Average Error: 0.0 → 0.0
Time: 10.5s
Precision: binary64
Cost: 26304
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\frac{0.5 \cdot \cos re}{e^{im}} + \left(0.5 \cdot \cos re\right) \cdot e^{im}\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\frac{0.5 \cdot \cos re}{e^{im}} + \left(0.5 \cdot \cos re\right) \cdot e^{im}
(FPCore (re im)
 :precision binary64
 (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))
↓
(FPCore (re im)
 :precision binary64
 (+ (/ (* 0.5 (cos re)) (exp im)) (* (* 0.5 (cos re)) (exp im))))
double code(double re, double im) {
	return (0.5 * cos(re)) * (exp(-im) + exp(im));
}
↓
double code(double re, double im) {
	return ((0.5 * cos(re)) / exp(im)) + ((0.5 * cos(re)) * exp(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
Error15.9
Cost52288
\[\sqrt{\left(0.5 \cdot \cos re\right) \cdot \left(e^{im} + e^{-im}\right)} \cdot \sqrt{\left(0.5 \cdot \cos re\right) \cdot \left(e^{im} + e^{-im}\right)}\]
Alternative 2
Error61.1
Cost45696
\[\frac{\left(0.5 \cdot \cos re\right) \cdot \left({\left(e^{im}\right)}^{-2} - {\left(e^{im}\right)}^{2}\right)}{e^{-im} - e^{im}}\]
Alternative 3
Error1.2
Cost45632
\[\left(0.5 \cdot \cos re\right) \cdot \left(\sqrt{e^{im} + e^{-im}} \cdot \sqrt{e^{im} + e^{-im}}\right)\]
Alternative 4
Error1.0
Cost45632
\[\sqrt{e^{im} + e^{-im}} \cdot \left(\left(0.5 \cdot \cos re\right) \cdot \sqrt{e^{im} + e^{-im}}\right)\]
Alternative 5
Error0.8
Cost45120
\[\log \left({\left(\sqrt{e^{e^{im} + e^{-im}}}\right)}^{\cos re}\right)\]
Alternative 6
Error61.1
Cost39360
\[\frac{\left(0.5 \cdot \cos re\right) \cdot \left(e^{im \cdot -2} - {\left(e^{im}\right)}^{2}\right)}{e^{-im} - e^{im}}\]
Alternative 7
Error0.2
Cost39168
\[\frac{0.5 \cdot \cos re}{e^{im}} + \sqrt[3]{0.125 \cdot {\left(\cos re \cdot e^{im}\right)}^{3}}\]
Alternative 8
Error63.1
Cost32832
\[\frac{\left(0.5 \cdot \cos re\right) \cdot \left({\left(e^{im}\right)}^{-2} - 1\right)}{e^{-im} - e^{im}}\]
Alternative 9
Error0.4
Cost32576
\[\sqrt[3]{0.125 \cdot {\left(\cos re \cdot \left(e^{im} + e^{-im}\right)\right)}^{3}}\]
Alternative 10
Error0.6
Cost20096
\[\cos re + \cos re \cdot \left(0.5 \cdot \left(im \cdot im\right) + 0.041666666666666664 \cdot {im}^{4}\right)\]
Alternative 11
Error28.0
Cost19776
\[\frac{0.5}{e^{im}} + \left(0.5 \cdot \cos re\right) \cdot e^{im}\]
Alternative 12
Error0.0
Cost19712
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{im} + e^{-im}\right)\]
Alternative 13
Error0.6
Cost13696
\[\cos re \cdot \left(0.5 \cdot \left(im \cdot im\right) + \left(1 + 0.041666666666666664 \cdot {im}^{4}\right)\right)\]
Alternative 14
Error31.2
Cost13568
\[\left(e^{im} + e^{-im}\right) \cdot \left(0.5 + \left(re \cdot re\right) \cdot -0.25\right)\]
Alternative 15
Error28.3
Cost13184
\[0.5 \cdot \left(e^{im} + e^{-im}\right)\]
Alternative 16
Error0.7
Cost6976
\[\cos re \cdot \left(1 + 0.5 \cdot \left(im \cdot im\right)\right)\]
Alternative 17
Error1.1
Cost6464
\[\cos re\]
Alternative 18
Error28.8
Cost64
\[1\]
Alternative 19
Error62.0
Cost64
\[0\]
Alternative 20
Error59.9
Cost64
\[-1\]

Error

Derivation

  1. Initial program 0.0

    \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
  2. Using strategy rm

  3. Applied distribute-rgt-in_binary64_3690.0

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

  4. Simplified0.0

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

  5. Simplified0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2021022 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))