Error

Target

Derivation

1. Initial program 58.1

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

2. Taylor expanded around 0 0.7

   \[\leadsto \left(0.5 \cdot \cos re\right) \cdot \color{blue}{\left(-\left(\frac{1}{3} \cdot {im}^{3} + \left(\frac{1}{60} \cdot {im}^{5} + 2 \cdot im\right)\right)\right)}\]

3. Simplified0.7

   \[\leadsto \left(0.5 \cdot \cos re\right) \cdot \color{blue}{(im \cdot \left((\frac{-1}{3} \cdot \left(im \cdot im\right) + -2)_*\right) + \left({im}^{5} \cdot \frac{-1}{60}\right))_*}\]
4. Using strategy rm

5. Applied fma-udef0.7

   \[\leadsto \left(0.5 \cdot \cos re\right) \cdot \color{blue}{\left(im \cdot (\frac{-1}{3} \cdot \left(im \cdot im\right) + -2)_* + {im}^{5} \cdot \frac{-1}{60}\right)}\]

6. Applied distribute-lft-in0.7

   \[\leadsto \color{blue}{\left(0.5 \cdot \cos re\right) \cdot \left(im \cdot (\frac{-1}{3} \cdot \left(im \cdot im\right) + -2)_*\right) + \left(0.5 \cdot \cos re\right) \cdot \left({im}^{5} \cdot \frac{-1}{60}\right)}\]

7. Final simplification0.7

   \[\leadsto \left(\frac{-1}{60} \cdot {im}^{5}\right) \cdot \left(0.5 \cdot \cos re\right) + \left(0.5 \cdot \cos re\right) \cdot \left(im \cdot (\frac{-1}{3} \cdot \left(im \cdot im\right) + -2)_*\right)\]

Reproduce

herbie shell --seed 2019002 +o rules:numerics
(FPCore (re im)
  :name "math.sin on complex, imaginary part"

  :herbie-target
  (if (< (fabs im) 1) (- (* (cos re) (+ (+ im (* (* (* 1/6 im) im) im)) (* (* (* (* (* 1/120 im) im) im) im) im)))) (* (* 0.5 (cos re)) (- (exp (- 0 im)) (exp im))))

  (* (* 0.5 (cos re)) (- (exp (- 0 im)) (exp im))))

Details

Time bar (total: 44.5s)Debug log