Average Error: 0.0 → 0.0
Time: 4.3s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\frac{0.5 \cdot \cos re}{e^{im}} + \left(0.5 \cdot \cos re\right) \cdot e^{im}\]
\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}
double f(double re, double im) {
        double r46565 = 0.5;
        double r46566 = re;
        double r46567 = cos(r46566);
        double r46568 = r46565 * r46567;
        double r46569 = im;
        double r46570 = -r46569;
        double r46571 = exp(r46570);
        double r46572 = exp(r46569);
        double r46573 = r46571 + r46572;
        double r46574 = r46568 * r46573;
        return r46574;
}
↓
double f(double re, double im) {
        double r46575 = 0.5;
        double r46576 = re;
        double r46577 = cos(r46576);
        double r46578 = r46575 * r46577;
        double r46579 = im;
        double r46580 = exp(r46579);
        double r46581 = r46578 / r46580;
        double r46582 = r46578 * r46580;
        double r46583 = r46581 + r46582;
        return r46583;
}

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. Using strategy rm

  3. Applied distribute-lft-in0.0

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

  4. Simplified0.0

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

  5. 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 2020034 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))