Average Error: 0.0 → 0.0
Time: 4.2s
Precision: binary64
Cost: 26304
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\frac{\cos re \cdot 0.5}{e^{im}} + \left(\cos re \cdot 0.5\right) \cdot e^{im}\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\frac{\cos re \cdot 0.5}{e^{im}} + \left(\cos re \cdot 0.5\right) \cdot e^{im}
(FPCore (re im)
 :precision binary64
 (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))
↓
(FPCore (re im)
 :precision binary64
 (+ (/ (* (cos re) 0.5) (exp im)) (* (* (cos re) 0.5) (exp im))))
double code(double re, double im) {
	return (0.5 * cos(re)) * (exp(-im) + exp(im));
}
↓
double code(double re, double im) {
	return ((cos(re) * 0.5) / exp(im)) + ((cos(re) * 0.5) * 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
Error0.0
Cost19712
\[\left(\cos re \cdot 0.5\right) \cdot \left(e^{im} + e^{-im}\right)\]
Alternative 2
Error0.9
Cost6976
\[\cos re \cdot \left(0.5 \cdot \left(im \cdot im\right) + 1\right)\]
Alternative 3
Error1.2
Cost6464
\[\cos re\]
Alternative 4
Error29.4
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_10510.0

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

  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

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2021044 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))