Average Error: 0.2 → 0.2
Time: 40.5s
Precision: 64
\[\left|\frac{1}{\sqrt{\pi}} \cdot \left(\left(\left(2 \cdot \left|x\right| + \frac{2}{3} \cdot \left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{5} \cdot \left(\left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{21} \cdot \left(\left(\left(\left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right)\right|\]
↓
\[\left|\left(\left(\frac{1}{5} \cdot \left(\left|x\right| \cdot \left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \left(\left|x\right| \cdot 2 + \left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \frac{2}{3}\right)\right) + \frac{1}{21} \cdot \left(\left|x\right| \cdot \left(\left|x\right| \cdot \left(\left(\left|x\right| \cdot {\left(\left|x\right|\right)}^{3}\right) \cdot \left|x\right|\right)\right)\right)\right) \cdot \frac{1}{\sqrt{\pi}}\right|\]
\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|
↓
\left|\left(\left(\frac{1}{5} \cdot \left(\left|x\right| \cdot \left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \left(\left|x\right| \cdot 2 + \left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \frac{2}{3}\right)\right) + \frac{1}{21} \cdot \left(\left|x\right| \cdot \left(\left|x\right| \cdot \left(\left(\left|x\right| \cdot {\left(\left|x\right|\right)}^{3}\right) \cdot \left|x\right|\right)\right)\right)\right) \cdot \frac{1}{\sqrt{\pi}}\right|
double f(double x) {
        double r4211613 = 1.0;
        double r4211614 = atan2(1.0, 0.0);
        double r4211615 = sqrt(r4211614);
        double r4211616 = r4211613 / r4211615;
        double r4211617 = 2.0;
        double r4211618 = x;
        double r4211619 = fabs(r4211618);
        double r4211620 = r4211617 * r4211619;
        double r4211621 = 3.0;
        double r4211622 = r4211617 / r4211621;
        double r4211623 = r4211619 * r4211619;
        double r4211624 = r4211623 * r4211619;
        double r4211625 = r4211622 * r4211624;
        double r4211626 = r4211620 + r4211625;
        double r4211627 = 5.0;
        double r4211628 = r4211613 / r4211627;
        double r4211629 = r4211624 * r4211619;
        double r4211630 = r4211629 * r4211619;
        double r4211631 = r4211628 * r4211630;
        double r4211632 = r4211626 + r4211631;
        double r4211633 = 21.0;
        double r4211634 = r4211613 / r4211633;
        double r4211635 = r4211630 * r4211619;
        double r4211636 = r4211635 * r4211619;
        double r4211637 = r4211634 * r4211636;
        double r4211638 = r4211632 + r4211637;
        double r4211639 = r4211616 * r4211638;
        double r4211640 = fabs(r4211639);
        return r4211640;
}
↓
double f(double x) {
        double r4211641 = 0.2;
        double r4211642 = x;
        double r4211643 = fabs(r4211642);
        double r4211644 = r4211643 * r4211643;
        double r4211645 = r4211644 * r4211643;
        double r4211646 = r4211645 * r4211643;
        double r4211647 = r4211643 * r4211646;
        double r4211648 = r4211641 * r4211647;
        double r4211649 = 2.0;
        double r4211650 = r4211643 * r4211649;
        double r4211651 = 0.6666666666666666;
        double r4211652 = r4211645 * r4211651;
        double r4211653 = r4211650 + r4211652;
        double r4211654 = r4211648 + r4211653;
        double r4211655 = 0.047619047619047616;
        double r4211656 = 3.0;
        double r4211657 = pow(r4211643, r4211656);
        double r4211658 = r4211643 * r4211657;
        double r4211659 = r4211658 * r4211643;
        double r4211660 = r4211643 * r4211659;
        double r4211661 = r4211643 * r4211660;
        double r4211662 = r4211655 * r4211661;
        double r4211663 = r4211654 + r4211662;
        double r4211664 = 1.0;
        double r4211665 = atan2(1.0, 0.0);
        double r4211666 = sqrt(r4211665);
        double r4211667 = r4211664 / r4211666;
        double r4211668 = r4211663 * r4211667;
        double r4211669 = fabs(r4211668);
        return r4211669;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Using strategy rm

  3. Applied pow30.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019141 
(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)))))))