Average Error: 0.0 → 0.0
Time: 8.7s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
double f(double re, double im) {
        double r46567 = 0.5;
        double r46568 = re;
        double r46569 = cos(r46568);
        double r46570 = r46567 * r46569;
        double r46571 = im;
        double r46572 = -r46571;
        double r46573 = exp(r46572);
        double r46574 = exp(r46571);
        double r46575 = r46573 + r46574;
        double r46576 = r46570 * r46575;
        return r46576;
}
↓
double f(double re, double im) {
        double r46577 = 0.5;
        double r46578 = re;
        double r46579 = cos(r46578);
        double r46580 = r46577 * r46579;
        double r46581 = im;
        double r46582 = -r46581;
        double r46583 = exp(r46582);
        double r46584 = exp(r46581);
        double r46585 = r46583 + r46584;
        double r46586 = r46580 * r46585;
        return r46586;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))