math.sin on complex, imaginary part

Average Error: 57.7 → 0.8

Time: 8.3s

Precision: binary64

Math

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↓

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Error

Bits error versus re

Bits error versus im

Target

Original	57.7
Target	0.3
Herbie	0.8

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Derivation

1. Initial program 57.7

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2. Taylor expanded around 0 0.8

   \[\leadsto \]

3. Simplified 0.8

   \[\leadsto \]

4. Taylor expanded around inf 0.8

   \[\leadsto \]

5. Simplified 0.8

   \[\leadsto \]

6. Final simplification 0.8

   \[\leadsto \]

Reproduce

herbie shell --seed 2020180 
(FPCore (re im)
  :name "math.sin on complex, imaginary part"
  :precision binary64

  :herbie-target
  (if (< (fabs im) 1.0) (neg (* (cos re) (+ (+ im (* (* (* 0.16666666666666666 im) im) im)) (* (* (* (* (* 0.008333333333333333 im) im) im) im) im)))) (* (* 0.5 (cos re)) (- (exp (- 0.0 im)) (exp im))))

  (* (* 0.5 (cos re)) (- (exp (- 0.0 im)) (exp im))))