Average Error: 0.0 → 0.2
Time: 21.9s
Precision: 64
Internal Precision: 576
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\frac{{\left(\frac{0.5}{e^{im}}\right)}^{3} + {\left(e^{im} \cdot 0.5\right)}^{3}}{\left(e^{im} \cdot 0.5\right) \cdot \left(e^{im} \cdot 0.5\right) + \left(\frac{0.5}{e^{im}} \cdot \frac{0.5}{e^{im}} - \frac{0.5}{e^{im}} \cdot \left(e^{im} \cdot 0.5\right)\right)} \cdot \sin re\]

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

    \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]

  2. Initial simplification0.0

    \[\leadsto \sin re \cdot \left(0.5 \cdot e^{im} + \frac{0.5}{e^{im}}\right)\]
  3. Using strategy rm

  4. Applied flip3-+0.2

    \[\leadsto \sin re \cdot \color{blue}{\frac{{\left(0.5 \cdot e^{im}\right)}^{3} + {\left(\frac{0.5}{e^{im}}\right)}^{3}}{\left(0.5 \cdot e^{im}\right) \cdot \left(0.5 \cdot e^{im}\right) + \left(\frac{0.5}{e^{im}} \cdot \frac{0.5}{e^{im}} - \left(0.5 \cdot e^{im}\right) \cdot \frac{0.5}{e^{im}}\right)}}\]

  5. Final simplification0.2

    \[\leadsto \frac{{\left(\frac{0.5}{e^{im}}\right)}^{3} + {\left(e^{im} \cdot 0.5\right)}^{3}}{\left(e^{im} \cdot 0.5\right) \cdot \left(e^{im} \cdot 0.5\right) + \left(\frac{0.5}{e^{im}} \cdot \frac{0.5}{e^{im}} - \frac{0.5}{e^{im}} \cdot \left(e^{im} \cdot 0.5\right)\right)} \cdot \sin re\]

Runtime

Time bar (total: 21.9s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes0.20.20.00.10%
herbie shell --seed 2018296 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))