Average Error: 0.0 → 0.0
Time: 4.2s
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 r22200 = 0.5;
        double r22201 = re;
        double r22202 = sin(r22201);
        double r22203 = r22200 * r22202;
        double r22204 = 0.0;
        double r22205 = im;
        double r22206 = r22204 - r22205;
        double r22207 = exp(r22206);
        double r22208 = exp(r22205);
        double r22209 = r22207 + r22208;
        double r22210 = r22203 * r22209;
        return r22210;
}
↓
double f(double re, double im) {
        double r22211 = 0.5;
        double r22212 = re;
        double r22213 = sin(r22212);
        double r22214 = r22211 * r22213;
        double r22215 = 0.0;
        double r22216 = im;
        double r22217 = r22215 - r22216;
        double r22218 = exp(r22217);
        double r22219 = exp(r22216);
        double r22220 = r22218 + r22219;
        double r22221 = r22214 * r22220;
        return r22221;
}

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 2020003 +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))))