Average Error: 2.0 → 1.7
Time: 51.4s
Precision: 64
Internal Precision: 576
\[\frac{x}{1 + {\left(1 - x\right)}^{\left(\frac{1}{3}\right)} \cdot \left(1 + {\left(1 - x\right)}^{\left(\frac{1}{3}\right)}\right)}\]
\[\frac{x}{1 + {\left(1 - x\right)}^{\left(\frac{1}{3}\right)} \cdot \left(1 + e^{\frac{\log \left(\sqrt[3]{1 - x} \cdot \sqrt[3]{1 - x}\right) + \log \left(\sqrt[3]{1 - x}\right)}{3}}\right)}\]

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 2.0

    \[\frac{x}{1 + {\left(1 - x\right)}^{\left(\frac{1}{3}\right)} \cdot \left(1 + {\left(1 - x\right)}^{\left(\frac{1}{3}\right)}\right)}\]
  2. Using strategy rm
  3. Applied add-exp-log2.0

    \[\leadsto \frac{x}{1 + {\left(1 - x\right)}^{\left(\frac{1}{3}\right)} \cdot \left(1 + {\color{blue}{\left(e^{\log \left(1 - x\right)}\right)}}^{\left(\frac{1}{3}\right)}\right)}\]
  4. Applied pow-exp1.9

    \[\leadsto \frac{x}{1 + {\left(1 - x\right)}^{\left(\frac{1}{3}\right)} \cdot \left(1 + \color{blue}{e^{\log \left(1 - x\right) \cdot \frac{1}{3}}}\right)}\]
  5. Applied simplify1.7

    \[\leadsto \frac{x}{1 + {\left(1 - x\right)}^{\left(\frac{1}{3}\right)} \cdot \left(1 + e^{\color{blue}{\frac{\log \left(1 - x\right)}{3}}}\right)}\]
  6. Using strategy rm
  7. Applied add-cube-cbrt1.7

    \[\leadsto \frac{x}{1 + {\left(1 - x\right)}^{\left(\frac{1}{3}\right)} \cdot \left(1 + e^{\frac{\log \color{blue}{\left(\left(\sqrt[3]{1 - x} \cdot \sqrt[3]{1 - x}\right) \cdot \sqrt[3]{1 - x}\right)}}{3}}\right)}\]
  8. Applied log-prod1.7

    \[\leadsto \frac{x}{1 + {\left(1 - x\right)}^{\left(\frac{1}{3}\right)} \cdot \left(1 + e^{\frac{\color{blue}{\log \left(\sqrt[3]{1 - x} \cdot \sqrt[3]{1 - x}\right) + \log \left(\sqrt[3]{1 - x}\right)}}{3}}\right)}\]

Runtime

Time bar (total: 51.4s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x)
  :name "x/(1+(1-x)^(1/3)*(1+(1-x)^(1/3)))"
  (/ x (+ 1 (* (pow (- 1 x) (/ 1 3)) (+ 1 (pow (- 1 x) (/ 1 3)))))))