Average Error: 1.9 → 2.7
Time: 3.7m
Precision: 64
Internal Precision: 576
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(t - 1.0\right) \cdot \log a \le -633.2291883233237 \lor \neg \left(\left(t - 1.0\right) \cdot \log a \le -233.52457813789584\right):\\ \;\;\;\;\frac{{e}^{\left(\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b\right)} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\log z \cdot \left(y \cdot x\right) + x}{\frac{y \cdot e^{b}}{{a}^{\left(t - 1.0\right)}}}\\ \end{array}\]

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 2 regimes

  2. if (* (- t 1.0) (log a)) < -633.2291883233237 or -233.52457813789584 < (* (- t 1.0) (log a))

    1. Initial program 1.0

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

    3. Applied *-un-lft-identity1.0

      \[\leadsto \frac{x \cdot e^{\color{blue}{1 \cdot \left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}}{y}\]

    4. Applied exp-prod1.0

      \[\leadsto \frac{x \cdot \color{blue}{{\left(e^{1}\right)}^{\left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}}{y}\]

    5. Applied simplify1.0

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

    if -633.2291883233237 < (* (- t 1.0) (log a)) < -233.52457813789584

    1. Initial program 7.2

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

    3. Applied sub-neg7.2

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

    4. Applied exp-sum13.2

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

    5. Applied associate-*r*13.2

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

    6. Applied simplify11.7

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

    7. Taylor expanded around 0 20.0

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

    8. Applied simplify11.9

      \[\leadsto \color{blue}{\frac{x + \log z \cdot \left(y \cdot x\right)}{\frac{e^{b} \cdot y}{{a}^{\left(t - 1.0\right)}}}}\]
  3. Recombined 2 regimes into one program.

  4. Applied simplify2.7

    \[\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;\left(t - 1.0\right) \cdot \log a \le -633.2291883233237 \lor \neg \left(\left(t - 1.0\right) \cdot \log a \le -233.52457813789584\right):\\ \;\;\;\;\frac{{e}^{\left(\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b\right)} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\log z \cdot \left(y \cdot x\right) + x}{\frac{y \cdot e^{b}}{{a}^{\left(t - 1.0\right)}}}\\ \end{array}}\]

Runtime

Time bar (total: 3.7m)Debug logProfile

herbie shell --seed '#(1072936661 1621281212 3440817831 3219514234 460296804 1258167384)' 
(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))