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

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Results

 In Out
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

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