Average Error: 18.4 → 0.2
Time: 20.6s
Precision: 64
Internal Precision: 320
\[{\left(\left(\log \left({x}^{2}\right) \cdot 42\right) \cdot y + 4\right)}^{z}\]
\[{\left(\left(\left(\log \left(\left|x\right|\right) + \log \left(\left|x\right|\right)\right) \cdot 42\right) \cdot y + 4\right)}^{z}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 18.4

    \[{\left(\left(\log \left({x}^{2}\right) \cdot 42\right) \cdot y + 4\right)}^{z}\]
  2. Using strategy rm
  3. Applied add-sqr-sqrt18.4

    \[\leadsto {\left(\left(\log \color{blue}{\left(\sqrt{{x}^{2}} \cdot \sqrt{{x}^{2}}\right)} \cdot 42\right) \cdot y + 4\right)}^{z}\]
  4. Applied log-prod18.4

    \[\leadsto {\left(\left(\color{blue}{\left(\log \left(\sqrt{{x}^{2}}\right) + \log \left(\sqrt{{x}^{2}}\right)\right)} \cdot 42\right) \cdot y + 4\right)}^{z}\]
  5. Applied simplify18.4

    \[\leadsto {\left(\left(\left(\color{blue}{\log \left(\left|x\right|\right)} + \log \left(\sqrt{{x}^{2}}\right)\right) \cdot 42\right) \cdot y + 4\right)}^{z}\]
  6. Applied simplify0.2

    \[\leadsto {\left(\left(\left(\log \left(\left|x\right|\right) + \color{blue}{\log \left(\left|x\right|\right)}\right) \cdot 42\right) \cdot y + 4\right)}^{z}\]

Runtime

Time bar (total: 20.6s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x y z)
  :name "(log(x^2) * 42y + 4)^z"
  (pow (+ (* (* (log (pow x 2)) 42) y) 4) z))