Average Error: 0.0 → 0.0
Time: 2.7s
Precision: binary64
Cost: 12992
\[e^{re} \cdot \cos im\]
↓
\[\cos im \cdot e^{re}\]
e^{re} \cdot \cos im
↓
\cos im \cdot e^{re}
(FPCore (re im) :precision binary64 (* (exp re) (cos im)))
↓
(FPCore (re im) :precision binary64 (* (cos im) (exp re)))
double code(double re, double im) {
	return exp(re) * cos(im);
}
↓
double code(double re, double im) {
	return cos(im) * exp(re);
}

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
Error0.5
Cost58304
\[\sqrt[3]{\cos im \cdot e^{re}} \cdot \left(\sqrt[3]{\cos im \cdot e^{re}} \cdot \sqrt[3]{\cos im \cdot e^{re}}\right)\]
Alternative 2
Error0.1
Cost45248
\[\left(\sqrt[3]{e^{re}} \cdot \sqrt[3]{e^{re}}\right) \cdot \left(\cos im \cdot \sqrt[3]{e^{re}}\right)\]
Alternative 3
Error0.1
Cost38784
\[\left(\cos im \cdot \sqrt[3]{e^{re}}\right) \cdot {\left(\sqrt[3]{e^{re}}\right)}^{2}\]
Alternative 4
Error0.0
Cost32384
\[\left(\cos im \cdot \sqrt[3]{e^{re}}\right) \cdot {\left(e^{re}\right)}^{0.6666666666666666}\]
Alternative 5
Error0.0
Cost26048
\[\left(\cos im \cdot \sqrt[3]{e^{re}}\right) \cdot e^{re \cdot 0.6666666666666666}\]
Alternative 6
Error21.7
Cost7360
\[\cos im \cdot \left(re + \left(1 + re \cdot \left(re \cdot \left(0.5 + re \cdot 0.16666666666666666\right)\right)\right)\right)\]
Alternative 7
Error21.7
Cost7104
\[\cos im \cdot \left(re + \left(1 + 0.5 \cdot \left(re \cdot re\right)\right)\right)\]
Alternative 8
Error21.6
Cost6720
\[\cos im \cdot \left(re + 1\right)\]
Alternative 9
Error21.9
Cost6464
\[\cos im\]
Alternative 10
Error19.3
Cost6464
\[e^{re}\]
Alternative 11
Error40.7
Cost64
\[1\]
Alternative 12
Error41.4
Cost64
\[0\]
Alternative 13
Error60.5
Cost64
\[-1\]

Error

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

    \[\leadsto \color{blue}{\cos im \cdot e^{re}}\]

  3. Final simplification0.0

    \[\leadsto \cos im \cdot e^{re}\]

Reproduce

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