Average Error: 1.7 → 0.5
Time: 1.0min
Precision: binary64
\[z \leq 0.5\]
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right) \]
↓
\[\begin{array}{l} t_0 := 0.9999999999996197 + \frac{\frac{457679.80848377093}{1 - z} + -676.5203681217565}{1 - z}\\ t_1 := \sqrt[3]{e^{z + -7.5}}\\ \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(t_1 \cdot \left(\left(\left(\sqrt{\pi} \cdot \sqrt{2}\right) \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot \left(t_1 \cdot t_1\right)\right)\right) \cdot \left(\left(\left(\left(\left(\left(\frac{\mathsf{fma}\left(-1259.1392167224028, t_0, \left(2 - z\right) \cdot \left(0.9999999999994297 + {\left(\frac{676.5203681218851}{1 - z}\right)}^{3}\right)\right)}{t_0 \cdot \left(2 - z\right)} + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z}\right) + \frac{12.507343278686905}{5 - z}\right) + \frac{-0.13857109526572012}{6 - z}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{7 - z}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right) \end{array} \]
\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^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)
↓
\begin{array}{l}
t_0 := 0.9999999999996197 + \frac{\frac{457679.80848377093}{1 - z} + -676.5203681217565}{1 - z}\\
t_1 := \sqrt[3]{e^{z + -7.5}}\\
\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(t_1 \cdot \left(\left(\left(\sqrt{\pi} \cdot \sqrt{2}\right) \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot \left(t_1 \cdot t_1\right)\right)\right) \cdot \left(\left(\left(\left(\left(\left(\frac{\mathsf{fma}\left(-1259.1392167224028, t_0, \left(2 - z\right) \cdot \left(0.9999999999994297 + {\left(\frac{676.5203681218851}{1 - z}\right)}^{3}\right)\right)}{t_0 \cdot \left(2 - z\right)} + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z}\right) + \frac{12.507343278686905}{5 - z}\right) + \frac{-0.13857109526572012}{6 - z}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{7 - z}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)
\end{array}

(FPCore (z)
 :precision binary64
 (*
  (/ PI (sin (* PI z)))
  (*
   (*
    (*
     (sqrt (* PI 2.0))
     (pow (+ (+ (- (- 1.0 z) 1.0) 7.0) 0.5) (+ (- (- 1.0 z) 1.0) 0.5)))
    (exp (- (+ (+ (- (- 1.0 z) 1.0) 7.0) 0.5))))
   (+
    (+
     (+
      (+
       (+
        (+
         (+
          (+
           0.9999999999998099
           (/ 676.5203681218851 (+ (- (- 1.0 z) 1.0) 1.0)))
          (/ -1259.1392167224028 (+ (- (- 1.0 z) 1.0) 2.0)))
         (/ 771.3234287776531 (+ (- (- 1.0 z) 1.0) 3.0)))
        (/ -176.6150291621406 (+ (- (- 1.0 z) 1.0) 4.0)))
       (/ 12.507343278686905 (+ (- (- 1.0 z) 1.0) 5.0)))
      (/ -0.13857109526572012 (+ (- (- 1.0 z) 1.0) 6.0)))
     (/ 9.984369578019572e-6 (+ (- (- 1.0 z) 1.0) 7.0)))
    (/ 1.5056327351493116e-7 (+ (- (- 1.0 z) 1.0) 8.0))))))
↓
(FPCore (z)
 :precision binary64
 (let* ((t_0
         (+
          0.9999999999996197
          (/
           (+ (/ 457679.80848377093 (- 1.0 z)) -676.5203681217565)
           (- 1.0 z))))
        (t_1 (cbrt (exp (+ z -7.5)))))
   (*
    (/ PI (sin (* PI z)))
    (*
     (*
      t_1
      (* (* (* (sqrt PI) (sqrt 2.0)) (pow (- 7.5 z) (- 0.5 z))) (* t_1 t_1)))
     (+
      (+
       (+
        (+
         (+
          (+
           (/
            (fma
             -1259.1392167224028
             t_0
             (*
              (- 2.0 z)
              (+
               0.9999999999994297
               (pow (/ 676.5203681218851 (- 1.0 z)) 3.0))))
            (* t_0 (- 2.0 z)))
           (/ 771.3234287776531 (- 3.0 z)))
          (/ -176.6150291621406 (- 4.0 z)))
         (/ 12.507343278686905 (- 5.0 z)))
        (/ -0.13857109526572012 (- 6.0 z)))
       (/ 9.984369578019572e-6 (- 7.0 z)))
      (/ 1.5056327351493116e-7 (- 8.0 z)))))))
double code(double z) {
	return (((double) M_PI) / sin((((double) M_PI) * z))) * (((sqrt((((double) M_PI) * 2.0)) * pow(((((1.0 - z) - 1.0) + 7.0) + 0.5), (((1.0 - z) - 1.0) + 0.5))) * exp(-((((1.0 - z) - 1.0) + 7.0) + 0.5))) * ((((((((0.9999999999998099 + (676.5203681218851 / (((1.0 - z) - 1.0) + 1.0))) + (-1259.1392167224028 / (((1.0 - z) - 1.0) + 2.0))) + (771.3234287776531 / (((1.0 - z) - 1.0) + 3.0))) + (-176.6150291621406 / (((1.0 - z) - 1.0) + 4.0))) + (12.507343278686905 / (((1.0 - z) - 1.0) + 5.0))) + (-0.13857109526572012 / (((1.0 - z) - 1.0) + 6.0))) + (9.984369578019572e-6 / (((1.0 - z) - 1.0) + 7.0))) + (1.5056327351493116e-7 / (((1.0 - z) - 1.0) + 8.0))));
}
↓
double code(double z) {
	double t_0 = 0.9999999999996197 + (((457679.80848377093 / (1.0 - z)) + -676.5203681217565) / (1.0 - z));
	double t_1 = cbrt(exp((z + -7.5)));
	return (((double) M_PI) / sin((((double) M_PI) * z))) * ((t_1 * (((sqrt(((double) M_PI)) * sqrt(2.0)) * pow((7.5 - z), (0.5 - z))) * (t_1 * t_1))) * (((((((fma(-1259.1392167224028, t_0, ((2.0 - z) * (0.9999999999994297 + pow((676.5203681218851 / (1.0 - z)), 3.0)))) / (t_0 * (2.0 - z))) + (771.3234287776531 / (3.0 - z))) + (-176.6150291621406 / (4.0 - z))) + (12.507343278686905 / (5.0 - z))) + (-0.13857109526572012 / (6.0 - z))) + (9.984369578019572e-6 / (7.0 - z))) + (1.5056327351493116e-7 / (8.0 - z))));
}

Error

Bits error versus z

Derivation

  1. Initial program 1.7

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

  2. Simplified1.7

    \[\leadsto \color{blue}{\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot e^{z + -7.5}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z}\right) + \frac{12.507343278686905}{5 - z}\right) + \frac{-0.13857109526572012}{6 - z}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{7 - z}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right)} \]

  3. Applied flip3-+_binary641.7

    \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot e^{z + -7.5}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\color{blue}{\frac{{0.9999999999998099}^{3} + {\left(\frac{676.5203681218851}{1 - z}\right)}^{3}}{0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z} - 0.9999999999998099 \cdot \frac{676.5203681218851}{1 - z}\right)}} + \frac{-1259.1392167224028}{2 - z}\right) + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z}\right) + \frac{12.507343278686905}{5 - z}\right) + \frac{-0.13857109526572012}{6 - z}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{7 - z}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right) \]

  4. Applied frac-add_binary641.0

    \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot e^{z + -7.5}\right) \cdot \left(\left(\left(\left(\left(\left(\color{blue}{\frac{\left({0.9999999999998099}^{3} + {\left(\frac{676.5203681218851}{1 - z}\right)}^{3}\right) \cdot \left(2 - z\right) + \left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z} - 0.9999999999998099 \cdot \frac{676.5203681218851}{1 - z}\right)\right) \cdot -1259.1392167224028}{\left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z} - 0.9999999999998099 \cdot \frac{676.5203681218851}{1 - z}\right)\right) \cdot \left(2 - z\right)}} + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z}\right) + \frac{12.507343278686905}{5 - z}\right) + \frac{-0.13857109526572012}{6 - z}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{7 - z}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right) \]

  5. Simplified1.0

    \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot e^{z + -7.5}\right) \cdot \left(\left(\left(\left(\left(\left(\frac{\color{blue}{\mathsf{fma}\left(-1259.1392167224028, 0.9999999999996197 + \frac{\frac{457679.80848377093}{1 - z} + -676.5203681217565}{1 - z}, \left(2 - z\right) \cdot \left(0.9999999999994297 + {\left(\frac{676.5203681218851}{1 - z}\right)}^{3}\right)\right)}}{\left(0.9999999999998099 \cdot 0.9999999999998099 + \left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z} - 0.9999999999998099 \cdot \frac{676.5203681218851}{1 - z}\right)\right) \cdot \left(2 - z\right)} + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z}\right) + \frac{12.507343278686905}{5 - z}\right) + \frac{-0.13857109526572012}{6 - z}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{7 - z}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right) \]

  6. Simplified1.0

    \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot e^{z + -7.5}\right) \cdot \left(\left(\left(\left(\left(\left(\frac{\mathsf{fma}\left(-1259.1392167224028, 0.9999999999996197 + \frac{\frac{457679.80848377093}{1 - z} + -676.5203681217565}{1 - z}, \left(2 - z\right) \cdot \left(0.9999999999994297 + {\left(\frac{676.5203681218851}{1 - z}\right)}^{3}\right)\right)}{\color{blue}{\left(2 - z\right) \cdot \left(0.9999999999996197 + \frac{\frac{457679.80848377093}{1 - z} + -676.5203681217565}{1 - z}\right)}} + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z}\right) + \frac{12.507343278686905}{5 - z}\right) + \frac{-0.13857109526572012}{6 - z}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{7 - z}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right) \]

  7. Applied sqrt-prod_binary640.5

    \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\color{blue}{\left(\sqrt{\pi} \cdot \sqrt{2}\right)} \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot e^{z + -7.5}\right) \cdot \left(\left(\left(\left(\left(\left(\frac{\mathsf{fma}\left(-1259.1392167224028, 0.9999999999996197 + \frac{\frac{457679.80848377093}{1 - z} + -676.5203681217565}{1 - z}, \left(2 - z\right) \cdot \left(0.9999999999994297 + {\left(\frac{676.5203681218851}{1 - z}\right)}^{3}\right)\right)}{\left(2 - z\right) \cdot \left(0.9999999999996197 + \frac{\frac{457679.80848377093}{1 - z} + -676.5203681217565}{1 - z}\right)} + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z}\right) + \frac{12.507343278686905}{5 - z}\right) + \frac{-0.13857109526572012}{6 - z}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{7 - z}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right) \]

  8. Applied add-cube-cbrt_binary640.5

    \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\left(\sqrt{\pi} \cdot \sqrt{2}\right) \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot \color{blue}{\left(\left(\sqrt[3]{e^{z + -7.5}} \cdot \sqrt[3]{e^{z + -7.5}}\right) \cdot \sqrt[3]{e^{z + -7.5}}\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\frac{\mathsf{fma}\left(-1259.1392167224028, 0.9999999999996197 + \frac{\frac{457679.80848377093}{1 - z} + -676.5203681217565}{1 - z}, \left(2 - z\right) \cdot \left(0.9999999999994297 + {\left(\frac{676.5203681218851}{1 - z}\right)}^{3}\right)\right)}{\left(2 - z\right) \cdot \left(0.9999999999996197 + \frac{\frac{457679.80848377093}{1 - z} + -676.5203681217565}{1 - z}\right)} + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z}\right) + \frac{12.507343278686905}{5 - z}\right) + \frac{-0.13857109526572012}{6 - z}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{7 - z}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right) \]

  9. Applied associate-*r*_binary640.5

    \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\color{blue}{\left(\left(\left(\left(\sqrt{\pi} \cdot \sqrt{2}\right) \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\sqrt[3]{e^{z + -7.5}} \cdot \sqrt[3]{e^{z + -7.5}}\right)\right) \cdot \sqrt[3]{e^{z + -7.5}}\right)} \cdot \left(\left(\left(\left(\left(\left(\frac{\mathsf{fma}\left(-1259.1392167224028, 0.9999999999996197 + \frac{\frac{457679.80848377093}{1 - z} + -676.5203681217565}{1 - z}, \left(2 - z\right) \cdot \left(0.9999999999994297 + {\left(\frac{676.5203681218851}{1 - z}\right)}^{3}\right)\right)}{\left(2 - z\right) \cdot \left(0.9999999999996197 + \frac{\frac{457679.80848377093}{1 - z} + -676.5203681217565}{1 - z}\right)} + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z}\right) + \frac{12.507343278686905}{5 - z}\right) + \frac{-0.13857109526572012}{6 - z}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{7 - z}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right) \]

  10. Final simplification0.5

    \[\leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\sqrt[3]{e^{z + -7.5}} \cdot \left(\left(\left(\sqrt{\pi} \cdot \sqrt{2}\right) \cdot {\left(7.5 - z\right)}^{\left(0.5 - z\right)}\right) \cdot \left(\sqrt[3]{e^{z + -7.5}} \cdot \sqrt[3]{e^{z + -7.5}}\right)\right)\right) \cdot \left(\left(\left(\left(\left(\left(\frac{\mathsf{fma}\left(-1259.1392167224028, 0.9999999999996197 + \frac{\frac{457679.80848377093}{1 - z} + -676.5203681217565}{1 - z}, \left(2 - z\right) \cdot \left(0.9999999999994297 + {\left(\frac{676.5203681218851}{1 - z}\right)}^{3}\right)\right)}{\left(0.9999999999996197 + \frac{\frac{457679.80848377093}{1 - z} + -676.5203681217565}{1 - z}\right) \cdot \left(2 - z\right)} + \frac{771.3234287776531}{3 - z}\right) + \frac{-176.6150291621406}{4 - z}\right) + \frac{12.507343278686905}{5 - z}\right) + \frac{-0.13857109526572012}{6 - z}\right) + \frac{9.984369578019572 \cdot 10^{-6}}{7 - z}\right) + \frac{1.5056327351493116 \cdot 10^{-7}}{8 - z}\right)\right) \]

Reproduce

herbie shell --seed 2022160 
(FPCore (z)
  :name "Jmat.Real.gamma, branch z less than 0.5"
  :precision binary64
  :pre (<= z 0.5)
  (* (/ PI (sin (* PI z))) (* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- (- 1.0 z) 1.0) 7.0) 0.5) (+ (- (- 1.0 z) 1.0) 0.5))) (exp (- (+ (+ (- (- 1.0 z) 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- (- 1.0 z) 1.0) 1.0))) (/ -1259.1392167224028 (+ (- (- 1.0 z) 1.0) 2.0))) (/ 771.3234287776531 (+ (- (- 1.0 z) 1.0) 3.0))) (/ -176.6150291621406 (+ (- (- 1.0 z) 1.0) 4.0))) (/ 12.507343278686905 (+ (- (- 1.0 z) 1.0) 5.0))) (/ -0.13857109526572012 (+ (- (- 1.0 z) 1.0) 6.0))) (/ 9.984369578019572e-6 (+ (- (- 1.0 z) 1.0) 7.0))) (/ 1.5056327351493116e-7 (+ (- (- 1.0 z) 1.0) 8.0))))))