Error

Derivation

1. Initial program 0.2

   \[\left|\frac{1}{\sqrt{\pi}} \cdot \left(\left(\left(2 \cdot \left|x\right| + \frac{2}{3} \cdot \left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{5} \cdot \left(\left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{21} \cdot \left(\left(\left(\left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right)\right|\]

2. Applied simplify0.2

   \[\leadsto \color{blue}{\left|(\left(\frac{1}{\sqrt{\pi}}\right) \cdot \left((\left(\left(\frac{1}{5} \cdot \left|x\right|\right) \cdot \left(\left|x\right| \cdot \left|x\right|\right)\right) \cdot \left(\left|x\right| \cdot \left|x\right|\right) + \left((\left(\left|x\right| \cdot \frac{2}{3}\right) \cdot \left(\left|x\right| \cdot \left|x\right|\right) + \left(2 \cdot \left|x\right|\right))_*\right))_*\right) + \left(\left({\left(\left|x\right|\right)}^{3} \cdot {\left(\left|x\right|\right)}^{3}\right) \cdot \left(\left(\frac{1}{21} \cdot \left|x\right|\right) \cdot \frac{1}{\sqrt{\pi}}\right)\right))_*\right|}\]
3. Using strategy rm

4. Applied add-cbrt-cube0.2

   \[\leadsto \left|(\left(\frac{1}{\sqrt{\pi}}\right) \cdot \left((\left(\left(\frac{1}{5} \cdot \left|x\right|\right) \cdot \left(\left|x\right| \cdot \left|x\right|\right)\right) \cdot \left(\left|x\right| \cdot \left|x\right|\right) + \left((\left(\left|x\right| \cdot \frac{2}{3}\right) \cdot \left(\left|x\right| \cdot \left|x\right|\right) + \left(2 \cdot \left|x\right|\right))_*\right))_*\right) + \left(\left({\left(\left|x\right|\right)}^{3} \cdot {\left(\left|x\right|\right)}^{3}\right) \cdot \left(\left(\frac{1}{21} \cdot \color{blue}{\sqrt[3]{\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|}}\right) \cdot \frac{1}{\sqrt{\pi}}\right)\right))_*\right|\]

5. Applied add-cbrt-cube0.2

   \[\leadsto \left|(\left(\frac{1}{\sqrt{\pi}}\right) \cdot \left((\left(\left(\frac{1}{5} \cdot \left|x\right|\right) \cdot \left(\left|x\right| \cdot \left|x\right|\right)\right) \cdot \left(\left|x\right| \cdot \left|x\right|\right) + \left((\left(\left|x\right| \cdot \frac{2}{3}\right) \cdot \left(\left|x\right| \cdot \left|x\right|\right) + \left(2 \cdot \left|x\right|\right))_*\right))_*\right) + \left(\left({\left(\left|x\right|\right)}^{3} \cdot {\left(\left|x\right|\right)}^{3}\right) \cdot \left(\left(\color{blue}{\sqrt[3]{\left(\frac{1}{21} \cdot \frac{1}{21}\right) \cdot \frac{1}{21}}} \cdot \sqrt[3]{\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|}\right) \cdot \frac{1}{\sqrt{\pi}}\right)\right))_*\right|\]

6. Applied cbrt-unprod0.2

   \[\leadsto \left|(\left(\frac{1}{\sqrt{\pi}}\right) \cdot \left((\left(\left(\frac{1}{5} \cdot \left|x\right|\right) \cdot \left(\left|x\right| \cdot \left|x\right|\right)\right) \cdot \left(\left|x\right| \cdot \left|x\right|\right) + \left((\left(\left|x\right| \cdot \frac{2}{3}\right) \cdot \left(\left|x\right| \cdot \left|x\right|\right) + \left(2 \cdot \left|x\right|\right))_*\right))_*\right) + \left(\left({\left(\left|x\right|\right)}^{3} \cdot {\left(\left|x\right|\right)}^{3}\right) \cdot \left(\color{blue}{\sqrt[3]{\left(\left(\frac{1}{21} \cdot \frac{1}{21}\right) \cdot \frac{1}{21}\right) \cdot \left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right)}} \cdot \frac{1}{\sqrt{\pi}}\right)\right))_*\right|\]

7. Applied simplify0.2

   \[\leadsto \left|(\left(\frac{1}{\sqrt{\pi}}\right) \cdot \left((\left(\left(\frac{1}{5} \cdot \left|x\right|\right) \cdot \left(\left|x\right| \cdot \left|x\right|\right)\right) \cdot \left(\left|x\right| \cdot \left|x\right|\right) + \left((\left(\left|x\right| \cdot \frac{2}{3}\right) \cdot \left(\left|x\right| \cdot \left|x\right|\right) + \left(2 \cdot \left|x\right|\right))_*\right))_*\right) + \left(\left({\left(\left|x\right|\right)}^{3} \cdot {\left(\left|x\right|\right)}^{3}\right) \cdot \left(\sqrt[3]{\color{blue}{\left(\left|x\right| \cdot \left|x\right|\right) \cdot \frac{\left|x\right|}{{21}^{3}}}} \cdot \frac{1}{\sqrt{\pi}}\right)\right))_*\right|\]

Runtime

Time bar (total: 53.1s)Debug logProfile

herbie shell --seed 2018198 +o rules:numerics
(FPCore (x)
  :name "Jmat.Real.erfi, branch x less than or equal to 0.5"
  (fabs (* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))))