Average Error: 0.0 → 0.1

Time: 9.8s

Precision: 64

Internal Precision: 576

\[e^{re} \cdot \sin im\]

↓

\[\sqrt{e^{re}} \cdot \left(\sin im \cdot \left(\sqrt[3]{\sqrt{e^{re}}} \cdot \left(\sqrt[3]{\sqrt{e^{re}}} \cdot \sqrt[3]{\sqrt{e^{re}}}\right)\right)\right)\]

Error

The X axis uses an exponential scale — Bits error versus `re`

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Derivation

Initial program 0.0
\[e^{re} \cdot \sin im\]
Initial simplification0.0
\[\leadsto \sin im \cdot e^{re}\]
Using strategy rm
Applied add-sqr-sqrt0.0
\[\leadsto \sin im \cdot \color{blue}{\left(\sqrt{e^{re}} \cdot \sqrt{e^{re}}\right)}\]
Applied associate-*r*0.0
\[\leadsto \color{blue}{\left(\sin im \cdot \sqrt{e^{re}}\right) \cdot \sqrt{e^{re}}}\]
Using strategy rm
Applied add-cube-cbrt0.1
\[\leadsto \left(\sin im \cdot \color{blue}{\left(\left(\sqrt[3]{\sqrt{e^{re}}} \cdot \sqrt[3]{\sqrt{e^{re}}}\right) \cdot \sqrt[3]{\sqrt{e^{re}}}\right)}\right) \cdot \sqrt{e^{re}}\]
Final simplification0.1
\[\leadsto \sqrt{e^{re}} \cdot \left(\sin im \cdot \left(\sqrt[3]{\sqrt{e^{re}}} \cdot \left(\sqrt[3]{\sqrt{e^{re}}} \cdot \sqrt[3]{\sqrt{e^{re}}}\right)\right)\right)\]

Runtime

	Baseline	Herbie	Oracle	Span	%
Regimes	0.1	0.1	0.0	0.0	0%

herbie shell --seed 2018297 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  (* (exp re) (sin im)))