Average Error: 0.0 → 0.0
Time: 3.2s
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 r13126 = 0.5;
        double r13127 = re;
        double r13128 = sin(r13127);
        double r13129 = r13126 * r13128;
        double r13130 = 0.0;
        double r13131 = im;
        double r13132 = r13130 - r13131;
        double r13133 = exp(r13132);
        double r13134 = exp(r13131);
        double r13135 = r13133 + r13134;
        double r13136 = r13129 * r13135;
        return r13136;
}
↓
double f(double re, double im) {
        double r13137 = 0.5;
        double r13138 = re;
        double r13139 = sin(r13138);
        double r13140 = r13137 * r13139;
        double r13141 = 0.0;
        double r13142 = im;
        double r13143 = r13141 - r13142;
        double r13144 = exp(r13143);
        double r13145 = exp(r13142);
        double r13146 = r13144 + r13145;
        double r13147 = r13140 * r13146;
        return r13147;
}

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 2019353 +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))))