Average Error: 0.0 → 0.0
Time: 13.7s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[e^{0.0 - im} \cdot \left(0.5 \cdot \sin re\right) + e^{im} \cdot \left(0.5 \cdot \sin re\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
e^{0.0 - im} \cdot \left(0.5 \cdot \sin re\right) + e^{im} \cdot \left(0.5 \cdot \sin re\right)
double f(double re, double im) {
        double r12964 = 0.5;
        double r12965 = re;
        double r12966 = sin(r12965);
        double r12967 = r12964 * r12966;
        double r12968 = 0.0;
        double r12969 = im;
        double r12970 = r12968 - r12969;
        double r12971 = exp(r12970);
        double r12972 = exp(r12969);
        double r12973 = r12971 + r12972;
        double r12974 = r12967 * r12973;
        return r12974;
}
↓
double f(double re, double im) {
        double r12975 = 0.0;
        double r12976 = im;
        double r12977 = r12975 - r12976;
        double r12978 = exp(r12977);
        double r12979 = 0.5;
        double r12980 = re;
        double r12981 = sin(r12980);
        double r12982 = r12979 * r12981;
        double r12983 = r12978 * r12982;
        double r12984 = exp(r12976);
        double r12985 = r12984 * r12982;
        double r12986 = r12983 + r12985;
        return r12986;
}

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. Simplified0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019212 +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))))