Average Error: 13.9 → 13.9
Time: 14.5s
Precision: binary64
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
↓
\[1 - \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \frac{0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\sqrt[3]{\frac{1}{1 + 0.3275911 \cdot \left|x\right|}} \cdot \left(\sqrt[3]{\frac{1}{1 + 0.3275911 \cdot \left|x\right|}} \cdot \sqrt[3]{\frac{1}{1 + 0.3275911 \cdot \left|x\right|}}\right)\right) \cdot 1.061405429\right)\right)\right)}{{\left(e^{\left|x\right|}\right)}^{\left(\left|x\right|\right)}}\]
1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}
↓
1 - \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \frac{0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\sqrt[3]{\frac{1}{1 + 0.3275911 \cdot \left|x\right|}} \cdot \left(\sqrt[3]{\frac{1}{1 + 0.3275911 \cdot \left|x\right|}} \cdot \sqrt[3]{\frac{1}{1 + 0.3275911 \cdot \left|x\right|}}\right)\right) \cdot 1.061405429\right)\right)\right)}{{\left(e^{\left|x\right|}\right)}^{\left(\left|x\right|\right)}}
(FPCore (x)
 :precision binary64
 (-
  1.0
  (*
   (*
    (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
    (+
     0.254829592
     (*
      (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
      (+
       -0.284496736
       (*
        (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
        (+
         1.421413741
         (*
          (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
          (+
           -1.453152027
           (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))))
   (exp (- (* (fabs x) (fabs x)))))))
↓
(FPCore (x)
 :precision binary64
 (-
  1.0
  (*
   (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
   (/
    (+
     0.254829592
     (*
      (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
      (+
       -0.284496736
       (*
        (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
        (+
         1.421413741
         (*
          (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
          (+
           -1.453152027
           (*
            (*
             (cbrt (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))))
             (*
              (cbrt (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))))
              (cbrt (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))))))
            1.061405429))))))))
    (pow (exp (fabs x)) (fabs x))))))
double code(double x) {
	return ((double) (1.0 - ((double) (((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * ((double) (0.254829592 + ((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * ((double) (-0.284496736 + ((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * ((double) (1.421413741 + ((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * ((double) (-1.453152027 + ((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * 1.061405429)))))))))))))))))) * ((double) exp(((double) -(((double) (((double) fabs(x)) * ((double) fabs(x))))))))))));
}
↓
double code(double x) {
	return ((double) (1.0 - ((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * (((double) (0.254829592 + ((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * ((double) (-0.284496736 + ((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * ((double) (1.421413741 + ((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * ((double) (-1.453152027 + ((double) (((double) (((double) cbrt((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))) * ((double) (((double) cbrt((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))) * ((double) cbrt((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))))))) * 1.061405429)))))))))))))))) / ((double) pow(((double) exp(((double) fabs(x)))), ((double) fabs(x)))))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 13.9

    \[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

  2. Simplified13.9

    \[\leadsto \color{blue}{1 - \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \frac{0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)}{{\left(e^{\left|x\right|}\right)}^{\left(\left|x\right|\right)}}}\]
  3. Using strategy rm

  4. Applied add-cube-cbrt13.9

    \[\leadsto 1 - \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \frac{0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \color{blue}{\left(\left(\sqrt[3]{\frac{1}{1 + 0.3275911 \cdot \left|x\right|}} \cdot \sqrt[3]{\frac{1}{1 + 0.3275911 \cdot \left|x\right|}}\right) \cdot \sqrt[3]{\frac{1}{1 + 0.3275911 \cdot \left|x\right|}}\right)} \cdot 1.061405429\right)\right)\right)}{{\left(e^{\left|x\right|}\right)}^{\left(\left|x\right|\right)}}\]

  5. Final simplification13.9

    \[\leadsto 1 - \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \frac{0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\sqrt[3]{\frac{1}{1 + 0.3275911 \cdot \left|x\right|}} \cdot \left(\sqrt[3]{\frac{1}{1 + 0.3275911 \cdot \left|x\right|}} \cdot \sqrt[3]{\frac{1}{1 + 0.3275911 \cdot \left|x\right|}}\right)\right) \cdot 1.061405429\right)\right)\right)}{{\left(e^{\left|x\right|}\right)}^{\left(\left|x\right|\right)}}\]

Reproduce

herbie shell --seed 2020198 
(FPCore (x)
  :name "Jmat.Real.erf"
  :precision binary64
  (- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x)))))))