Average Error: 1.8 → 1.8
Time: 1.5m
Precision: 64
Internal Precision: 576
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{\sqrt[3]{e^{\left(\log z \cdot y + \log a \cdot \left(t - 1.0\right)\right) - b} \cdot x} \cdot \left(\sqrt[3]{e^{\left(\log z \cdot y + \log a \cdot \left(t - 1.0\right)\right) - b} \cdot x} \cdot \sqrt[3]{e^{\left(\log z \cdot y + \log a \cdot \left(t - 1.0\right)\right) - b} \cdot x}\right)}{y}\]

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.8

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

  3. Applied add-cube-cbrt1.8

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

  4. Final simplification1.8

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

Runtime

Time bar (total: 1.5m)Debug logProfile

herbie shell --seed 2018215 +o rules:numerics
(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))