Error

Derivation

1. Initial program 1.8

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

2. Applied simplify0.9

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

4. Applied add-exp-log0.9

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

5. Applied div-exp0.5

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

6. Applied simplify0.5

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

8. Applied flip-+0.5

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

9. Applied flip3-+0.5

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

10. Applied frac-add2.3

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

11. Applied simplify0.5

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

12. Applied simplify0.5

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

Runtime

Time bar (total: 4.3m)Debug logProfile

herbie shell --seed '#(1071373924 2949776965 1885069702 3247780810 90874544 2263903749)' +o rules:numerics
(FPCore (z)
  :name "Jmat.Real.gamma, branch z less than 0.5"
  (* (/ PI (sin (* PI z))) (* (* (* (sqrt (* PI 2)) (pow (+ (+ (- (- 1 z) 1) 7) 0.5) (+ (- (- 1 z) 1) 0.5))) (exp (- (+ (+ (- (- 1 z) 1) 7) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- (- 1 z) 1) 1))) (/ -1259.1392167224028 (+ (- (- 1 z) 1) 2))) (/ 771.3234287776531 (+ (- (- 1 z) 1) 3))) (/ -176.6150291621406 (+ (- (- 1 z) 1) 4))) (/ 12.507343278686905 (+ (- (- 1 z) 1) 5))) (/ -0.13857109526572012 (+ (- (- 1 z) 1) 6))) (/ 9.984369578019572e-06 (+ (- (- 1 z) 1) 7))) (/ 1.5056327351493116e-07 (+ (- (- 1 z) 1) 8))))))