Average Error: 0.0 → 0.0
Time: 4.5s
Precision: binary64
Cost: 19776
\[e^{re} \cdot \sin im\]
↓
\[e^{re \cdot 0.5} \cdot \left(e^{re \cdot 0.5} \cdot \sin im\right)\]
e^{re} \cdot \sin im
↓
e^{re \cdot 0.5} \cdot \left(e^{re \cdot 0.5} \cdot \sin im\right)
(FPCore (re im) :precision binary64 (* (exp re) (sin im)))
↓
(FPCore (re im)
 :precision binary64
 (* (exp (* re 0.5)) (* (exp (* re 0.5)) (sin im))))
double code(double re, double im) {
	return exp(re) * sin(im);
}
↓
double code(double re, double im) {
	return exp(re * 0.5) * (exp(re * 0.5) * sin(im));
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error1.0
Cost58304
\[\sqrt[3]{\sin im \cdot e^{re}} \cdot \left(\sqrt[3]{\sin im \cdot e^{re}} \cdot \sqrt[3]{\sin im \cdot e^{re}}\right)\]
Alternative 2
Error0.0
Cost58048
\[\sqrt{e^{re}} \cdot \left(\left(\sin im \cdot \left|\sqrt[3]{e^{re}}\right|\right) \cdot \sqrt{\sqrt[3]{e^{re}}}\right)\]
Alternative 3
Error0.1
Cost45248
\[\left(\sqrt[3]{e^{re}} \cdot \sqrt[3]{e^{re}}\right) \cdot \left(\sin im \cdot \sqrt[3]{e^{re}}\right)\]
Alternative 4
Error0.2
Cost45120
\[\sqrt{e^{re}} \cdot \left(\sin im \cdot \log \left(e^{\sqrt{e^{re}}}\right)\right)\]
Alternative 5
Error21.6
Cost38848
\[\sqrt{\sin im \cdot e^{re}} \cdot \sqrt{\sin im \cdot e^{re}}\]
Alternative 6
Error0.0
Cost38784
\[\sqrt{\sqrt{e^{re}}} \cdot \left(\sin im \cdot {\left(e^{re}\right)}^{0.75}\right)\]
Alternative 7
Error0.1
Cost38784
\[\sqrt{e^{re}} \cdot \left(\sin im \cdot \sqrt[3]{{\left(e^{re}\right)}^{1.5}}\right)\]
Alternative 8
Error0.0
Cost32320
\[\sqrt{e^{re}} \cdot \left(\sin im \cdot \sqrt{e^{re}}\right)\]
Alternative 9
Error32.4
Cost32320
\[\sqrt{\sin im} \cdot \left(e^{re} \cdot \sqrt{\sin im}\right)\]
Alternative 10
Error0.0
Cost26048
\[\left(\sin im \cdot e^{re \cdot 0.5}\right) \cdot \sqrt{e^{re}}\]
Alternative 11
Error21.4
Cost25920
\[\sqrt{e^{re}} \cdot \left(im \cdot \sqrt{e^{re}}\right)\]
Alternative 12
Error13.3
Cost25856
\[\sqrt[3]{{\left(\sin im \cdot e^{re}\right)}^{3}}\]
Alternative 13
Error0.0
Cost19776
\[e^{re \cdot 0.5} \cdot \left(\sin im \cdot e^{re \cdot 0.5}\right)\]
Alternative 14
Error0.8
Cost19776
\[\sqrt{e^{re}} \cdot \left(\left(re \cdot 0.5 + 1\right) \cdot \sin im\right)\]
Alternative 15
Error21.4
Cost19648
\[e^{re \cdot 0.5} \cdot \left(im \cdot \sqrt{e^{re}}\right)\]
Alternative 16
Error1.3
Cost19392
\[\sin im \cdot \sqrt{e^{re}}\]
Alternative 17
Error33.2
Cost19392
\[e^{re + \log \sin im}\]
Alternative 18
Error0.8
Cost13504
\[\left(re \cdot 0.5 + 1\right) \cdot \left(\sin im \cdot e^{re \cdot 0.5}\right)\]
Alternative 19
Error1.3
Cost13120
\[\sin im \cdot e^{re \cdot 0.5}\]
Alternative 20
Error0.0
Cost12992
\[\sin im \cdot e^{re}\]
Alternative 21
Error21.6
Cost7104
\[\sin im \cdot \left(re + \left(1 + 0.5 \cdot \left(re \cdot re\right)\right)\right)\]
Alternative 22
Error21.5
Cost6720
\[\sin im \cdot \left(re + 1\right)\]
Alternative 23
Error21.4
Cost6592
\[im \cdot e^{re}\]
Alternative 24
Error21.7
Cost6464
\[\sin im\]
Alternative 25
Error60.1
Cost64
\[1\]
Alternative 26
Error40.9
Cost64
\[0\]
Alternative 27
Error60.1
Cost64
\[-1\]

Error

Derivation

  1. Initial program 0.0

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

  3. Applied add-sqr-sqrt_binary64_14250.0

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

  4. Applied associate-*l*_binary64_13440.0

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

  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_binary64_14410.0

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

  8. Simplified0.0

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

  10. Applied add-exp-log_binary64_14410.0

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

  11. Simplified0.0

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

  12. Simplified0.0

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

  13. Final simplification0.0

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

Reproduce

herbie shell --seed 2021042 
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  :precision binary64
  (* (exp re) (sin im)))