Average Error: 0.0 → 0.0
Time: 13.7s
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 r28222 = 0.5;
        double r28223 = re;
        double r28224 = cos(r28223);
        double r28225 = r28222 * r28224;
        double r28226 = im;
        double r28227 = -r28226;
        double r28228 = exp(r28227);
        double r28229 = exp(r28226);
        double r28230 = r28228 + r28229;
        double r28231 = r28225 * r28230;
        return r28231;
}
↓
double f(double re, double im) {
        double r28232 = 0.5;
        double r28233 = re;
        double r28234 = cos(r28233);
        double r28235 = r28232 * r28234;
        double r28236 = im;
        double r28237 = -r28236;
        double r28238 = exp(r28237);
        double r28239 = exp(r28236);
        double r28240 = r28238 + r28239;
        double r28241 = r28235 * r28240;
        return r28241;
}

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 2019326 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))