Error

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Target

Derivation

1. Initial program 43.6

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

2. Taylor expanded around 0 0.8

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

4. Applied distribute-neg-in0.8

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

5. Applied distribute-lft-in0.8

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

6. Simplified0.8

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

7. Final simplification0.8

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

Reproduce

herbie shell --seed 2019004 
(FPCore (re im)
  :name "math.cos on complex, imaginary part"

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

  (* (* 0.5 (sin re)) (- (exp (- im)) (exp im))))

Details

Time bar (total: 35.0s)Debug log