Derivation

Initial program 1.8
\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]
Simplified0.6
\[\leadsto \color{blue}{\left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right) \cdot \left(\sqrt{2 \cdot \pi} \cdot {\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right)\right) \cdot \left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right) + \left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right)\right) + \left(\left(\frac{-0.13857109526572012}{7 - \left(z + 1\right)} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(z + -7\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) + 6}\right)\right)\right)}\]
Using strategy rm
Applied *-un-lft-identity0.6
\[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right) \cdot \left(\sqrt{2 \cdot \pi} \cdot {\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right)\right) \cdot \left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \color{blue}{1 \cdot \frac{-1259.1392167224028}{\left(1 - z\right) + 1}}\right) + \left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right)\right) + \left(\left(\frac{-0.13857109526572012}{7 - \left(z + 1\right)} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(z + -7\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) + 6}\right)\right)\right)\]
Applied *-un-lft-identity0.6
\[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right) \cdot \left(\sqrt{2 \cdot \pi} \cdot {\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right)\right) \cdot \left(\left(\left(\color{blue}{1 \cdot \left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right)} + 1 \cdot \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right) + \left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right)\right) + \left(\left(\frac{-0.13857109526572012}{7 - \left(z + 1\right)} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(z + -7\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) + 6}\right)\right)\right)\]
Applied distribute-lft-out0.6
\[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right) \cdot \left(\sqrt{2 \cdot \pi} \cdot {\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right)\right) \cdot \left(\left(\color{blue}{1 \cdot \left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - z}\right) + \frac{-1259.1392167224028}{\left(1 - z\right) + 1}\right)} + \left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right)\right) + \left(\left(\frac{-0.13857109526572012}{7 - \left(z + 1\right)} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(z + -7\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) + 6}\right)\right)\right)\]
Simplified0.6
\[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right) \cdot \left(\sqrt{2 \cdot \pi} \cdot {\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right)\right) \cdot \left(\left(1 \cdot \color{blue}{\left(\left(\frac{676.5203681218851}{1 - z} + 0.9999999999998099\right) + \frac{-1259.1392167224028}{2 - z}\right)} + \left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right)\right) + \left(\left(\frac{-0.13857109526572012}{7 - \left(z + 1\right)} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(z + -7\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) + 6}\right)\right)\right)\]
Using strategy rm
Applied flip-+0.6
\[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right) \cdot \left(\sqrt{2 \cdot \pi} \cdot {\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right)\right) \cdot \left(\left(1 \cdot \left(\color{blue}{\frac{\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z} - 0.9999999999998099 \cdot 0.9999999999998099}{\frac{676.5203681218851}{1 - z} - 0.9999999999998099}} + \frac{-1259.1392167224028}{2 - z}\right) + \left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right)\right) + \left(\left(\frac{-0.13857109526572012}{7 - \left(z + 1\right)} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(z + -7\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) + 6}\right)\right)\right)\]
Applied frac-add1.0
\[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right) \cdot \left(\sqrt{2 \cdot \pi} \cdot {\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right)\right) \cdot \left(\left(1 \cdot \color{blue}{\frac{\left(\frac{676.5203681218851}{1 - z} \cdot \frac{676.5203681218851}{1 - z} - 0.9999999999998099 \cdot 0.9999999999998099\right) \cdot \left(2 - z\right) + \left(\frac{676.5203681218851}{1 - z} - 0.9999999999998099\right) \cdot -1259.1392167224028}{\left(\frac{676.5203681218851}{1 - z} - 0.9999999999998099\right) \cdot \left(2 - z\right)}} + \left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right)\right) + \left(\left(\frac{-0.13857109526572012}{7 - \left(z + 1\right)} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(z + -7\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) + 6}\right)\right)\right)\]
Simplified0.6
\[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right) \cdot \left(\sqrt{2 \cdot \pi} \cdot {\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right)\right) \cdot \left(\left(1 \cdot \frac{\color{blue}{\left(\frac{676.5203681218851}{1 - z} - 0.9999999999998099\right) \cdot \left(\frac{676.5203681218851}{1 - z} \cdot \left(2 - z\right) + \left(\left(2 - z\right) \cdot 0.9999999999998099 + -1259.1392167224028\right)\right)}}{\left(\frac{676.5203681218851}{1 - z} - 0.9999999999998099\right) \cdot \left(2 - z\right)} + \left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right)\right) + \left(\left(\frac{-0.13857109526572012}{7 - \left(z + 1\right)} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(z + -7\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) + 6}\right)\right)\right)\]
Using strategy rm
Applied flip-+0.6
\[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right) \cdot \left(\sqrt{2 \cdot \pi} \cdot {\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right)\right) \cdot \left(\left(1 \cdot \frac{\left(\frac{676.5203681218851}{1 - z} - 0.9999999999998099\right) \cdot \left(\frac{676.5203681218851}{1 - z} \cdot \left(2 - z\right) + \color{blue}{\frac{\left(\left(2 - z\right) \cdot 0.9999999999998099\right) \cdot \left(\left(2 - z\right) \cdot 0.9999999999998099\right) - -1259.1392167224028 \cdot -1259.1392167224028}{\left(2 - z\right) \cdot 0.9999999999998099 - -1259.1392167224028}}\right)}{\left(\frac{676.5203681218851}{1 - z} - 0.9999999999998099\right) \cdot \left(2 - z\right)} + \left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right)\right) + \left(\left(\frac{-0.13857109526572012}{7 - \left(z + 1\right)} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(z + -7\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) + 6}\right)\right)\right)\]
Applied flip--0.6
\[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right) \cdot \left(\sqrt{2 \cdot \pi} \cdot {\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right)\right) \cdot \left(\left(1 \cdot \frac{\left(\frac{676.5203681218851}{1 - z} - 0.9999999999998099\right) \cdot \left(\frac{676.5203681218851}{1 - z} \cdot \color{blue}{\frac{2 \cdot 2 - z \cdot z}{2 + z}} + \frac{\left(\left(2 - z\right) \cdot 0.9999999999998099\right) \cdot \left(\left(2 - z\right) \cdot 0.9999999999998099\right) - -1259.1392167224028 \cdot -1259.1392167224028}{\left(2 - z\right) \cdot 0.9999999999998099 - -1259.1392167224028}\right)}{\left(\frac{676.5203681218851}{1 - z} - 0.9999999999998099\right) \cdot \left(2 - z\right)} + \left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right)\right) + \left(\left(\frac{-0.13857109526572012}{7 - \left(z + 1\right)} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(z + -7\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) + 6}\right)\right)\right)\]
Applied frac-times0.6
\[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right) \cdot \left(\sqrt{2 \cdot \pi} \cdot {\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right)\right) \cdot \left(\left(1 \cdot \frac{\left(\frac{676.5203681218851}{1 - z} - 0.9999999999998099\right) \cdot \left(\color{blue}{\frac{676.5203681218851 \cdot \left(2 \cdot 2 - z \cdot z\right)}{\left(1 - z\right) \cdot \left(2 + z\right)}} + \frac{\left(\left(2 - z\right) \cdot 0.9999999999998099\right) \cdot \left(\left(2 - z\right) \cdot 0.9999999999998099\right) - -1259.1392167224028 \cdot -1259.1392167224028}{\left(2 - z\right) \cdot 0.9999999999998099 - -1259.1392167224028}\right)}{\left(\frac{676.5203681218851}{1 - z} - 0.9999999999998099\right) \cdot \left(2 - z\right)} + \left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right)\right) + \left(\left(\frac{-0.13857109526572012}{7 - \left(z + 1\right)} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(z + -7\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) + 6}\right)\right)\right)\]
Applied frac-add1.3
\[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right) \cdot \left(\sqrt{2 \cdot \pi} \cdot {\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right)\right) \cdot \left(\left(1 \cdot \frac{\left(\frac{676.5203681218851}{1 - z} - 0.9999999999998099\right) \cdot \color{blue}{\frac{\left(676.5203681218851 \cdot \left(2 \cdot 2 - z \cdot z\right)\right) \cdot \left(\left(2 - z\right) \cdot 0.9999999999998099 - -1259.1392167224028\right) + \left(\left(1 - z\right) \cdot \left(2 + z\right)\right) \cdot \left(\left(\left(2 - z\right) \cdot 0.9999999999998099\right) \cdot \left(\left(2 - z\right) \cdot 0.9999999999998099\right) - -1259.1392167224028 \cdot -1259.1392167224028\right)}{\left(\left(1 - z\right) \cdot \left(2 + z\right)\right) \cdot \left(\left(2 - z\right) \cdot 0.9999999999998099 - -1259.1392167224028\right)}}}{\left(\frac{676.5203681218851}{1 - z} - 0.9999999999998099\right) \cdot \left(2 - z\right)} + \left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right)\right) + \left(\left(\frac{-0.13857109526572012}{7 - \left(z + 1\right)} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(z + -7\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) + 6}\right)\right)\right)\]
Simplified0.6
\[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right) \cdot \left(\sqrt{2 \cdot \pi} \cdot {\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right)\right) \cdot \left(\left(1 \cdot \frac{\left(\frac{676.5203681218851}{1 - z} - 0.9999999999998099\right) \cdot \frac{\color{blue}{\left(\left(2 - z\right) \cdot 0.9999999999998099 - -1259.1392167224028\right) \cdot \left(\left(4 - z \cdot z\right) \cdot 676.5203681218851 + \left(-1259.1392167224028 + \left(2 - z\right) \cdot 0.9999999999998099\right) \cdot \left(\left(2 + z\right) \cdot \left(1 - z\right)\right)\right)}}{\left(\left(1 - z\right) \cdot \left(2 + z\right)\right) \cdot \left(\left(2 - z\right) \cdot 0.9999999999998099 - -1259.1392167224028\right)}}{\left(\frac{676.5203681218851}{1 - z} - 0.9999999999998099\right) \cdot \left(2 - z\right)} + \left(\frac{771.3234287776531}{1 - \left(z + -2\right)} + \frac{-176.6150291621406}{5 - \left(z + 1\right)}\right)\right) + \left(\left(\frac{-0.13857109526572012}{7 - \left(z + 1\right)} + \frac{12.507343278686905}{6 - \left(z + 1\right)}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(z + -7\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) + 6}\right)\right)\right)\]
Final simplification0.6
\[\leadsto \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \frac{1}{e^{\left(1 - z\right) - \left(-6 - 0.5\right)}}\right) \cdot \left(\sqrt{\pi \cdot 2} \cdot {\left(\left(1 - z\right) - \left(-6 - 0.5\right)\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}\right)\right) \cdot \left(\left(\left(\frac{-176.6150291621406}{5 - \left(z + 1\right)} + \frac{771.3234287776531}{1 - \left(z + -2\right)}\right) + \frac{\left(\frac{676.5203681218851}{1 - z} - 0.9999999999998099\right) \cdot \frac{\left(676.5203681218851 \cdot \left(4 - z \cdot z\right) + \left(0.9999999999998099 \cdot \left(2 - z\right) + -1259.1392167224028\right) \cdot \left(\left(z + 2\right) \cdot \left(1 - z\right)\right)\right) \cdot \left(0.9999999999998099 \cdot \left(2 - z\right) - -1259.1392167224028\right)}{\left(\left(z + 2\right) \cdot \left(1 - z\right)\right) \cdot \left(0.9999999999998099 \cdot \left(2 - z\right) - -1259.1392167224028\right)}}{\left(\frac{676.5203681218851}{1 - z} - 0.9999999999998099\right) \cdot \left(2 - z\right)}\right) + \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{1 - \left(-7 + z\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) + 6}\right) + \left(\frac{12.507343278686905}{6 - \left(z + 1\right)} + \frac{-0.13857109526572012}{7 - \left(z + 1\right)}\right)\right)\right)\]

Details

sample1.8s

Algorithm: intervals

simplify471.0ms

Counts

1 → 1

Calls

1 calls. Slowest were:

470.0ms

(* (/ 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)))))

prune81.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize201.0ms

Local error

Found 4 expressions with local error:

2.6b	(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
1.0b	(sqrt (* 2 PI))
1.0b	(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
1.0b	(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Counts

4 → 66

Calls

4 calls. Slowest were:

61.0ms

(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))

7.0ms

(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))

5.0ms

(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))

series125.0ms

Counts

4 → 10

Calls

4 calls. Slowest were:

55.0ms	(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))
38.0ms	(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
31.0ms	(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1 z))) (/ -1259.1392167224028 (+ (- 1 z) 1)))
0.0ms	(sqrt (* 2 PI))

simplify18.6s

Counts

49 → 76

Calls

49 calls. Slowest were:

1.4s

(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))

1.3s

(* (* (exp (/ -0.13857109526572012 (- 7 (+ z 1)))) (exp (/ 12.507343278686905 (- 6 (+ z 1))))) (* (exp (/ 1.5056327351493116e-07 (- 1 (+ z -7)))) (exp (/ 9.984369578019572e-06 (+ (- 1 z) 6)))))

1.3s

(+ (+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1)))) (+ (/ 1.5056327351493116e-07 (- 1 (+ z -7))) (/ 9.984369578019572e-06 (+ (- 1 z) 6))))

prune4.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize42.0ms

Local error

Found 4 expressions with local error:

2.6b	(+ (+ (/ 676.5203681218851 (- 1 z)) 0.9999999999998099) (/ -1259.1392167224028 (- 2 z)))
1.0b	(sqrt (* 2 PI))
1.0b	(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
1.0b	(+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Counts

4 → 50

Calls

4 calls. Slowest were:

17.0ms

(+ (+ (/ 676.5203681218851 (- 1 z)) 0.9999999999998099) (/ -1259.1392167224028 (- 2 z)))

5.0ms

(+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1))))

5.0ms

(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))

series92.0ms

Counts

4 → 10

Calls

4 calls. Slowest were:

38.0ms	(+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1))))
34.0ms	(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
20.0ms	(+ (+ (/ 676.5203681218851 (- 1 z)) 0.9999999999998099) (/ -1259.1392167224028 (- 2 z)))
0.0ms	(sqrt (* 2 PI))

simplify3.6s

Counts

26 → 60

Calls

26 calls. Slowest were:

334.0ms

(+ (* -0.13857109526572012 (- 6 (+ z 1))) (* (- 7 (+ z 1)) 12.507343278686905))

310.0ms

(- (+ (* 307.69502253760675 (/ 1 (pow z 3))) (+ (* 61.7052898218402 (/ 1 (pow z 2))) (* 12.368772183421186 (/ 1 z)))))

294.0ms

(+ (* (- (* (/ 676.5203681218851 (- 1 z)) (/ 676.5203681218851 (- 1 z))) (* 0.9999999999998099 0.9999999999998099)) (- 2 z)) (* (- (/ 676.5203681218851 (- 1 z)) 0.9999999999998099) -1259.1392167224028))

prune2.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize44.0ms

Local error

Found 4 expressions with local error:

2.6b	(+ (* (/ 676.5203681218851 (- 1 z)) (- 2 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028))
1.0b	(sqrt (* 2 PI))
1.0b	(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
1.0b	(+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Counts

4 → 61

Calls

4 calls. Slowest were:

10.0ms

(+ (* (/ 676.5203681218851 (- 1 z)) (- 2 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028))

8.0ms

(+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1))))

5.0ms

(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))

series81.0ms

Counts

4 → 10

Calls

4 calls. Slowest were:

34.0ms	(+ (* (/ 676.5203681218851 (- 1 z)) (- 2 z)) (+ (* (- 2 z) 0.9999999999998099) -1259.1392167224028))
25.0ms	(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
22.0ms	(+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1))))
0.0ms	(sqrt (* 2 PI))

simplify7.1s

Counts

44 → 71

Calls

44 calls. Slowest were:

552.0ms

(* (- 1 z) (- (* (- 2 z) 0.9999999999998099) -1259.1392167224028))

472.0ms

(+ (* (* 676.5203681218851 (- (pow 2 3) (pow z 3))) (+ (* (* (- 2 z) 0.9999999999998099) (* (- 2 z) 0.9999999999998099)) (- (* -1259.1392167224028 -1259.1392167224028) (* (* (- 2 z) 0.9999999999998099) -1259.1392167224028)))) (* (* (- 1 z) (+ (* 2 2) (+ (* z z) (* 2 z)))) (+ (pow (* (- 2 z) 0.9999999999998099) 3) (pow -1259.1392167224028 3))))

312.0ms

(+ (* (* (/ 676.5203681218851 (- 1 z)) (- (pow 2 3) (pow z 3))) (+ (* (* (- 2 z) 0.9999999999998099) (* (- 2 z) 0.9999999999998099)) (- (* -1259.1392167224028 -1259.1392167224028) (* (* (- 2 z) 0.9999999999998099) -1259.1392167224028)))) (* (+ (* 2 2) (+ (* z z) (* 2 z))) (+ (pow (* (- 2 z) 0.9999999999998099) 3) (pow -1259.1392167224028 3))))

prune4.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize90.0ms

Local error

Found 4 expressions with local error:

2.6b	(+ (* (- 4 (* z z)) 676.5203681218851) (* (+ -1259.1392167224028 (* (- 2 z) 0.9999999999998099)) (* (+ 2 z) (- 1 z))))
1.0b	(sqrt (* 2 PI))
1.0b	(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
1.0b	(+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Counts

4 → 106

Calls

4 calls. Slowest were:

10.0ms

(+ (* (- 4 (* z z)) 676.5203681218851) (* (+ -1259.1392167224028 (* (- 2 z) 0.9999999999998099)) (* (+ 2 z) (- 1 z))))

7.0ms

(+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1))))

5.0ms

(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))

series80.0ms

Counts

4 → 10

Calls

4 calls. Slowest were:

34.0ms	(+ (/ -0.13857109526572012 (- 7 (+ z 1))) (/ 12.507343278686905 (- 6 (+ z 1))))
30.0ms	(+ (/ 771.3234287776531 (- 1 (+ z -2))) (/ -176.6150291621406 (- 5 (+ z 1))))
16.0ms	(+ (* (- 4 (* z z)) 676.5203681218851) (* (+ -1259.1392167224028 (* (- 2 z) 0.9999999999998099)) (* (+ 2 z) (- 1 z))))
0.0ms	(sqrt (* 2 PI))

simplify37.5s

Counts

132 → 116

Calls

132 calls. Slowest were:

823.0ms

(* (exp (* (- 4 (* z z)) 676.5203681218851)) (exp (* (+ -1259.1392167224028 (* (- 2 z) 0.9999999999998099)) (* (+ 2 z) (- 1 z)))))

760.0ms

(+ (* (* (- (pow 4 3) (pow (* z z) 3)) 676.5203681218851) (* (- -1259.1392167224028 (* (- 2 z) 0.9999999999998099)) (* (- 2 z) (+ (* 1 1) (+ (* z z) (* 1 z)))))) (* (+ (* 4 4) (+ (* (* z z) (* z z)) (* 4 (* z z)))) (* (- (* -1259.1392167224028 -1259.1392167224028) (* (* (- 2 z) 0.9999999999998099) (* (- 2 z) 0.9999999999998099))) (* (- (* 2 2) (* z z)) (- (pow 1 3) (pow z 3))))))

751.0ms

(+ (* (* (- (pow 4 3) (pow (* z z) 3)) 676.5203681218851) (* (- -1259.1392167224028 (* (- 2 z) 0.9999999999998099)) (* (+ (* 2 2) (- (* z z) (* 2 z))) (+ (* 1 1) (+ (* z z) (* 1 z)))))) (* (+ (* 4 4) (+ (* (* z z) (* z z)) (* 4 (* z z)))) (* (- (* -1259.1392167224028 -1259.1392167224028) (* (* (- 2 z) 0.9999999999998099) (* (- 2 z) 0.9999999999998099))) (* (+ (pow 2 3) (pow z 3)) (- (pow 1 3) (pow z 3))))))

prune9.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

regimes272.0ms

Accuracy

0% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 0.6b

bsearch22.0ms

end0.0ms

sample42.9s

Algorithm: intervals

Error

Try it out

Derivation

Reproduce

Details

sample1.8s

simplify471.0ms

prune81.0ms

localize201.0ms

rewrite74.0ms

series125.0ms

simplify18.6s

prune4.3s

localize42.0ms

rewrite27.0ms

series92.0ms

simplify3.6s

prune2.9s

localize44.0ms

rewrite24.0ms

series81.0ms

simplify7.1s

prune4.1s

localize90.0ms

rewrite25.0ms

series80.0ms

simplify37.5s

prune9.5s

regimes272.0ms

bsearch22.0ms

end0.0ms

sample42.9s

In
Out