Average Error: 0.0 → 0.0
Time: 2.9s
Precision: binary64
\[e^{re} \cdot \sin im\]
↓
\[\sqrt{e^{re}} \cdot \left(\sin im \cdot e^{re \cdot 0.5}\right)\]
e^{re} \cdot \sin im
↓
\sqrt{e^{re}} \cdot \left(\sin im \cdot e^{re \cdot 0.5}\right)
(FPCore (re im) :precision binary64 (* (exp re) (sin im)))
↓
(FPCore (re im)
 :precision binary64
 (* (sqrt (exp re)) (* (sin im) (exp (* re 0.5)))))
double code(double re, double im) {
	return exp(re) * sin(im);
}
↓
double code(double re, double im) {
	return sqrt(exp(re)) * (sin(im) * exp(re * 0.5));
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[e^{re} \cdot \sin im\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt_binary640.0

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

  4. Applied associate-*l*_binary640.0

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

  5. Simplified0.0

    \[\leadsto \sqrt{e^{re}} \cdot \color{blue}{\left(\sin im \cdot \sqrt{e^{re}}\right)}\]
  6. Using strategy rm

  7. Applied add-exp-log_binary640.0

    \[\leadsto \sqrt{e^{re}} \cdot \left(\sin im \cdot \color{blue}{e^{\log \left(\sqrt{e^{re}}\right)}}\right)\]

  8. Simplified0.0

    \[\leadsto \sqrt{e^{re}} \cdot \left(\sin im \cdot e^{\color{blue}{re \cdot 0.5}}\right)\]

  9. Final simplification0.0

    \[\leadsto \sqrt{e^{re}} \cdot \left(\sin im \cdot e^{re \cdot 0.5}\right)\]

Reproduce

herbie shell --seed 2020260 
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  :precision binary64
  (* (exp re) (sin im)))