Average Error: 1.9 → 3.7
Time: 1.5m
Precision: 64
Internal Precision: 128
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\log a \cdot \left(t - 1.0\right) \le -691.6049690940783:\\ \;\;\;\;\frac{x \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b} \cdot \left(e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b} \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}\right)}}{y}\\ \mathbf{elif}\;\log a \cdot \left(t - 1.0\right) \le -164.65653419163408:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{a}^{\left(t - 1.0\right)} \cdot {z}^{y}}{e^{b}}}}\\ \mathbf{elif}\;\log a \cdot \left(t - 1.0\right) \le 311.1925546605293 \lor \neg \left(\log a \cdot \left(t - 1.0\right) \le 642.8878594422955\right):\\ \;\;\;\;\frac{x \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b} \cdot \left(e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b} \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{a}^{\left(t - 1.0\right)} \cdot {z}^{y}}{e^{b}} \cdot x}{y}\\ \end{array}\]

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

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if (* (- t 1.0) (log a)) < -691.6049690940783 or -164.65653419163408 < (* (- t 1.0) (log a)) < 311.1925546605293 or 642.8878594422955 < (* (- t 1.0) (log a))

    1. Initial program 0.6

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

    3. Applied add-cbrt-cube1.7

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

    if -691.6049690940783 < (* (- t 1.0) (log a)) < -164.65653419163408

    1. Initial program 6.1

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

    3. Applied exp-diff12.6

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

    4. Simplified11.3

      \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1.0\right)} \cdot {z}^{y}}}{e^{b}}}{y}\]
    5. Using strategy rm

    6. Applied associate-/l*6.8

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

    if 311.1925546605293 < (* (- t 1.0) (log a)) < 642.8878594422955

    1. Initial program 1.5

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

    3. Applied exp-diff11.0

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

    4. Simplified9.6

      \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1.0\right)} \cdot {z}^{y}}}{e^{b}}}{y}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification3.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\log a \cdot \left(t - 1.0\right) \le -691.6049690940783:\\ \;\;\;\;\frac{x \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b} \cdot \left(e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b} \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}\right)}}{y}\\ \mathbf{elif}\;\log a \cdot \left(t - 1.0\right) \le -164.65653419163408:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{a}^{\left(t - 1.0\right)} \cdot {z}^{y}}{e^{b}}}}\\ \mathbf{elif}\;\log a \cdot \left(t - 1.0\right) \le 311.1925546605293 \lor \neg \left(\log a \cdot \left(t - 1.0\right) \le 642.8878594422955\right):\\ \;\;\;\;\frac{x \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b} \cdot \left(e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b} \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{a}^{\left(t - 1.0\right)} \cdot {z}^{y}}{e^{b}} \cdot x}{y}\\ \end{array}\]

Runtime

Time bar (total: 1.5m)Debug logProfile

herbie shell --seed 2018258 
(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))