Average Error: 18.1 → 1.8

Time: 2.4m

Precision: 64

Internal Precision: 576

\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]

↓

\[\frac{\sqrt[3]{\frac{t1}{u + t1}} \cdot \sqrt[3]{\frac{t1}{u + t1}}}{\frac{\frac{u + t1}{-v}}{\sqrt[3]{\frac{t1}{u + t1}}}}\]

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Initial program 18.1
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
Initial simplification1.5
\[\leadsto \frac{\frac{t1}{t1 + u}}{\frac{t1 + u}{-v}}\]
Using strategy rm
Applied add-cube-cbrt1.8
\[\leadsto \frac{\color{blue}{\left(\sqrt[3]{\frac{t1}{t1 + u}} \cdot \sqrt[3]{\frac{t1}{t1 + u}}\right) \cdot \sqrt[3]{\frac{t1}{t1 + u}}}}{\frac{t1 + u}{-v}}\]
Applied associate-/l*1.8
\[\leadsto \color{blue}{\frac{\sqrt[3]{\frac{t1}{t1 + u}} \cdot \sqrt[3]{\frac{t1}{t1 + u}}}{\frac{\frac{t1 + u}{-v}}{\sqrt[3]{\frac{t1}{t1 + u}}}}}\]
Final simplification1.8
\[\leadsto \frac{\sqrt[3]{\frac{t1}{u + t1}} \cdot \sqrt[3]{\frac{t1}{u + t1}}}{\frac{\frac{u + t1}{-v}}{\sqrt[3]{\frac{t1}{u + t1}}}}\]

	Baseline	Herbie	Oracle	Span	%
Regimes	1.8	1.8	0.0	1.7	0%

herbie shell --seed 2018263 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))