Error

Derivation

1. Initial program 1.5

   \[\left(\frac{1}{\sqrt{\pi}} \cdot e^{\left|x\right| \cdot \left|x\right|}\right) \cdot \left(\left(\left(\frac{1}{\left|x\right|} + \frac{1}{2} \cdot \left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \frac{3}{4} \cdot \left(\left(\left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \frac{15}{8} \cdot \left(\left(\left(\left(\left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right)\]

2. Applied simplify 1.5

   \[\leadsto \color{blue}{\left(\left(\left(\frac{1}{\left|x\right|} + \frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2}\right) + \left(\left(\frac{3}{4} \cdot \frac{1}{\left|x\right|}\right) \cdot {\left(\frac{1}{\left|x\right|}\right)}^3\right) \cdot \frac{1}{\left|x\right|}\right) + \left(\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot {\left(\frac{1}{\left|x\right|}\right)}^3\right) \cdot \frac{15}{8}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}}\]

3. Applied taylor 1.5

   \[\leadsto \left(\left(\left(\frac{1}{\left|x\right|} + \frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2}\right) + \left(\left(\frac{3}{4} \cdot \frac{1}{\left|x\right|}\right) \cdot {\left(\frac{1}{\left|x\right|}\right)}^{3}\right) \cdot \frac{1}{\left|x\right|}\right) + \left(\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot {\left(\frac{1}{\left|x\right|}\right)}^3\right) \cdot \frac{15}{8}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\]

4. Taylor expanded around 0 1.5

   \[\leadsto \left(\left(\left(\frac{1}{\left|x\right|} + \frac{{\left(\frac{1}{\left|x\right|}\right)}^3}{2}\right) + \left(\left(\frac{3}{4} \cdot \frac{1}{\left|x\right|}\right) \cdot \color{blue}{{\left(\frac{1}{\left|x\right|}\right)}^{3}}\right) \cdot \frac{1}{\left|x\right|}\right) + \left(\left({\left(\frac{1}{\left|x\right|}\right)}^3 \cdot {\left(\frac{1}{\left|x\right|}\right)}^3\right) \cdot \frac{15}{8}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{e^{\left|x\right| \cdot \left|x\right|}}{\sqrt{\pi}}\]

5. Applied simplify 0.9

   \[\leadsto \color{blue}{\frac{\frac{1}{{\left(\left|x\right|\right)}^3 + {\left(\left|x\right|\right)}^3} + \frac{1}{\left|x\right|}}{\frac{\sqrt{\pi}}{e^{\left|x\right| \cdot \left|x\right|}}} + \frac{e^{\left|x\right| \cdot \left|x\right|} \cdot \frac{1}{\left|x\right|}}{\sqrt{\pi}} \cdot \left(\frac{\frac{\frac{15}{8}}{{\left(\left|x\right|\right)}^3}}{{\left(\left|x\right|\right)}^3} + \frac{\frac{\frac{3}{4}}{\left|x\right|}}{{\left(\left|x\right|\right)}^3}\right)}\]

6. Applied taylor 0.8

   \[\leadsto \frac{\frac{1}{{\left(\left|x\right|\right)}^3 + {\left(\left|x\right|\right)}^3} + \frac{1}{\left|x\right|}}{\frac{\sqrt{\pi}}{e^{\left|x\right| \cdot \left|x\right|}}} + \left(\frac{e^{{\left(\left|x\right|\right)}^2}}{\left|x\right|} \cdot \sqrt{\frac{1}{\pi}}\right) \cdot \left(\frac{\frac{\frac{15}{8}}{{\left(\left|x\right|\right)}^3}}{{\left(\left|x\right|\right)}^3} + \frac{\frac{\frac{3}{4}}{\left|x\right|}}{{\left(\left|x\right|\right)}^3}\right)\]

7. Taylor expanded around 0 0.8

   \[\leadsto \frac{\frac{1}{{\left(\left|x\right|\right)}^3 + {\left(\left|x\right|\right)}^3} + \frac{1}{\left|x\right|}}{\frac{\sqrt{\pi}}{e^{\left|x\right| \cdot \left|x\right|}}} + \color{blue}{\left(\frac{e^{{\left(\left|x\right|\right)}^2}}{\left|x\right|} \cdot \sqrt{\frac{1}{\pi}}\right)} \cdot \left(\frac{\frac{\frac{15}{8}}{{\left(\left|x\right|\right)}^3}}{{\left(\left|x\right|\right)}^3} + \frac{\frac{\frac{3}{4}}{\left|x\right|}}{{\left(\left|x\right|\right)}^3}\right)\]

8. Applied simplify 0.8

   \[\leadsto \color{blue}{\frac{\frac{1}{\left|x\right|} + \frac{\frac{1}{2}}{{\left(\left|x\right|\right)}^3}}{\frac{\sqrt{\pi}}{e^{\left|x\right| \cdot \left|x\right|}}} + \left(\frac{\frac{15}{8}}{{\left({\left(\left|x\right|\right)}^3\right)}^2} + \frac{\frac{\frac{3}{4}}{\left|x\right|}}{{\left(\left|x\right|\right)}^3}\right) \cdot \left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\left|x\right|} \cdot \sqrt{\frac{1}{\pi}}\right)}\]

9. Applied taylor 0.6

   \[\leadsto \frac{\frac{1}{\left|x\right|} + \frac{\frac{1}{2}}{{\left(\left|x\right|\right)}^3}}{\frac{\sqrt{\pi}}{e^{\left|x\right| \cdot \left|x\right|}}} + \left(\frac{\frac{15}{8}}{{\left(\left|x\right|\right)}^{6}} + \frac{\frac{\frac{3}{4}}{\left|x\right|}}{{\left(\left|x\right|\right)}^3}\right) \cdot \left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\left|x\right|} \cdot \sqrt{\frac{1}{\pi}}\right)\]

10. Taylor expanded around 0 0.6

    \[\leadsto \frac{\frac{1}{\left|x\right|} + \frac{\frac{1}{2}}{{\left(\left|x\right|\right)}^3}}{\frac{\sqrt{\pi}}{e^{\left|x\right| \cdot \left|x\right|}}} + \left(\frac{\frac{15}{8}}{\color{blue}{{\left(\left|x\right|\right)}^{6}}} + \frac{\frac{\frac{3}{4}}{\left|x\right|}}{{\left(\left|x\right|\right)}^3}\right) \cdot \left(\frac{e^{\left|x\right| \cdot \left|x\right|}}{\left|x\right|} \cdot \sqrt{\frac{1}{\pi}}\right)\]
11. Removed slow pow expressions

Runtime

Time bar (total: 1.1m) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1064524629 4159152179 2999149171 575749698 4006532819 692958815)'
(FPCore (x)
  :name "Jmat.Real.erfi, branch x greater than or equal to 5"
  (* (* (/ 1 (sqrt PI)) (exp (* (fabs x) (fabs x)))) (+ (+ (+ (/ 1 (fabs x)) (* (/ 1 2) (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))))) (* (/ 3 4) (* (* (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))))) (* (/ 15 8) (* (* (* (* (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x)))))))