Average Error: 15.5 → 15.6
Time: 1.3m
Precision: 64
Internal Precision: 576
\[3 \cdot x - 0.1 \cdot \sqrt{400 \cdot {x}^{2} + 80}\]
\[\frac{\left(x \cdot 3\right) \cdot \left(x \cdot 3\right) - \left(0.1 \cdot 0.1\right) \cdot \left(x \cdot \left(x \cdot 400\right) + 80\right)}{3 \cdot x + 0.1 \cdot \sqrt{400 \cdot {x}^{2} + 80}}\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.5

    \[3 \cdot x - 0.1 \cdot \sqrt{400 \cdot {x}^{2} + 80}\]
  2. Using strategy rm
  3. Applied flip--15.6

    \[\leadsto \color{blue}{\frac{\left(3 \cdot x\right) \cdot \left(3 \cdot x\right) - \left(0.1 \cdot \sqrt{400 \cdot {x}^{2} + 80}\right) \cdot \left(0.1 \cdot \sqrt{400 \cdot {x}^{2} + 80}\right)}{3 \cdot x + 0.1 \cdot \sqrt{400 \cdot {x}^{2} + 80}}}\]
  4. Applied simplify15.6

    \[\leadsto \frac{\color{blue}{\left(x \cdot 3\right) \cdot \left(x \cdot 3\right) - \left(0.1 \cdot 0.1\right) \cdot \left(x \cdot \left(x \cdot 400\right) + 80\right)}}{3 \cdot x + 0.1 \cdot \sqrt{400 \cdot {x}^{2} + 80}}\]

Runtime

Time bar (total: 1.3m)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x)
  :name "3*x - 0.1 sqrt(400 x^2 + 80)"
  (- (* 3 x) (* 0.1 (sqrt (+ (* 400 (pow x 2)) 80)))))