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 simplify1.1

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

3. Taylor expanded around 0 1.1

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

4. Applied simplify0.9

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

6. Applied add-sqr-sqrt0.9

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

8. Applied add-sqr-sqrt1.0

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

9. Applied times-frac1.0

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

Runtime

Time bar (total: 2.9m)Debug logProfile

herbie shell --seed '#(1064269945 2896236262 301053905 1701069080 1701464310 1614783279)' 
(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)))))))