Average Error: 2.0 → 0.3
Time: 30.0s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -8.9526966727005439 \cdot 10^{73} \lor \neg \left(x \le 1.54253563263351339 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{x \cdot \frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{y}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{1}{a}\right)}^{1} \cdot \frac{\frac{1}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{\frac{y}{x}}\\ \end{array}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -8.9526966727005439 \cdot 10^{73} \lor \neg \left(x \le 1.54253563263351339 \cdot 10^{-62}\right):\\
\;\;\;\;\frac{x \cdot \frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{y}\\

\mathbf{else}:\\
\;\;\;\;{\left(\frac{1}{a}\right)}^{1} \cdot \frac{\frac{1}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{\frac{y}{x}}\\

\end{array}
double code(double x, double y, double z, double t, double a, double b) {
	return ((x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y);
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	double temp;
	if (((x <= -8.952696672700544e+73) || !(x <= 1.5425356326335134e-62))) {
		temp = ((x * (pow((1.0 / a), 1.0) / exp(((y * log((1.0 / z))) + ((log((1.0 / a)) * t) + b))))) / y);
	} else {
		temp = (pow((1.0 / a), 1.0) * ((1.0 / exp(((y * log((1.0 / z))) + ((log((1.0 / a)) * t) + b)))) / (y / x)));
	}
	return temp;
}

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. Split input into 2 regimes

  2. if x < -8.952696672700544e+73 or 1.5425356326335134e-62 < x

    1. Initial program 0.9

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

    2. Taylor expanded around inf 0.9

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

    3. Simplified0.2

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

    if -8.952696672700544e+73 < x < 1.5425356326335134e-62

    1. Initial program 3.0

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

    2. Taylor expanded around inf 3.0

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

    3. Simplified0.4

      \[\leadsto \color{blue}{\frac{\frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{\frac{y}{x}}}\]
    4. Using strategy rm

    5. Applied *-un-lft-identity0.4

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

    6. Applied *-un-lft-identity0.4

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

    7. Applied times-frac0.4

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

    8. Applied div-inv0.4

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

    9. Applied times-frac0.4

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

    10. Simplified0.4

      \[\leadsto \color{blue}{{\left(\frac{1}{a}\right)}^{1}} \cdot \frac{\frac{1}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{\frac{y}{x}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -8.9526966727005439 \cdot 10^{73} \lor \neg \left(x \le 1.54253563263351339 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{x \cdot \frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{y}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{1}{a}\right)}^{1} \cdot \frac{\frac{1}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{\frac{y}{x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020057 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2"
  :precision binary64
  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1) (log a))) b))) y))