Average Error: 7.6 → 0.9
Time: 12.1s
Precision: 64
Internal Precision: 576
\[\sqrt[3]{u \cdot \left(0.03125 - \sqrt{1 - u}\right)}\]
\[\sqrt[3]{u} \cdot \left(\sqrt[3]{\sqrt[3]{0.03125 - \sqrt{1 - u}}} \cdot \sqrt[3]{\sqrt[3]{0.03125 - \sqrt{1 - u}} \cdot \sqrt[3]{0.03125 - \sqrt{1 - u}}}\right)\]

Error

Bits error versus u

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 7.6

    \[\sqrt[3]{u \cdot \left(0.03125 - \sqrt{1 - u}\right)}\]
  2. Initial simplification7.6

    \[\leadsto \sqrt[3]{\left(0.03125 - \sqrt{1 - u}\right) \cdot u}\]
  3. Using strategy rm
  4. Applied cbrt-prod0.8

    \[\leadsto \color{blue}{\sqrt[3]{0.03125 - \sqrt{1 - u}} \cdot \sqrt[3]{u}}\]
  5. Using strategy rm
  6. Applied add-cube-cbrt0.8

    \[\leadsto \sqrt[3]{\color{blue}{\left(\sqrt[3]{0.03125 - \sqrt{1 - u}} \cdot \sqrt[3]{0.03125 - \sqrt{1 - u}}\right) \cdot \sqrt[3]{0.03125 - \sqrt{1 - u}}}} \cdot \sqrt[3]{u}\]
  7. Applied cbrt-prod0.9

    \[\leadsto \color{blue}{\left(\sqrt[3]{\sqrt[3]{0.03125 - \sqrt{1 - u}} \cdot \sqrt[3]{0.03125 - \sqrt{1 - u}}} \cdot \sqrt[3]{\sqrt[3]{0.03125 - \sqrt{1 - u}}}\right)} \cdot \sqrt[3]{u}\]
  8. Final simplification0.9

    \[\leadsto \sqrt[3]{u} \cdot \left(\sqrt[3]{\sqrt[3]{0.03125 - \sqrt{1 - u}}} \cdot \sqrt[3]{\sqrt[3]{0.03125 - \sqrt{1 - u}} \cdot \sqrt[3]{0.03125 - \sqrt{1 - u}}}\right)\]

Runtime

Time bar (total: 12.1s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (u)
  :name "cbrt(u * (0.03125 - sqrt(1 - u)))"
  (cbrt (* u (- 0.03125 (sqrt (- 1 u))))))