Average Error: 61.6 → 1.0
Time: 30.7s
Precision: binary64
\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)\]
↓
\[\left(\sqrt{\pi \cdot 2} \cdot {\left(z + \left(7 + \left(0.5 - 1\right)\right)\right)}^{\left(z + \left(0.5 - 1\right)\right)}\right) \cdot \left(e^{1} \cdot \left(\left(0.9999999999998099 + \left(\left(\frac{-0.13857109526572012}{z + \left(6 - 1\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{z + \left(7 - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + \left(8 - 1\right)}\right)\right) + \left(\frac{12.507343278686905}{z + \left(5 - 1\right)} + \left(\frac{676.5203681218851}{z} + \left(\frac{-1259.1392167224028}{2 + \left(z - 1\right)} + \left(\frac{771.3234287776531}{z + \left(3 - 1\right)} + \frac{-176.6150291621406}{z + \left(4 - 1\right)}\right)\right)\right)\right)\right)\right) \cdot e^{\left(-z\right) - \left(7 + 0.5\right)}\right)\right)\]
\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)
↓
\left(\sqrt{\pi \cdot 2} \cdot {\left(z + \left(7 + \left(0.5 - 1\right)\right)\right)}^{\left(z + \left(0.5 - 1\right)\right)}\right) \cdot \left(e^{1} \cdot \left(\left(0.9999999999998099 + \left(\left(\frac{-0.13857109526572012}{z + \left(6 - 1\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{z + \left(7 - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + \left(8 - 1\right)}\right)\right) + \left(\frac{12.507343278686905}{z + \left(5 - 1\right)} + \left(\frac{676.5203681218851}{z} + \left(\frac{-1259.1392167224028}{2 + \left(z - 1\right)} + \left(\frac{771.3234287776531}{z + \left(3 - 1\right)} + \frac{-176.6150291621406}{z + \left(4 - 1\right)}\right)\right)\right)\right)\right)\right) \cdot e^{\left(-z\right) - \left(7 + 0.5\right)}\right)\right)
double code(double z) {
	return ((double) (((double) (((double) (((double) sqrt(((double) (((double) M_PI) * 2.0)))) * ((double) pow(((double) (((double) (((double) (z - 1.0)) + 7.0)) + 0.5)), ((double) (((double) (z - 1.0)) + 0.5)))))) * ((double) exp(((double) -(((double) (((double) (((double) (z - 1.0)) + 7.0)) + 0.5)))))))) * ((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (0.9999999999998099 + (676.5203681218851 / ((double) (((double) (z - 1.0)) + 1.0))))) + (-1259.1392167224028 / ((double) (((double) (z - 1.0)) + 2.0))))) + (771.3234287776531 / ((double) (((double) (z - 1.0)) + 3.0))))) + (-176.6150291621406 / ((double) (((double) (z - 1.0)) + 4.0))))) + (12.507343278686905 / ((double) (((double) (z - 1.0)) + 5.0))))) + (-0.13857109526572012 / ((double) (((double) (z - 1.0)) + 6.0))))) + (9.984369578019572e-06 / ((double) (((double) (z - 1.0)) + 7.0))))) + (1.5056327351493116e-07 / ((double) (((double) (z - 1.0)) + 8.0)))))));
}
↓
double code(double z) {
	return ((double) (((double) (((double) sqrt(((double) (((double) M_PI) * 2.0)))) * ((double) pow(((double) (z + ((double) (7.0 + ((double) (0.5 - 1.0)))))), ((double) (z + ((double) (0.5 - 1.0)))))))) * ((double) (((double) exp(1.0)) * ((double) (((double) (0.9999999999998099 + ((double) (((double) ((-0.13857109526572012 / ((double) (z + ((double) (6.0 - 1.0))))) + ((double) ((9.984369578019572e-06 / ((double) (z + ((double) (7.0 - 1.0))))) + (1.5056327351493116e-07 / ((double) (z + ((double) (8.0 - 1.0))))))))) + ((double) ((12.507343278686905 / ((double) (z + ((double) (5.0 - 1.0))))) + ((double) ((676.5203681218851 / z) + ((double) ((-1259.1392167224028 / ((double) (2.0 + ((double) (z - 1.0))))) + ((double) ((771.3234287776531 / ((double) (z + ((double) (3.0 - 1.0))))) + (-176.6150291621406 / ((double) (z + ((double) (4.0 - 1.0))))))))))))))))) * ((double) exp(((double) (((double) -(z)) - ((double) (7.0 + 0.5))))))))))));
}

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 61.6

    \[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)\]

  2. Simplified1.2

    \[\leadsto \color{blue}{\sqrt{\pi \cdot 2} \cdot \left({\left(z + \left(\left(7 - 1\right) + 0.5\right)\right)}^{\left(z + \left(0.5 - 1\right)\right)} \cdot \left(e^{1 - \left(z + \left(7 + 0.5\right)\right)} \cdot \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{z} + \left(\frac{-1259.1392167224028}{2 + \left(z - 1\right)} + \left(\frac{771.3234287776531}{z + \left(3 - 1\right)} + \frac{-176.6150291621406}{z + \left(4 - 1\right)}\right)\right)\right) + \left(\frac{12.507343278686905}{z + \left(5 - 1\right)} + \left(\frac{-0.13857109526572012}{z + \left(6 - 1\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{z + \left(7 - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + \left(8 - 1\right)}\right)\right)\right)\right)\right)\right)\right)}\]
  3. Using strategy rm

  4. Applied sub-neg1.2

    \[\leadsto \sqrt{\pi \cdot 2} \cdot \left({\left(z + \left(\left(7 - 1\right) + 0.5\right)\right)}^{\left(z + \left(0.5 - 1\right)\right)} \cdot \left(e^{\color{blue}{1 + \left(-\left(z + \left(7 + 0.5\right)\right)\right)}} \cdot \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{z} + \left(\frac{-1259.1392167224028}{2 + \left(z - 1\right)} + \left(\frac{771.3234287776531}{z + \left(3 - 1\right)} + \frac{-176.6150291621406}{z + \left(4 - 1\right)}\right)\right)\right) + \left(\frac{12.507343278686905}{z + \left(5 - 1\right)} + \left(\frac{-0.13857109526572012}{z + \left(6 - 1\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{z + \left(7 - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + \left(8 - 1\right)}\right)\right)\right)\right)\right)\right)\right)\]

  5. Applied exp-sum1.0

    \[\leadsto \sqrt{\pi \cdot 2} \cdot \left({\left(z + \left(\left(7 - 1\right) + 0.5\right)\right)}^{\left(z + \left(0.5 - 1\right)\right)} \cdot \left(\color{blue}{\left(e^{1} \cdot e^{-\left(z + \left(7 + 0.5\right)\right)}\right)} \cdot \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{z} + \left(\frac{-1259.1392167224028}{2 + \left(z - 1\right)} + \left(\frac{771.3234287776531}{z + \left(3 - 1\right)} + \frac{-176.6150291621406}{z + \left(4 - 1\right)}\right)\right)\right) + \left(\frac{12.507343278686905}{z + \left(5 - 1\right)} + \left(\frac{-0.13857109526572012}{z + \left(6 - 1\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{z + \left(7 - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + \left(8 - 1\right)}\right)\right)\right)\right)\right)\right)\right)\]

  6. Applied associate-*l*1.0

    \[\leadsto \sqrt{\pi \cdot 2} \cdot \left({\left(z + \left(\left(7 - 1\right) + 0.5\right)\right)}^{\left(z + \left(0.5 - 1\right)\right)} \cdot \color{blue}{\left(e^{1} \cdot \left(e^{-\left(z + \left(7 + 0.5\right)\right)} \cdot \left(0.9999999999998099 + \left(\left(\frac{676.5203681218851}{z} + \left(\frac{-1259.1392167224028}{2 + \left(z - 1\right)} + \left(\frac{771.3234287776531}{z + \left(3 - 1\right)} + \frac{-176.6150291621406}{z + \left(4 - 1\right)}\right)\right)\right) + \left(\frac{12.507343278686905}{z + \left(5 - 1\right)} + \left(\frac{-0.13857109526572012}{z + \left(6 - 1\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{z + \left(7 - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + \left(8 - 1\right)}\right)\right)\right)\right)\right)\right)\right)}\right)\]

  7. Simplified1.0

    \[\leadsto \sqrt{\pi \cdot 2} \cdot \left({\left(z + \left(\left(7 - 1\right) + 0.5\right)\right)}^{\left(z + \left(0.5 - 1\right)\right)} \cdot \left(e^{1} \cdot \color{blue}{\left(\left(0.9999999999998099 + \left(\left(\frac{-0.13857109526572012}{z + \left(6 - 1\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{z + \left(7 - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + \left(8 - 1\right)}\right)\right) + \left(\frac{12.507343278686905}{z + \left(5 - 1\right)} + \left(\frac{676.5203681218851}{z} + \left(\frac{-1259.1392167224028}{2 + \left(z - 1\right)} + \left(\frac{771.3234287776531}{z + \left(3 - 1\right)} + \frac{-176.6150291621406}{z + \left(4 - 1\right)}\right)\right)\right)\right)\right)\right) \cdot e^{\left(-z\right) - \left(7 + 0.5\right)}\right)}\right)\right)\]
  8. Using strategy rm

  9. Applied associate-*r*1.0

    \[\leadsto \color{blue}{\left(\sqrt{\pi \cdot 2} \cdot {\left(z + \left(\left(7 - 1\right) + 0.5\right)\right)}^{\left(z + \left(0.5 - 1\right)\right)}\right) \cdot \left(e^{1} \cdot \left(\left(0.9999999999998099 + \left(\left(\frac{-0.13857109526572012}{z + \left(6 - 1\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{z + \left(7 - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + \left(8 - 1\right)}\right)\right) + \left(\frac{12.507343278686905}{z + \left(5 - 1\right)} + \left(\frac{676.5203681218851}{z} + \left(\frac{-1259.1392167224028}{2 + \left(z - 1\right)} + \left(\frac{771.3234287776531}{z + \left(3 - 1\right)} + \frac{-176.6150291621406}{z + \left(4 - 1\right)}\right)\right)\right)\right)\right)\right) \cdot e^{\left(-z\right) - \left(7 + 0.5\right)}\right)\right)}\]

  10. Simplified1.0

    \[\leadsto \color{blue}{\left(\sqrt{\pi \cdot 2} \cdot {\left(z + \left(7 + \left(0.5 - 1\right)\right)\right)}^{\left(z + \left(0.5 - 1\right)\right)}\right)} \cdot \left(e^{1} \cdot \left(\left(0.9999999999998099 + \left(\left(\frac{-0.13857109526572012}{z + \left(6 - 1\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{z + \left(7 - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + \left(8 - 1\right)}\right)\right) + \left(\frac{12.507343278686905}{z + \left(5 - 1\right)} + \left(\frac{676.5203681218851}{z} + \left(\frac{-1259.1392167224028}{2 + \left(z - 1\right)} + \left(\frac{771.3234287776531}{z + \left(3 - 1\right)} + \frac{-176.6150291621406}{z + \left(4 - 1\right)}\right)\right)\right)\right)\right)\right) \cdot e^{\left(-z\right) - \left(7 + 0.5\right)}\right)\right)\]

  11. Final simplification1.0

    \[\leadsto \left(\sqrt{\pi \cdot 2} \cdot {\left(z + \left(7 + \left(0.5 - 1\right)\right)\right)}^{\left(z + \left(0.5 - 1\right)\right)}\right) \cdot \left(e^{1} \cdot \left(\left(0.9999999999998099 + \left(\left(\frac{-0.13857109526572012}{z + \left(6 - 1\right)} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{z + \left(7 - 1\right)} + \frac{1.5056327351493116 \cdot 10^{-07}}{z + \left(8 - 1\right)}\right)\right) + \left(\frac{12.507343278686905}{z + \left(5 - 1\right)} + \left(\frac{676.5203681218851}{z} + \left(\frac{-1259.1392167224028}{2 + \left(z - 1\right)} + \left(\frac{771.3234287776531}{z + \left(3 - 1\right)} + \frac{-176.6150291621406}{z + \left(4 - 1\right)}\right)\right)\right)\right)\right)\right) \cdot e^{\left(-z\right) - \left(7 + 0.5\right)}\right)\right)\]

Reproduce

herbie shell --seed 2020196 
(FPCore (z)
  :name "Jmat.Real.gamma, branch z greater than 0.5"
  :precision binary64
  (* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (- (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- z 1.0) 1.0))) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)))))