Average Error: 13.8 → 13.8
Time: 7.5s
Precision: binary64
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↓
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Error

Bits error versus x

Derivation

  1. Initial program 13.8

    \[\]

  2. Simplified13.8

    \[\leadsto \]
  3. Using strategy rm

  4. Applied add-log-exp13.8

    \[\leadsto \]

  5. Applied add-log-exp13.8

    \[\leadsto \]

  6. Applied diff-log14.6

    \[\leadsto \]

  7. Simplified13.8

    \[\leadsto \]
  8. Using strategy rm

  9. Applied flip-+13.8

    \[\leadsto \]

  10. Applied associate-/r/13.8

    \[\leadsto \]

  11. Simplified13.8

    \[\leadsto \]

  12. Final simplification13.8

    \[\leadsto \]

Reproduce

herbie shell --seed 2020180 
(FPCore (x)
  :name "Jmat.Real.erf"
  :precision binary64
  (- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (neg (* (fabs x) (fabs x)))))))