Average Error: 1.9 → 1.2
Time: 15.3s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{x \cdot \frac{{\left(\frac{1}{a}\right)}^{1}}{e^{\left(y \cdot \log \left(\frac{1}{\sqrt{z}}\right) + y \cdot \log \left(\frac{1}{\sqrt{z}}\right)\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{y}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{x \cdot \frac{{\left(\frac{1}{a}\right)}^{1}}{e^{\left(y \cdot \log \left(\frac{1}{\sqrt{z}}\right) + y \cdot \log \left(\frac{1}{\sqrt{z}}\right)\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{y}
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) {
	return ((x * (pow((1.0 / a), 1.0) / exp((((y * log((1.0 / sqrt(z)))) + (y * log((1.0 / sqrt(z))))) + ((log((1.0 / a)) * t) + b))))) / 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 1.9

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

  2. Taylor expanded around inf 1.9

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

  3. Simplified1.2

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

  5. Applied add-sqr-sqrt1.2

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

  6. Applied add-sqr-sqrt1.2

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

  7. Applied times-frac1.2

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

  8. Applied log-prod1.2

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

  9. Applied distribute-lft-in1.2

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

  10. Simplified1.2

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

  11. Simplified1.2

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

  12. Final simplification1.2

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

Reproduce

herbie shell --seed 2020058 
(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))