Average Error: 0.0 → 0.0
Time: 5.5s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot e^{0.0 - im} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\left(0.5 \cdot \sin re\right) \cdot e^{0.0 - im} + \left(0.5 \cdot \sin re\right) \cdot e^{im}
double f(double re, double im) {
        double r30217 = 0.5;
        double r30218 = re;
        double r30219 = sin(r30218);
        double r30220 = r30217 * r30219;
        double r30221 = 0.0;
        double r30222 = im;
        double r30223 = r30221 - r30222;
        double r30224 = exp(r30223);
        double r30225 = exp(r30222);
        double r30226 = r30224 + r30225;
        double r30227 = r30220 * r30226;
        return r30227;
}
↓
double f(double re, double im) {
        double r30228 = 0.5;
        double r30229 = re;
        double r30230 = sin(r30229);
        double r30231 = r30228 * r30230;
        double r30232 = 0.0;
        double r30233 = im;
        double r30234 = r30232 - r30233;
        double r30235 = exp(r30234);
        double r30236 = r30231 * r30235;
        double r30237 = exp(r30233);
        double r30238 = r30231 * r30237;
        double r30239 = r30236 + r30238;
        return r30239;
}

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

    \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{\left(0.5 \cdot \sin re\right) \cdot e^{0.0 - im} + \left(0.5 \cdot \sin re\right) \cdot e^{im}}\]

  4. Final simplification0.0

    \[\leadsto \left(0.5 \cdot \sin re\right) \cdot e^{0.0 - im} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]

Reproduce

herbie shell --seed 2020033 +o rules:numerics
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))