Average Error: 0.0 → 1.0
Time: 6.0s
Precision: binary64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right) \]
↓
\[\left(0.5 \cdot \cos re\right) \cdot 2 \]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(0.5 \cdot \cos re\right) \cdot 2

(FPCore (re im)
 :precision binary64
 (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))
↓
(FPCore (re im) :precision binary64 (* (* 0.5 (cos re)) 2.0))
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)) * 2.0;
}

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

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

  2. Taylor expanded in im around 0 1.0

    \[\leadsto \left(0.5 \cdot \cos re\right) \cdot \color{blue}{2} \]

  3. Final simplification1.0

    \[\leadsto \left(0.5 \cdot \cos re\right) \cdot 2 \]

Reproduce

herbie shell --seed 2022127 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))