Average Error: 0.1 → 0.1
Time: 4.2s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\mathsf{fma}\left(0.5 \cdot \sin re, e^{0.0 - im}, \left(0.5 \cdot \sin re\right) \cdot e^{im}\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\mathsf{fma}\left(0.5 \cdot \sin re, e^{0.0 - im}, \left(0.5 \cdot \sin re\right) \cdot e^{im}\right)
double code(double re, double im) {
	return ((0.5 * sin(re)) * (exp((0.0 - im)) + exp(im)));
}
↓
double code(double re, double im) {
	return fma((0.5 * sin(re)), exp((0.0 - im)), ((0.5 * sin(re)) * exp(im)));
}

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 0.1

    \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-in0.1

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

  5. Applied fma-def0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020078 +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))))