Average Error: 2.0 → 1.2
Time: 55.1s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{{\left(\frac{1}{{a}^{1}}\right)}^{1} \cdot \frac{x}{\sqrt{e^{\log \left(\frac{1}{z}\right) \cdot y + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}{\sqrt{e^{\log \left(\frac{1}{z}\right) \cdot y + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}} \cdot y}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{{\left(\frac{1}{{a}^{1}}\right)}^{1} \cdot \frac{x}{\sqrt{e^{\log \left(\frac{1}{z}\right) \cdot y + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}{\sqrt{e^{\log \left(\frac{1}{z}\right) \cdot y + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}} \cdot 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 ((pow((1.0 / pow(a, 1.0)), 1.0) * (x / sqrt(exp(((log((1.0 / z)) * y) + ((log((1.0 / a)) * t) + b)))))) / (sqrt(exp(((log((1.0 / z)) * y) + ((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 2.0

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

  2. Taylor expanded around inf 2.0

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

  3. Simplified1.4

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

  4. Taylor expanded around inf 1.5

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

  6. Applied add-sqr-sqrt1.5

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

  7. Applied associate-*l*1.5

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

  8. Applied associate-/r*1.5

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

  9. Applied associate-*r/1.2

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

  10. Final simplification1.2

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

Reproduce

herbie shell --seed 2020066 
(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))