot {\left(\log r\right)}^{3} + \left(a2 \cdot {\left(\log r\right)}^{2} + \left(\log r \cdot a1 + a0\right)\right)}} - 273.15\]

Error

Bits error versus a0

Bits error versus a1

Bits error versus r

Bits error versus a2

Bits error versus a3

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{1}{\left(\left(a0 + a1 \cdot \log r\right) + a2 \cdot {\left(\log r\right)}^{2}\right) + a3 \cdot {\left(\log r\right)}^{3}} - 273.15\]
  2. Using strategy rm
  3. Applied add-cube-cbrt0.1

    \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{1}{\left(\left(a0 + a1 \cdot \log r\right) + a2 \cdot {\left(\log r\right)}^{2}\right) + a3 \cdot {\left(\log r\right)}^{3}}} \cdot \sqrt[3]{\frac{1}{\left(\left(a0 + a1 \cdot \log r\right) + a2 \cdot {\left(\log r\right)}^{2}\right) + a3 \cdot {\left(\log r\right)}^{3}}}\right) \cdot \sqrt[3]{\frac{1}{\left(\left(a0 + a1 \cdot \log r\right) + a2 \cdot {\left(\log r\right)}^{2}\right) + a3 \cdot {\left(\log r\right)}^{3}}}} - 273.15\]
  4. Final simplification0.1

    \[\leadsto \left(\sqrt[3]{\frac{1}{a3 \cdot {\left(\log r\right)}^{3} + \left(a2 \cdot {\left(\log r\right)}^{2} + \left(\log r \cdot a1 + a0\right)\right)}} \cdot \sqrt[3]{\frac{1}{a3 \cdot {\left(\log r\right)}^{3} + \left(a2 \cdot {\left(\log r\right)}^{2} + \left(\log r \cdot a1 + a0\right)\right)}}\right) \cdot \sqrt[3]{\frac{1}{a3 \cdot {\left(\log r\right)}^{3} + \left(a2 \cdot {\left(\log r\right)}^{2} + \left(\log r \cdot a1 + a0\right)\right)}} - 273.15\]

Runtime

Time bar (total: 37.1s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (a0 a1 r a2 a3)
  :name "1 / (a0 + a1 * log(r) + a2 * pow(log(r),2) + a3 * pow(log(r),3)) - 273.15"
  (- (/ 1 (+ (+ (+ a0 (* a1 (log r))) (* a2 (pow (log r) 2))) (* a3 (pow (log r) 3)))) 273.15))