Jmat.Real.gamma, branch z less than 0.5

Average Error: 1.8 → 0.5

Time: 19.9s

Precision: binary64

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Math

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↓

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Error

Bits error versus z

Derivation

1. Initial program 1.8

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2. Simplified 1.3

   \[\leadsto \]
3. Using strategy rm

4. Applied exp-diff 1.3

   \[\leadsto \]

5. Applied associate-*l/ 1.3

   \[\leadsto \]

6. Simplified 0.4

   \[\leadsto \]
7. Using strategy rm

8. Applied div-inv 0.5

   \[\leadsto \]

9. Final simplification 0.5

   \[\leadsto \]

Reproduce

herbie shell --seed 2020191 
(FPCore (z)
  :name "Jmat.Real.gamma, branch z less than 0.5"
  :precision binary64
  :pre (<= z 0.5)
  (* (/ PI (sin (* PI z))) (* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- (- 1.0 z) 1.0) 7.0) 0.5) (+ (- (- 1.0 z) 1.0) 0.5))) (exp (neg (+ (+ (- (- 1.0 z) 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- (- 1.0 z) 1.0) 1.0))) (/ -1259.1392167224028 (+ (- (- 1.0 z) 1.0) 2.0))) (/ 771.3234287776531 (+ (- (- 1.0 z) 1.0) 3.0))) (/ -176.6150291621406 (+ (- (- 1.0 z) 1.0) 4.0))) (/ 12.507343278686905 (+ (- (- 1.0 z) 1.0) 5.0))) (/ -0.13857109526572012 (+ (- (- 1.0 z) 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- (- 1.0 z) 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- (- 1.0 z) 1.0) 8.0))))))