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 simplify1.2

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

4. Applied inv-pow1.2

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

5. Applied pow-pow0.7

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

6. Applied simplify0.7

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

7. Taylor expanded around 0 0.7

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

8. Applied simplify1.0

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

10. Applied add-sqr-sqrt0.6

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

Runtime

Time bar (total: 3.4m)Debug logProfile

herbie shell --seed '#(1070386091 2509006183 1430610344 1025408621 36622005 1425925650)' 
(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)))))))