Average Error: 0.0 → 0.0
Time: 5.1s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
double f(double re, double im) {
        double r21017 = 0.5;
        double r21018 = re;
        double r21019 = sin(r21018);
        double r21020 = r21017 * r21019;
        double r21021 = 0.0;
        double r21022 = im;
        double r21023 = r21021 - r21022;
        double r21024 = exp(r21023);
        double r21025 = exp(r21022);
        double r21026 = r21024 + r21025;
        double r21027 = r21020 * r21026;
        return r21027;
}
↓
double f(double re, double im) {
        double r21028 = 0.5;
        double r21029 = re;
        double r21030 = sin(r21029);
        double r21031 = r21028 * r21030;
        double r21032 = 0.0;
        double r21033 = im;
        double r21034 = r21032 - r21033;
        double r21035 = exp(r21034);
        double r21036 = exp(r21033);
        double r21037 = r21035 + r21036;
        double r21038 = r21031 * r21037;
        return r21038;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020057 +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))))