Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, B

Average Error: 6.2 → 0.3

Time: 5.5s

Precision: binary64

Math

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↓

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Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	6.2
Target	1.2
Herbie	0.3

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Derivation

1. Split input into 2 regimes

2. if x < 2246989294872715

   1. Initial program 0.2

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   2. Simplified 0.2

      \[\leadsto \]
   3. Using strategy rm

   4. Applied flip-- 0.2

      \[\leadsto \]

   5. Applied associate-*l/ 0.2

      \[\leadsto \]

   6. Simplified 0.2

      \[\leadsto \]

   if 2246989294872715 < x

   1. Initial program 11.0

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   2. Simplified 11.0

      \[\leadsto \]

   3. Taylor expanded around inf 11.1

      \[\leadsto \]

   4. Simplified 0.4

      \[\leadsto \]
3. Recombined 2 regimes into one program.

4. Final simplification 0.3

   \[\leadsto \]

Reproduce

herbie shell --seed 2020179 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, B"
  :precision binary64

  :herbie-target
  (+ (+ (+ (* (- x 0.5) (log x)) (- 0.91893853320467 x)) (/ 0.083333333333333 x)) (* (/ z x) (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))

  (+ (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467) (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)))