Average Error: 10.0 → 10.0
Time: 2.8m
Precision: 64
Internal Precision: 1408
\[x + \frac{y - z}{\left(t + 1.0\right) - z} \cdot \left(a - x\right)\]
↓
\[\left(x + \frac{y - z}{\left(t + 1.0\right) - z} \cdot a\right) + \frac{y - z}{\left(t + 1.0\right) - z} \cdot \left(-x\right)\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Derivation

  1. Initial program 10.0

    \[x + \frac{y - z}{\left(t + 1.0\right) - z} \cdot \left(a - x\right)\]
  2. Using strategy rm

  3. Applied sub-neg10.0

    \[\leadsto x + \frac{y - z}{\left(t + 1.0\right) - z} \cdot \color{blue}{\left(a + \left(-x\right)\right)}\]

  4. Applied distribute-lft-in10.0

    \[\leadsto x + \color{blue}{\left(\frac{y - z}{\left(t + 1.0\right) - z} \cdot a + \frac{y - z}{\left(t + 1.0\right) - z} \cdot \left(-x\right)\right)}\]

  5. Applied associate-+r+10.0

    \[\leadsto \color{blue}{\left(x + \frac{y - z}{\left(t + 1.0\right) - z} \cdot a\right) + \frac{y - z}{\left(t + 1.0\right) - z} \cdot \left(-x\right)}\]
  6. Removed slow pow expressions.

Runtime

Time bar (total: 2.8m)Debug logProfile

herbie shell --seed '#(1063154770 1824007522 645063331 41291047 494775821 1237684644)' 
(FPCore (x y z t a)
  :name "Hakyll.Web.Tags:renderTagCloud from hakyll-4.7.2.3"
  (+ x (* (/ (- y z) (- (+ t 1.0) z)) (- a x))))