Average Error: 0.0 → 0.0
Time: 12.2s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\frac{e^{0.0} \cdot \left(0.5 \cdot \sin re\right)}{e^{im}} + e^{im} \cdot \left(0.5 \cdot \sin re\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\frac{e^{0.0} \cdot \left(0.5 \cdot \sin re\right)}{e^{im}} + e^{im} \cdot \left(0.5 \cdot \sin re\right)
double f(double re, double im) {
        double r84042 = 0.5;
        double r84043 = re;
        double r84044 = sin(r84043);
        double r84045 = r84042 * r84044;
        double r84046 = 0.0;
        double r84047 = im;
        double r84048 = r84046 - r84047;
        double r84049 = exp(r84048);
        double r84050 = exp(r84047);
        double r84051 = r84049 + r84050;
        double r84052 = r84045 * r84051;
        return r84052;
}
↓
double f(double re, double im) {
        double r84053 = 0.0;
        double r84054 = exp(r84053);
        double r84055 = 0.5;
        double r84056 = re;
        double r84057 = sin(r84056);
        double r84058 = r84055 * r84057;
        double r84059 = r84054 * r84058;
        double r84060 = im;
        double r84061 = exp(r84060);
        double r84062 = r84059 / r84061;
        double r84063 = r84061 * r84058;
        double r84064 = r84062 + r84063;
        return r84064;
}

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. Using strategy rm

  7. Applied exp-diff0.0

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

  8. Applied associate-*l/0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))