Average Error: 36.5 → 32.1
Time: 8.2s
Precision: binary64
\[\]
↓
\[\]

Error

Bits error versus g

Bits error versus h

Bits error versus a

Derivation

  1. Split input into 2 regimes

  2. if g < -7.00429167903756521e-202

    1. Initial program 35.8

      \[\]
    2. Using strategy rm

    3. Applied associate-*l/35.8

      \[\leadsto \]

    4. Applied cbrt-div31.8

      \[\leadsto \]

    5. Simplified31.8

      \[\leadsto \]
    6. Using strategy rm

    7. Applied add-cube-cbrt31.8

      \[\leadsto \]

    8. Applied sqrt-prod31.8

      \[\leadsto \]

    9. Simplified31.8

      \[\leadsto \]

    if -7.00429167903756521e-202 < g

    1. Initial program 37.1

      \[\]
    2. Using strategy rm

    3. Applied associate-*l/37.1

      \[\leadsto \]

    4. Applied cbrt-div33.3

      \[\leadsto \]

    5. Taylor expanded around inf 32.3

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

  4. Final simplification32.1

    \[\leadsto \]

Reproduce

herbie shell --seed 2020181 
(FPCore (g h a)
  :name "2-ancestry mixing, positive discriminant"
  :precision binary64
  (+ (cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h)))))) (cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))))