Average Error: 0.1 → 0.0
Time: 3.3m
Precision: 64
Internal Precision: 384
\[\left(\left(x \cdot y + \frac{z \cdot t}{16.0}\right) - \frac{a \cdot b}{4.0}\right) + c\]
↓
\[\left(\left(c + y \cdot x\right) - \frac{a}{4.0} \cdot b\right) + z \cdot \left(t \cdot 0.0625\right)\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Derivation

  1. Initial program 0.1

    \[\left(\left(x \cdot y + \frac{z \cdot t}{16.0}\right) - \frac{a \cdot b}{4.0}\right) + c\]
  2. Using strategy rm

  3. Applied add-cbrt-cube27.6

    \[\leadsto \left(\color{blue}{\sqrt[3]{\left(\left(x \cdot y + \frac{z \cdot t}{16.0}\right) \cdot \left(x \cdot y + \frac{z \cdot t}{16.0}\right)\right) \cdot \left(x \cdot y + \frac{z \cdot t}{16.0}\right)}} - \frac{a \cdot b}{4.0}\right) + c\]

  4. Applied simplify27.6

    \[\leadsto \left(\sqrt[3]{\color{blue}{{\left(\frac{z}{\frac{16.0}{t}} + y \cdot x\right)}^{3}}} - \frac{a \cdot b}{4.0}\right) + c\]

  5. Taylor expanded around 0 46.4

    \[\leadsto \left(\color{blue}{\left(e^{\log y + \log x} + 0.0625 \cdot \left(z \cdot t\right)\right)} - \frac{a \cdot b}{4.0}\right) + c\]

  6. Applied simplify0.0

    \[\leadsto \color{blue}{\left(\left(c + y \cdot x\right) - \frac{a}{4.0} \cdot b\right) + z \cdot \left(t \cdot 0.0625\right)}\]
  7. Removed slow pow expressions.

Runtime

Time bar (total: 3.3m)Debug log

herbie shell --seed '#(1567391828 2030694642 2833800258 828025724 3004380912 3532991858)' +o setup:early-exit +o reduce:binary-search
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, C"
  (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))