Average Error: 9.6 → 10.1
Time: 1.9m
Precision: 64
Internal Precision: 1408
\[x + \frac{y - z}{\left(t + 1.0\right) - z} \cdot \left(a - x\right)\]
↓
\[x + \left(\frac{1}{\sqrt[3]{\left(t + 1.0\right) - z} \cdot \sqrt[3]{\left(t + 1.0\right) - z}} \cdot \frac{y - z}{\sqrt[3]{\left(t + 1.0\right) - z}}\right) \cdot \left(a - x\right)\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original9.6
Target9.6
Herbie10.1
\[x + \frac{y - z}{\left(t + 1.0\right) - z} \cdot \left(a - x\right)\]

Derivation

  1. Initial program 9.6

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

  3. Applied add-cube-cbrt10.1

    \[\leadsto x + \frac{y - z}{\color{blue}{\left(\sqrt[3]{\left(t + 1.0\right) - z} \cdot \sqrt[3]{\left(t + 1.0\right) - z}\right) \cdot \sqrt[3]{\left(t + 1.0\right) - z}}} \cdot \left(a - x\right)\]

  4. Applied *-un-lft-identity10.1

    \[\leadsto x + \frac{\color{blue}{1 \cdot \left(y - z\right)}}{\left(\sqrt[3]{\left(t + 1.0\right) - z} \cdot \sqrt[3]{\left(t + 1.0\right) - z}\right) \cdot \sqrt[3]{\left(t + 1.0\right) - z}} \cdot \left(a - x\right)\]

  5. Applied times-frac10.1

    \[\leadsto x + \color{blue}{\left(\frac{1}{\sqrt[3]{\left(t + 1.0\right) - z} \cdot \sqrt[3]{\left(t + 1.0\right) - z}} \cdot \frac{y - z}{\sqrt[3]{\left(t + 1.0\right) - z}}\right)} \cdot \left(a - x\right)\]
  6. Removed slow pow expressions.

Runtime

Time bar (total: 1.9m)Debug log

herbie shell --seed '#(1567391828 2030694642 2833800258 828025724 3004380912 3532991858)' +o setup:early-exit
(FPCore (x y z t a)
  :name "Hakyll.Web.Tags:renderTagCloud from hakyll-4.7.2.3"

  :herbie-target
  (+ x (* (/ (- y z) (- (+ t 1.0) z)) (- a x)))

  (+ x (* (/ (- y z) (- (+ t 1.0) z)) (- a x))))