Average Error: 0.2 → 0.2
Time: 23.3s
Precision: 64
\[\left|\frac{1}{\sqrt{\pi}} \cdot \left(\left(\left(2 \cdot \left|x\right| + \frac{2}{3} \cdot \left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{5} \cdot \left(\left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{21} \cdot \left(\left(\left(\left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right)\right|\]
↓
\[\left|\frac{1}{\sqrt{\pi}} \cdot \left(\left(\frac{1}{5} \cdot \left(\left|x\right| \cdot \left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \left(\left|x\right| \cdot 2 + \left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \frac{2}{3}\right)\right) + \left(\left|x\right| \cdot \left(\left|x\right| \cdot \left(\left|x\right| \cdot \left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right)\right)\right) \cdot \frac{1}{21}\right)\right|\]
\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|\frac{1}{\sqrt{\pi}} \cdot \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) + \left(\left|x\right| \cdot \left(\left|x\right| \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)\right)\right) \cdot \frac{1}{21}\right)\right|
double f(double x) {
        double r2920375 = 1.0;
        double r2920376 = atan2(1.0, 0.0);
        double r2920377 = sqrt(r2920376);
        double r2920378 = r2920375 / r2920377;
        double r2920379 = 2.0;
        double r2920380 = x;
        double r2920381 = fabs(r2920380);
        double r2920382 = r2920379 * r2920381;
        double r2920383 = 3.0;
        double r2920384 = r2920379 / r2920383;
        double r2920385 = r2920381 * r2920381;
        double r2920386 = r2920385 * r2920381;
        double r2920387 = r2920384 * r2920386;
        double r2920388 = r2920382 + r2920387;
        double r2920389 = 5.0;
        double r2920390 = r2920375 / r2920389;
        double r2920391 = r2920386 * r2920381;
        double r2920392 = r2920391 * r2920381;
        double r2920393 = r2920390 * r2920392;
        double r2920394 = r2920388 + r2920393;
        double r2920395 = 21.0;
        double r2920396 = r2920375 / r2920395;
        double r2920397 = r2920392 * r2920381;
        double r2920398 = r2920397 * r2920381;
        double r2920399 = r2920396 * r2920398;
        double r2920400 = r2920394 + r2920399;
        double r2920401 = r2920378 * r2920400;
        double r2920402 = fabs(r2920401);
        return r2920402;
}
↓
double f(double x) {
        double r2920403 = 1.0;
        double r2920404 = atan2(1.0, 0.0);
        double r2920405 = sqrt(r2920404);
        double r2920406 = r2920403 / r2920405;
        double r2920407 = 0.2;
        double r2920408 = x;
        double r2920409 = fabs(r2920408);
        double r2920410 = r2920409 * r2920409;
        double r2920411 = r2920410 * r2920409;
        double r2920412 = r2920411 * r2920409;
        double r2920413 = r2920409 * r2920412;
        double r2920414 = r2920407 * r2920413;
        double r2920415 = 2.0;
        double r2920416 = r2920409 * r2920415;
        double r2920417 = 0.6666666666666666;
        double r2920418 = r2920411 * r2920417;
        double r2920419 = r2920416 + r2920418;
        double r2920420 = r2920414 + r2920419;
        double r2920421 = r2920409 * r2920413;
        double r2920422 = r2920409 * r2920421;
        double r2920423 = 0.047619047619047616;
        double r2920424 = r2920422 * r2920423;
        double r2920425 = r2920420 + r2920424;
        double r2920426 = r2920406 * r2920425;
        double r2920427 = fabs(r2920426);
        return r2920427;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019154 
(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)))))))