Average Error: 0.1 → 0.3
Time: 17.9s
Precision: 64
Internal Precision: 576
\[\left(\left(\left(\left(a \cdot x\right) \cdot x\right) \cdot x + \left(b \cdot x\right) \cdot x\right) + c \cdot x\right) + d\]
\[\left(x \cdot \left(\sqrt[3]{x \cdot \left(b + x \cdot a\right)} \cdot \left(\sqrt[3]{x \cdot \left(b + x \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(b + x \cdot a\right)}\right)\right) + c \cdot x\right) + d\]

Error

Bits error versus a

Bits error versus x

Bits error versus b

Bits error versus c

Bits error versus d

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(\left(\left(a \cdot x\right) \cdot x\right) \cdot x + \left(b \cdot x\right) \cdot x\right) + c \cdot x\right) + d\]
  2. Using strategy rm
  3. Applied distribute-rgt-out0.1

    \[\leadsto \left(\color{blue}{x \cdot \left(\left(a \cdot x\right) \cdot x + b \cdot x\right)} + c \cdot x\right) + d\]
  4. Simplified0.1

    \[\leadsto \left(x \cdot \color{blue}{\left(x \cdot \left(a \cdot x + b\right)\right)} + c \cdot x\right) + d\]
  5. Using strategy rm
  6. Applied add-cube-cbrt0.3

    \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{x \cdot \left(a \cdot x + b\right)} \cdot \sqrt[3]{x \cdot \left(a \cdot x + b\right)}\right) \cdot \sqrt[3]{x \cdot \left(a \cdot x + b\right)}\right)} + c \cdot x\right) + d\]
  7. Final simplification0.3

    \[\leadsto \left(x \cdot \left(\sqrt[3]{x \cdot \left(b + x \cdot a\right)} \cdot \left(\sqrt[3]{x \cdot \left(b + x \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(b + x \cdot a\right)}\right)\right) + c \cdot x\right) + d\]

Runtime

Time bar (total: 17.9s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (a x b c d)
  :name "a*x*x*x + b*x*x + c*x + d"
  (+ (+ (+ (* (* (* a x) x) x) (* (* b x) x)) (* c x)) d))