Average Error: 18.6 → 1.2
Time: 3.4s
Precision: binary64
\[\]
↓
\[\]

Error

Bits error versus u

Bits error versus v

Bits error versus t1

Derivation

  1. Initial program 18.6

    \[\]

  2. Simplified18.3

    \[\leadsto \]
  3. Using strategy rm

  4. Applied add-cube-cbrt18.6

    \[\leadsto \]

  5. Applied times-frac11.9

    \[\leadsto \]

  6. Applied associate-*r*1.0

    \[\leadsto \]

  7. Simplified1.0

    \[\leadsto \]
  8. Using strategy rm

  9. Applied add-cube-cbrt1.2

    \[\leadsto \]

  10. Final simplification1.2

    \[\leadsto \]

Reproduce

herbie shell --seed 2020179 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (neg t1) v) (* (+ t1 u) (+ t1 u))))