Average Error: 2.0 → 2.0
Time: 2.5m
Precision: 64
Internal Precision: 576
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\sqrt[3]{\frac{e^{\left(\log z \cdot y + \log a \cdot \left(t - 1.0\right)\right) - b} \cdot x}{y}} \cdot \left(\sqrt[3]{\frac{e^{\left(\log z \cdot y + \log a \cdot \left(t - 1.0\right)\right) - b} \cdot x}{y}} \cdot \sqrt[3]{\frac{e^{\left(\log z \cdot y + \log a \cdot \left(t - 1.0\right)\right) - b} \cdot x}{y}}\right)\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Bits error versus b

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 2.0

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

  3. Applied add-cube-cbrt2.0

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

  4. Final simplification2.0

    \[\leadsto \sqrt[3]{\frac{e^{\left(\log z \cdot y + \log a \cdot \left(t - 1.0\right)\right) - b} \cdot x}{y}} \cdot \left(\sqrt[3]{\frac{e^{\left(\log z \cdot y + \log a \cdot \left(t - 1.0\right)\right) - b} \cdot x}{y}} \cdot \sqrt[3]{\frac{e^{\left(\log z \cdot y + \log a \cdot \left(t - 1.0\right)\right) - b} \cdot x}{y}}\right)\]

Runtime

Time bar (total: 2.5m)Debug logProfile

herbie shell --seed 2018214 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2"
  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))